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Unbiased statistical estimator minimizing variance
minimum-variance unbiased estimator (MVUE) or uniformly minimum-variance unbiased estimator (UMVUE) is an unbiased estimator that has lower variance than
Minimum-variance unbiased estimator
Minimum-variance_unbiased_estimator
Statistical property
estimated. An estimator or decision rule with zero bias is called unbiased. In statistics, "bias" is an objective property of an estimator. Bias is a distinct
Bias_of_an_estimator
Rule for calculating an estimate of a given quantity based on observed data
parameter. The unbiased estimator with the smallest variance is known as the minimum-variance unbiased estimator (MVUE). To find if an estimator θ ^ {\displaystyle
Estimator
Problem in statistical estimation
numbers: 19, 40, 42 and 60. A frequentist approach (using the minimum-variance unbiased estimator) predicts the total number of tanks produced will be: N ≈
German_tank_problem
Theorem related to ordinary least squares
squares (OLS) estimator has the lowest sampling variance (variance of the estimator across samples) within the class of linear unbiased estimators, if the errors
Gauss–Markov_theorem
Measure of the error of an estimator
the unbiased estimator). Further, while the corrected sample variance is the best unbiased estimator (minimum mean squared error among unbiased estimators)
Mean_squared_error
Uniform distribution on an interval
{\displaystyle [0,b]} with unknown b , {\displaystyle b,} the minimum-variance unbiased estimator (UMVUE) for the maximum is: b ^ UMVU = k + 1 k m = m + m
Continuous uniform distribution
Continuous_uniform_distribution
Middle quantile of a data set or probability distribution
estimators that are optimal (in a sense analogous to the minimum-variance property for mean-unbiased estimators). Such constructions exist for probability distributions
Median
Theorem in statistics
a complete, sufficient statistic is the unique uniformly minimum-variance unbiased estimator (UMVUE) of that quantity. The Lehmann–Scheffé theorem is
Lehmann–Scheffé_theorem
Class of statistics in estimation theory
stands for unbiased.[citation needed] In elementary statistics, U-statistics arise naturally in producing minimum-variance unbiased estimators. The theory
U-statistic
Estimation method that minimizes the mean square error
speech. This is in contrast to the non-Bayesian approach like minimum-variance unbiased estimator (MVUE) where absolutely nothing is assumed to be known about
Minimum mean square error estimator
Minimum_mean_square_error_estimator
Statistical theorem
unbiased, δ 1 {\displaystyle \delta _{1}} is the unique minimum variance unbiased estimator by the Lehmann–Scheffé theorem. Suppose n independent positive
Rao–Blackwell_theorem
Indicator for how well data points fit a line or curve
Despite using unbiased estimators for the population variances of the error and the dependent variable, adjusted R2 is not an unbiased estimator of the population
Coefficient_of_determination
Measure of linear correlation
\quad } therefore r is a biased estimator of ρ . {\displaystyle \rho .} The unique minimum variance unbiased estimator radj is given by where: r , n {\displaystyle
Pearson correlation coefficient
Pearson_correlation_coefficient
Branch of statistics to estimate models based on measured data
Minimum variance unbiased estimator (MVUE) Nonlinear system identification Best linear unbiased estimator (BLUE) Unbiased estimators — see estimator bias
Estimation_theory
Property of a model
theorem Hyperparameter optimization Law of total variance Minimum-variance unbiased estimator Model selection Regression model validation Supervised learning
Bias–variance_tradeoff
Statistics term
statistics exist for unbiased estimation of θ, while some of them have lower variance than others. See also minimum-variance unbiased estimator. Bounded completeness
Completeness_(statistics)
Parameter estimation via sample statistics
the estimator is considered unbiased. This is called an unbiased estimator. The estimator will become a best unbiased estimator if it has minimum variance
Point_estimation
Statistical property
that OLS estimators are not the Best Linear Unbiased Estimators (BLUE) and their variance is not the lowest of all other unbiased estimators. Heteroscedasticity
Homoscedasticity and heteroscedasticity
