Class BootstrapStatistics


  • public class BootstrapStatistics
    extends java.lang.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
    • Method Summary

      All Methods Static Methods Concrete Methods 
      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 Detail

      • BootstrapStatistics

        public BootstrapStatistics()
    • Method Detail

      • 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)