Class BootstrapStatistics

java.lang.Object
pal.statistics.BootstrapStatistics

public class BootstrapStatistics extends Object
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
  • Constructor Summary

    Constructors
    Constructor
    Description
     
  • Method Summary

    Modifier and Type
    Method
    Description
    static double
    biasCorrectedEstimate(double thetaHat, double[] thetaHatStar)
    correct a statistic thetaHat for its bias
    static double
    computeBIAS(double thetaHat, double[] thetaHatStar)
    compute bias of a statistic thetaHat in estimating the true theta
    static double
    computeSD(double[] thetaHatStar)
    compute standard error (accuracy) of a statistic thetaHat
    static double
    computeVAR(double[] thetaHatStar)
    compute variance of a statistic thetaHat
    static 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)

    Methods inherited from class java.lang.Object

    clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
  • Constructor Details

    • BootstrapStatistics

      public BootstrapStatistics()
  • Method Details

    • computeBIAS

      public static double computeBIAS(double thetaHat, double[] thetaHatStar)
      compute bias of a statistic thetaHat in estimating the true theta
      Parameters:
      thetaHat - the statistic
      thetaHatStar - bootstrap replicates of thetaHat
      Returns:
      estimate of bias (notation: BIAS with hat)
    • biasCorrectedEstimate

      public static double biasCorrectedEstimate(double thetaHat, double[] thetaHatStar)
      correct a statistic thetaHat for its bias
      Parameters:
      thetaHat - the statistic
      thetaHatStar - bootstrap replicates of thetaHat
      Returns:
      bias-corrected estimate
    • 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)
    • 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)
    • 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)
    • 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 thetaHat
      array - helper integer array (same length as thetaHatStar)
      Returns:
      confidence set (array of two doubles)
    • 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 statistic
      thetaHatStar - bootstrap replicates of statistic thetaHat
      Returns:
      confidence set (array of two doubles)
    • 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 statistic
      thetaHatStar - bootstrap replicates of statistic thetaHat
      array - helper integer array (same length as thetaHatStar)
      Returns:
      confidence set (array of two doubles)