Homoscedasticity_and_heteroscedasticity
Branch of statistics
Uniformly minimum-variance unbiased estimators (UMVUE), sometimes called best unbiased estimators as well, are estimators that have minimum variance among
Parametric_statistics
Lower bound on variance of an estimator
error among all unbiased methods, and is, therefore, the minimum variance unbiased (MVU) estimator. However, in some cases, no unbiased technique exists
Cramér–Rao_bound
Quality measure of a statistical method
unbiased estimator, representing the "best" an unbiased estimator can be. An efficient estimator is also the minimum variance unbiased estimator (MVUE)
Efficiency_(statistics)
Statistical estimator for ratio of means
the bias will asymptotically approach 0. Therefore, the estimator is approximately unbiased for large sample sizes. Assume there are two characteristics
Ratio_estimator
Procedure to estimate standard deviation from a sample
a biased estimator of the standard deviation of the population is to start from the result that s2 is an unbiased estimator for the variance σ2 of the
Unbiased estimation of standard deviation
Unbiased_estimation_of_standard_deviation
Measure of variation in statistics
An unbiased estimator for the variance is given by applying Bessel's correction, using N − 1 instead of N to yield the unbiased sample variance, denoted
Standard_deviation
Statistical measure of how far values spread from their average
correction. The resulting estimator is unbiased and is called the (corrected) sample variance or unbiased sample variance. If the mean is determined
Variance
Probability distribution
experiment is k, the number of failures. In estimating p, the minimum variance unbiased estimator is p ^ = r − 1 r + k − 1 . {\displaystyle {\widehat {p}}={\frac
Negative binomial distribution
Negative_binomial_distribution
Statistical method for resampling
{x}})_{\text{jack}}]=V[x]/n=V[{\bar {x}}]} , so this is an unbiased estimator of the variance of x ¯ {\displaystyle {\bar {x}}} . The jackknife technique
Jackknife_resampling
Method for estimating the unknown parameters in a linear regression model
there are no unbiased estimators of σ2 with variance smaller than that of the estimator s2. If we are willing to allow biased estimators, and consider
Ordinary_least_squares
Arithmetic mean of the maximum and the minimum
and minimum, the mid-range is the uniformly minimum-variance unbiased estimator (UMVU) estimator for the mean. The sample maximum and sample minimum, together
Mid-range
Problem in computer science
Count–min sketch Streaming algorithm Maximum likelihood Minimum-variance unbiased estimator Ullman, Jeff; Rajaraman, Anand; Leskovec, Jure. "Mining data
Count-distinct_problem
Statistical method
w i = 1 / σ i 2 {\displaystyle w_{i}=1/\sigma _{i}^{2}} . The variance of the estimator V a r ( μ ^ ) = ∑ i w i 2 σ i 2 ( ∑ i w i ) 2 {\displaystyle Var({\hat
Inverse-variance_weighting
Statistical amount
formula for the variance of the mean (but notice that it uses the maximum likelihood estimator for the variance instead of the unbiased variance. I.e.: dividing
Weighted_arithmetic_mean
Correction for sample variance bias
factor n n − 1 {\displaystyle {\frac {n}{n-1}}} gives an unbiased estimator of the population variance. In some literature, the above factor is called Bessel's
Bessel's_correction
Statistical principle
is a function of only θ and T(x) = max{xi}. In fact, the minimum-variance unbiased estimator (MVUE) for θ is n + 1 n T ( X ) . {\displaystyle {\frac {n+1}{n}}T(X)
Sufficient_statistic
Mathematical decision rule
In estimation theory and decision theory, a Bayes estimator or a Bayes action is an estimator or decision rule that minimizes the posterior expected value
Bayes_estimator
Process of using data analysis for predicting population data from sample data
frequentist developments of optimal inference (such as minimum-variance unbiased estimators, or uniformly most powerful testing) make use of loss functions
Statistical_inference
Method for fitting a statistical model to data
asymptotically normal, minimum-distance estimators are generally not statistically efficient when compared to maximum likelihood estimators, because they omit
Minimum-distance_estimation
Approximation method in statistics
distributed, and have equal variances, the best linear unbiased estimator of the coefficients is the least-squares estimator. An extended version of this
