BootstrapStatistics

java.lang.Object
- pal.statistics.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

Constructor Summary

Constructors
Constructor and Description

BootstrapStatistics()

Constructors
Constructor and Description
`BootstrapStatistics()`

Method Summary

All Methods Static Methods Concrete Methods
Modifier and Type	Method and 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)

Class BootstrapStatistics

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Constructor Detail

BootstrapStatistics

Method Detail

computeBIAS

biasCorrectedEstimate

computeVAR

computeSD

efronCI

efronCI

hallCI

hallCI