Package it.unimi.dsi.stat

Class Jackknife

java.lang.Object

it.unimi.dsi.stat.Jackknife

public class Jackknife
extends Object

Applies the jackknife to generic statistics.

This class applies the jackknife method (see, e.g., “A leisurely look at the bootstrap, the jackknife, and cross-validation”, by Bradley Efron and Gail Gong, The American Statistician, 37(1):36−48, 1983) to reduce the bias in the estimation of a nonlinear statistic of interest (linear statistics, such as the mean, pass through the jackknife without change). The statistic must take a sample (an array of big decimals) and return corresponding values (again as an array of big decimals). In case high-precision arithmetic is not required, an instance of Jackknife.AbstractStatistic just takes an array of doubles and returns an array of doubles, handling all necessary type conversions.

The static method compute(List, Statistic, MathContext) takes a list of samples (arrays of doubles of the same length) and returns an instance of this class containing estimates and standard errors for every value computed by the statistic (estimates of the statistic are available both as an array of big decimals and as an array of doubles, whereas estimates of standard errors are provided in double format, only).

All computations are performed internally using BigDecimal and a provided MathContext. The method compute(List, Statistic) uses 100 decimal digits.

The identical statistic can be used to compute the (pointwise) empirical mean and standard error of a sample.

Author:

Sebastiano Vigna

Nested Class Summary

Nested Classes

Modifier and Type	Class	Description
static class	Jackknife.AbstractStatistic	An abstract statistic with a template method that accepts an array of doubles, returns an array of doubles and handles the data conversions that are necessary to call Jackknife.Statistic.compute(BigDecimal[], MathContext).
static interface	Jackknife.Statistic	A statistic to be estimated using the jackknife on a set of samples.

Field Summary

Fields

Modifier and Type	Field	Description
BigDecimal[]	bigEstimate	A vector of high-precision estimates for a statistic of interest.
static MathContext	DEFAULT_MATH_CONTEXT	The default MathContext used by compute(List, Statistic): 100 digits and RoundingMode.HALF_EVEN.
double[]	estimate	A vector of estimates for a statistic of interest (obtained by invoking BigDecimal.doubleValue() on bigEstimate).
static Jackknife.Statistic	IDENTITY	A statistic that returns the sample.
double[]	standardError	A vector of (estimates of the) standard error parallel to bigEstimate/estimate.

Method Summary

Modifier and Type	Method	Description
static double[]	bigDecimalArray2DoubleArray(BigDecimal[] input)
static Jackknife	compute(List<double[]> samples, Jackknife.Statistic f)	Applies the jackknife to a statistic of interest using a list of samples using DEFAULT_MATH_CONTEXT as context.
static Jackknife	compute(List<double[]> samples, Jackknife.Statistic f, MathContext mc)	Applies the jackknife to a statistic of interest using a list of samples.
static BigDecimal[]	doubleArray2BigDecimalArray(double[] input)
String	toString()

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, wait, wait, wait

Field Details

DEFAULT_MATH_CONTEXT

public static final MathContext DEFAULT_MATH_CONTEXT

The default MathContext used by compute(List, Statistic): 100 digits and RoundingMode.HALF_EVEN.

bigEstimate

public final BigDecimal[] bigEstimate

A vector of high-precision estimates for a statistic of interest.

estimate

public final double[] estimate

A vector of estimates for a statistic of interest (obtained by invoking BigDecimal.doubleValue() on bigEstimate).

standardError

public final double[] standardError

A vector of (estimates of the) standard error parallel to bigEstimate/estimate.

IDENTITY

public static Jackknife.Statistic IDENTITY

A statistic that returns the sample. Useful to compute the average and the empirical standard error.

Method Details

bigDecimalArray2DoubleArray

public static double[] bigDecimalArray2DoubleArray(BigDecimal[] input)

doubleArray2BigDecimalArray

public static BigDecimal[] doubleArray2BigDecimalArray(double[] input)

toString

public String toString()

Overrides:

toString in class Object

compute

public static Jackknife compute(List<double[]> samples, Jackknife.Statistic f)

Applies the jackknife to a statistic of interest using a list of samples using DEFAULT_MATH_CONTEXT as context.

Parameters:

samples - a list of samples (arrays of doubles of the same length).

f - a statistic of interest.

Returns:

an instance of this class containing estimates of f and corresponding standard errors obtained by the jackknife on the given set of samples.

compute

public static Jackknife compute(List<double[]> samples, Jackknife.Statistic f, MathContext mc)

Applies the jackknife to a statistic of interest using a list of samples.

Parameters:

samples - a list of samples (arrays of doubles of the same length).

f - a statistic of interest.

mc - the mathematical context to be used when dividing big decimals.

Returns:

an instance of this class containing estimates of f and corresponding standard errors obtained by the jackknife on the given set of samples.