Least_squares
Experimental design that is optimal with respect to some statistical criterion
average variance of the estimates of the regression coefficients. C-optimality This criterion minimizes the variance of a best linear unbiased estimator of
Optimal_experimental_design
Non-parametric statistic used to estimate the survival function
The Kaplan–Meier estimator, also known as the product limit estimator, is a non-parametric statistic used to estimate the survival function from lifetime
Kaplan–Meier_estimator
Single measure of some attribute of a sample
sample taken from the population. For example, the sample mean is an unbiased estimator of the population mean. This means that the expected value of the
Statistic
Statistical property
< 20. See unbiased estimation of standard deviation for further discussion. The standard error on the mean may be derived from the variance of a sum of
Standard_error
Method of estimating the parameters of a statistical model, given observations
estimator is unbiased up to the terms of order 1/ n , and is called the bias-corrected maximum likelihood estimator. This bias-corrected estimator is
Maximum_likelihood_estimation
square error Minimum-variance unbiased estimator Minimum viable population Minitab MINQUE – minimum norm quadratic unbiased estimation Misleading graph
List_of_statistics_articles
Loss function used in robust regression
the mean-unbiased, minimum-variance estimator of the mean (using the quadratic loss function) and the robustness of the median-unbiased estimator (using
Huber_loss
population variance or population standard deviation, one generally must multiply by a scale factor to make it an unbiased consistent estimator; see scale
L-estimator
Statistical modeling method
_{1}'+w_{2}\beta _{2}'+\dots +w_{q}\beta _{q}',} and its minimum-variance unbiased linear estimator is ξ ^ ′ ( w ) = w 1 β ^ 1 ′ + w 2 β ^ 2 ′ + ⋯ + w q β
Linear_regression
Statistical hypothesis test
samples: it is defined in this way so that its square is an unbiased estimator of the common variance, whether or not the population means are the same. In
Student's_t-test
Probability distribution
theorem the estimator s 2 {\textstyle s^{2}} is uniformly minimum variance unbiased (UMVU), which makes it the "best" estimator among all unbiased ones. However
Normal_distribution
Family of statistical methods based on sampling of available data
freedom (n being the sample size). The basic idea behind the jackknife variance estimator lies in systematically recomputing the statistic estimate, leaving
Resampling_(statistics)
Statistical method
estimators. Popular families of point-estimators include mean-unbiased minimum-variance estimators, median-unbiased estimators, Bayesian estimators (for
Bootstrapping_(statistics)
Overview of and topical guide to statistics
Estimation theory Estimator Bayes estimator Maximum likelihood Trimmed estimator M-estimator Minimum-variance unbiased estimator Consistent estimator Efficiency
Outline_of_statistics
Empirical law on the variance of species in a habitat
Lysyk, TL (1991). "Simulation studies of binomial sampling: a new variance estimator and density pre&ctor, with special reference to the Russian wheat
Taylor's_law
Relative measure of dispersion expressed as the ratio of standard deviation to the mean
low: it is a biased estimator. For normally distributed data, an unbiased estimator for a sample of size n is: c v ^ ∗ = ( 1 + 1 4 n ) c v ^ {\displaystyle
Coefficient_of_variation
Robust and nonparametric estimator of a population's location parameter
Hodges–Lehmann estimator is a consistent and median-unbiased estimate of the population median. For non-symmetric populations, the Hodges–Lehmann estimator estimates
Hodges–Lehmann_estimator
Set of quantities in probability theory
Cornish–Fisher expansion Edgeworth expansion Polykay k-statistic, a minimum-variance unbiased estimator of a cumulant Ursell function Total position spread tensor
Cumulant
Concept in statistics
population variance or population standard deviation, one generally must multiply by a scale factor to make it an unbiased consistent estimator; see scale
Trimmed_estimator
Study of convergence properties of statistical estimators
theory, or large sample theory, is a framework for assessing properties of estimators and statistical tests. Within this framework, it is often assumed that
