Package pal.statistics
Class BootstrapStatistics
java.lang.Object
pal.statistics.BootstrapStatistics
computation of bootstrap estimators (BIAS, SD, VAR, CI)
given a statistic theta and corresponding bootstrap replicates.
See for background theory:
i) B. Efron and R. J.Tibshirani. 1993. An introduction
to the bootstrap. Chapman and Hall, New York
ii) P. Hall. 1992. The bootstrap and Edgeworth expansion.
Springer, New York
- Version:
- $Id: BootstrapStatistics.java,v 1.3 2001/07/13 14:39:13 korbinian Exp $
- Author:
- Korbinian Strimmer
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Constructor Summary
Constructors -
Method Summary
Modifier and TypeMethodDescriptionstatic double
biasCorrectedEstimate
(double thetaHat, double[] thetaHatStar) correct a statistic thetaHat for its biasstatic double
computeBIAS
(double thetaHat, double[] thetaHatStar) compute bias of a statistic thetaHat in estimating the true thetastatic double
computeSD
(double[] thetaHatStar) compute standard error (accuracy) of a statistic thetaHatstatic double
computeVAR
(double[] thetaHatStar) compute variance of a statistic thetaHatstatic double[]
efronCI
(double level, double[] thetaHatStar) compute approximate central confidence interval for thetaHat (Efron percentile method)static double[]
efronCI
(double level, double[] thetaHatStar, int[] array) compute approximate central confidence interval for thetaHat (Efron percentile method)static double[]
hallCI
(double level, double thetaHat, double[] thetaHatStar) compute approximate central confidence interval for thetaHat (Hall percentile method)static double[]
hallCI
(double level, double thetaHat, double[] thetaHatStar, int[] array) compute approximate central confidence interval for thetaHat (Hall percentile method)
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Constructor Details
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BootstrapStatistics
public BootstrapStatistics()
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Method Details
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computeBIAS
public static double computeBIAS(double thetaHat, double[] thetaHatStar) compute bias of a statistic thetaHat in estimating the true theta- Parameters:
thetaHat
- the statisticthetaHatStar
- bootstrap replicates of thetaHat- Returns:
- estimate of bias (notation: BIAS with hat)
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biasCorrectedEstimate
public static double biasCorrectedEstimate(double thetaHat, double[] thetaHatStar) correct a statistic thetaHat for its bias- Parameters:
thetaHat
- the statisticthetaHatStar
- bootstrap replicates of thetaHat- Returns:
- bias-corrected estimate
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computeVAR
public static double computeVAR(double[] thetaHatStar) compute variance of a statistic thetaHat- Parameters:
thetaHatStar
- bootstrap replicates of statistic thetaHat- Returns:
- estimate of variance of thetaHat (notation: VAR with hat)
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computeSD
public static double computeSD(double[] thetaHatStar) compute standard error (accuracy) of a statistic thetaHat- Parameters:
thetaHatStar
- bootstrap replicates of statistic thetaHat- Returns:
- estimate of standard error of thetaHat (notation: SD with hat)
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efronCI
public static double[] efronCI(double level, double[] thetaHatStar) compute approximate central confidence interval for thetaHat (Efron percentile method)- Parameters:
level
- confidence level (e.g., 0.95)thetaHatStar
- bootstrap replicates of statistic thetaHat- Returns:
- confidence set (array of two doubles)
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efronCI
public static double[] efronCI(double level, double[] thetaHatStar, int[] array) compute approximate central confidence interval for thetaHat (Efron percentile method)- Parameters:
level
- confidence level (e.g., 0.95)thetaHatStar
- bootstrap replicates of statistic thetaHatarray
- helper integer array (same length as thetaHatStar)- Returns:
- confidence set (array of two doubles)
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hallCI
public static double[] hallCI(double level, double thetaHat, double[] thetaHatStar) compute approximate central confidence interval for thetaHat (Hall percentile method)- Parameters:
level
- confidence level (e.g., 0.95)thetaHat
- the statisticthetaHatStar
- bootstrap replicates of statistic thetaHat- Returns:
- confidence set (array of two doubles)
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hallCI
public static double[] hallCI(double level, double thetaHat, double[] thetaHatStar, int[] array) compute approximate central confidence interval for thetaHat (Hall percentile method)- Parameters:
level
- confidence level (e.g., 0.95)thetaHat
- the statisticthetaHatStar
- bootstrap replicates of statistic thetaHatarray
- helper integer array (same length as thetaHatStar)- Returns:
- confidence set (array of two doubles)
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