Asymptotic theory (statistics)
Asymptotic_theory_(statistics)
Linear regression model with a single explanatory variable
2}}{\sum _{i=1}^{n}(x_{i}-{\bar {x}})^{2}}}}} is the unbiased standard error estimator of the estimator β ^ {\displaystyle {\widehat {\beta }}} . This t-value
Simple_linear_regression
Phenomenon in statistics
discussed at mean squared error: variance, but one can always do better (in terms of MSE) than the unbiased estimator; for the normal distribution a divisor
Shrinkage_(statistics)
Statistical hypothesis test
consideration is restricted to continuous distributions, this is a minimum variance unbiased estimator of p 2 {\displaystyle p_{2}} . sgn {\displaystyle \operatorname
Wilcoxon_signed-rank_test
Measure of covariance of components of a random vector
matrix (also known as auto-covariance matrix, dispersion matrix, variance matrix, or variance–covariance matrix) is a square matrix giving the covariance between
Covariance_matrix
Known channel properties of a communication link
distributions are unknown, then the least-square estimator (also known as the minimum-variance unbiased estimator) is H LS-estimate = Y P H ( P P H ) − 1 {\displaystyle
Channel_state_information
Regularization technique for ill-posed problems
ridge parameters estimate, as its variance and mean square estimator are often smaller than the least square estimators previously derived. In the ordinary
Ridge_regression
Statistics concept
covariance matrix. The sample covariance matrix (SCM) is an unbiased and efficient estimator of the covariance matrix if the space of covariance matrices
Estimation of covariance matrices
Estimation_of_covariance_matrices
Type of statistics
met, the robust estimator will still have a reasonable efficiency, and reasonably small bias, as well as being asymptotically unbiased, meaning having
Robust_statistics
Probability distribution
estimator is found using maximum likelihood estimator and also the method of moments. This estimator is unbiased and uniformly with minimum variance,
Binomial_distribution
Parameter estimation technique in statistics, particularly econometrics
However, these estimators are mathematically equivalent to those based on "orthogonality conditions" (Sargan, 1958, 1959) or "unbiased estimating equations"
Generalized_method_of_moments
Generalization of the one-dimensional normal distribution to higher dimensions
deviation ellipse is lower. The derivation of the maximum-likelihood estimator of the covariance matrix of a multivariate normal distribution is straightforward
Multivariate normal distribution
Multivariate_normal_distribution
Fourth standardized moment in statistics
unique symmetric unbiased estimator of the fourth cumulant, k2 is the unbiased estimate of the second cumulant (identical to the unbiased estimate of the
Kurtosis
Asymptotic variances under heteroskedasticity
the OLS point estimator remains unbiased, it is not "best" in the sense of having minimum mean square error, and the OLS variance estimator V ^ [ β ^ O
Heteroskedasticity-consistent standard errors
Heteroskedasticity-consistent_standard_errors
Correlation of a signal with a time-shifted copy of itself, as a function of shift
Markov theorem does not apply, and that OLS estimators are no longer the Best Linear Unbiased Estimators (BLUE). While it does not bias the OLS coefficient
Autocorrelation
Because of this the usual sample mean (arithmetic mean) is a biased estimator of the true mean. To see this consider g ( x ) = x f ( x ) m {\displaystyle
Contraharmonic_mean
Measure of the asymmetry of random variables
unique symmetric unbiased estimator of the third cumulant and k 2 = s 2 {\displaystyle k_{2}=s^{2}} is the symmetric unbiased estimator of the second cumulant
Skewness
Class of statistical estimators
In statistics, M-estimators are a broad class of extremum estimators for which the objective function is a sample average. Both non-linear least squares
M-estimator
Study of collection and analysis of data
parameter: an estimator is a statistic used to estimate such function. Commonly used estimators include sample mean, unbiased sample variance and sample
Statistics
Statistical measure
{\theta }}-\theta )^{2}{\big )}}}.} For an unbiased estimator, the RMSD is the square root of the variance, known as the standard deviation. If X1, .
Root_mean_square_deviation
In statistics, a k-statistic is a minimum-variance unbiased estimator of a cumulant. McHugh, Mary L. (2012-10-15). "Interrater reliability: the kappa
K-statistic
Probability distribution
μ {\displaystyle \mu } and variance σ 2 . {\displaystyle \ \sigma ^{2}~.} The sample mean and unbiased sample variance are given by: x ¯ = x 1 +
Student's_t-distribution
Statistical considerations on how many observations to make
(narrow confidence interval) this translates to a low target variance of the estimator. the use of a power target, i.e. the power of statistical test
Sample_size_determination
Data mining technique
hmin(B) and zero otherwise, then r is an unbiased estimator of J(A,B). r has too high a variance to be a useful estimator for the Jaccard similarity on its own
MinHash
Estimate of an interval in which future observations will fall
sample variance s2 as an estimate for σ2. There are two natural choices for s2 here – dividing by ( n − 1 ) {\displaystyle (n-1)} yields an unbiased estimate
Prediction_interval
Statistical measure of the magnitude of a phenomenon
not unbiased), ω2 is preferable to η2; however, it can be more inconvenient to calculate for complex analyses. A generalized form of the estimator has
Effect_size
Statistical hypothesis test
statistical test that compares variances. It is used to determine if the variances of two samples, or if the ratios of variances among multiple samples, are
F-test
Probability distribution
distribution are these logarithmic variances. The Cramér–Rao bound states that the variance of any unbiased estimator α ^ {\displaystyle {\hat {\alpha }}}
Beta_distribution
Measure of the shape of a function
population, if that moment exists, for any sample size n. It is thus an unbiased estimator. This contrasts with the situation for central moments, whose computation
Moment_(mathematics)
Probability distribution
Other estimators also exist, such as Finney's UMVUE estimator, the "Approximately Minimum Mean Squared Error Estimator", the "Approximately Unbiased Estimator"
Log-normal_distribution
Family of iterative methods
g(\theta _{n}).} Here H ( θ , X ) {\displaystyle H(\theta ,X)} is an unbiased estimator of ∇ g ( θ ) {\displaystyle \nabla g(\theta )} . If X {\displaystyle
Stochastic_approximation
Statistical test
evaluated at the sample estimator. This result is obtained using the delta method, which uses a first order approximation of the variance. The fact that one
Wald_test
Statistical hypothesis test
exactly is the test that the variance of a normally distributed population has a given value based on a sample variance. Such tests are uncommon in practice
Chi-squared_test
Method of interpolation
determines the difference between the quality of estimators. To find an estimator with minimum variance, we need to minimize E [ ϵ ( x 0 ) 2 ] {\displaystyle
Kriging
Method for model fitting in statistics
^ {\displaystyle {\hat {\boldsymbol {\beta }}}} is a best linear unbiased estimator (BLUE). If, however, the measurements are uncorrelated but have different
Weighted_least_squares
Probability distribution on equally likely outcomes
seeking to estimate German tank production. A uniformly minimum variance unbiased (UMVU) estimator for the distribution's maximum in terms of m, the sample
Discrete_uniform_distribution
Statistical model allowing for frequent zero values
sample mean and s 2 {\displaystyle s^{2}} is the sample variance. The maximum likelihood estimator can be found by solving the following equation m ( 1 −
Zero-inflated_model
Class of statistical models
response variable via a link function and by allowing the magnitude of the variance of each measurement to be a function of its predicted value. Generalized
Generalized_linear_model
Nonparametric test of the null hypothesis
quantified using the Hodges–Lehmann (HL) estimator, which is consistent with the Wilcoxon test. This estimator (HLΔ) is the median of all possible differences
Mann–Whitney_U_test
Set of statistical processes for estimating the relationships among variables
that the parameter estimates will be unbiased, consistent, and efficient in the class of linear unbiased estimators. Practitioners have developed a variety
Regression_analysis
Collection of statistical models
Analysis of variance (ANOVA) is a family of statistical methods used to compare the means of two or more groups by analyzing variance. Specifically, ANOVA
Analysis_of_variance
Statistical measure of association
described in the following section. Cramér's V can be a heavily biased estimator of its population counterpart and will tend to overestimate the strength
Cramér's_V
MINIMUM VARIANCE-UNBIASED-ESTIMATOR
MINIMUM VARIANCE-UNBIASED-ESTIMATOR
Boy/Male
Latin
Fidde.
Girl/Female
American, British, English, German
Bearer of Good News; Modern Blend of Ava and Ana
Female
French
French form of Latin Ariadne, ARIANNE means "utterly pure."
Girl/Female
Scandinavian
Abbreviation of Katherine. Pure.
Girl/Female
French
Bitter.
Girl/Female
English, Hindu, Indian, Marathi
Small Daughter
Girl/Female
Norse American Latin Russian French
Bitter grace.
Female
French
French form of Latin Ariadne, ARIANE means "utterly pure."
Girl/Female
British, Danish, English, Scandinavian, Swedish
Pure; Abbreviation of Katherine
Girl/Female
American, Australian, British, Chinese, Christian, Danish, Dutch, English, Finnish, French, German, Greek, Hebrew, Latin, Lebanese, Netherlands, Norse, Swedish, Swiss
Bitter; Sea of Bitterness; A Combination of Marie and Anne; Rebelliousnesses Wished for Child; A Blend of Marie Star of the Sea and Anne; Star of the Sea
Girl/Female
American, Australian, Chinese, Dutch, Finnish, French, German, Greek, Latin, Swedish
The Holy One; Black Beauty; Dark One; Very Holy Woman; Similar to Ariadne; Utterly Pure
Surname or Lastname
English and Scottish (of Norman origin)
English and Scottish (of Norman origin) : habitational name from Valence in Drôme, France, which probably has the same origin as Valencia.
Girl/Female
English
Modern blend of Ava and Ana.
Girl/Female
Hindu, Indian, Traditional
Pure; Unbiased
Girl/Female
Australian, British, English, French, German, Hebrew, Lebanese
Variant of Mary Bitter; Bitter; Beloved
Boy/Male
American, British, English
Blend of Darell and Clarence
Female
English
French form of Latin Marianna, MARIANNE means "like Marius."
Female
Dutch
, Marie Anne.
Girl/Female
Christian, Gujarati, Hindu, Indian, Kannada, Marathi, Sindhi, Telugu
Wished-for Child
Girl/Female
Latin
Mythological Ariadne who aided Theseus to escape from the Cretan labyrinth.
MINIMUM VARIANCE-UNBIASED-ESTIMATOR
MINIMUM VARIANCE-UNBIASED-ESTIMATOR
Girl/Female
Tamil
Kalapini | கலாபிநீ
Peacock, Night
Boy/Male
Czechoslovakian
Bird.
Boy/Male
Indian, Telugu
One in Million
Girl/Female
Indian
Whiteness, Martyr in the cause of Islam
Girl/Female
Australian, Danish, Swedish
Branch
Boy/Male
Tamil
Girl/Female
Hindu
Blue wave of sea
Boy/Male
Arabic, Muslim
Servant of the Death-giver
Girl/Female
Indian
Beautiful
Girl/Female
Teutonic
Wise strength.
MINIMUM VARIANCE-UNBIASED-ESTIMATOR
MINIMUM VARIANCE-UNBIASED-ESTIMATOR
MINIMUM VARIANCE-UNBIASED-ESTIMATOR
MINIMUM VARIANCE-UNBIASED-ESTIMATOR
MINIMUM VARIANCE-UNBIASED-ESTIMATOR
n.
A self-registering thermometer, especially one that registers the maximum and minimum during long periods.
a.
Liable to vary; too susceptible of change; mutable; fickle; unsteady; inconstant; as, the affections of men are variable; passions are variable.
n.
The quality or state of being variant; change of condition; variation.
n.
That which is variable; that which varies, or is subject to change.
a.
Fair or impartial; unbiased.
n.
Alt. of Valiancy
a.
Greatest in quantity or highest in degree attainable or attained; as, a maximum consumption of fuel; maximum pressure; maximum heat.
v. t.
To furnish with a valance; to decorate with hangings or drapery.
pl.
of Minimus
n.
The greatest quantity or value attainable in a given case; or, the greatest value attained by a quantity which first increases and then begins to decrease; the highest point or degree; -- opposed to minimum.
a.
Free from bias or prejudice; unprejudiced; impartial.
n.
The least quantity assignable, admissible, or possible, in a given case; hence, a thing of small consequence; -- opposed to maximum.
n.
A minim.
n.
Minimum.
a.
Having the capacity of varying or changing; capable of alternation in any manner; changeable; as, variable winds or seasons; a variable quantity.
n.
Something which differs in form from another thing, though really the same; as, a variant from a type in natural history; a variant of a story or a word.
n.
Conversation; discourse; talk; diction; phrase; as, in legal parlance; in common parlance.
pl.
of Minimum
a.
Varying in from, character, or the like; variable; different; diverse.
n.
In a curve referred to polar coordinates, any point for which the radius vector is a maximum or minimum.