Package dev.nm.stat.random.sampler.resampler.bootstrap.block

Class PattonPolitisWhite2009

java.lang.Object

dev.nm.stat.random.sampler.resampler.bootstrap.block.PattonPolitisWhite2009

All Implemented Interfaces:

Resampler, Seedable

public class PattonPolitisWhite2009
extends Object
implements Resampler

This class implements the stationary and circular block bootstrapping method with optimized block length.

See Also:

• • Politis, N. Dimitris, White Halbert, "Automatic Block-Length Selection for the Dependent Bootstrap", Econometric Reviews , 2004
  • Politis, D., White, H., Patton Andrew,"CORRECTION TO 'Automatic Block-Length Selection for the Dependent Bootstrap'", Econometric Reviews, 28(4):372–375, 2009
  • R-code

Constructor Summary

Constructors

Constructor	Description
PattonPolitisWhite2009(double[] sample)	Constructs a block bootstrap sample generator.
PattonPolitisWhite2009(double[] sample, long blockLength, PattonPolitisWhite2009ForObject.Type type, ConcurrentCachedRLG rlg, ConcurrentCachedRNG rng)	Constructs a block bootstrap sample generator.
PattonPolitisWhite2009(double[] sample, long blockLength, PattonPolitisWhite2009ForObject.Type type, RandomLongGenerator uniform, RandomNumberGenerator rng)	Constructs a block bootstrap sample generator.
PattonPolitisWhite2009(double[] sample, PattonPolitisWhite2009ForObject.Type type)	Constructs a block bootstrap sample generator.
PattonPolitisWhite2009(double[] sample, PattonPolitisWhite2009ForObject.Type type, RandomLongGenerator uniform, RandomNumberGenerator rng)	Constructs a block bootstrap sample generator.

Method Summary

Modifier and Type	Method	Description
static long	getOptimalBlockLength(double[] x, PattonPolitisWhite2009ForObject.Type type)	Computes the optimal of block length.
static long	getOptimalLag(double[] x)	Finds the smallest lag \(\hat{m}\) such that the autocorrelation for lags \((\hat{m} + k),~k=1,\dots,K_N\) are all insignificant regarding to the critical value.
double[]	newResample()	Gets a resample from the original sample.
void	seed(long... seeds)	Seed the random number/vector/scenario generator to produce repeatable experiments.

Methods inherited from class java.lang.Object

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

Constructor Details

PattonPolitisWhite2009

public PattonPolitisWhite2009(double[] sample,
 long blockLength,
 PattonPolitisWhite2009ForObject.Type type,
 ConcurrentCachedRLG rlg,
 ConcurrentCachedRNG rng)

Constructs a block bootstrap sample generator.

Parameters:

sample - the original sample

blockLength - the block length

type - the type of block bootstrap, either PattonPolitisWhite2009ForObject.Type.STATIONARY or PattonPolitisWhite2009ForObject.Type.CIRCULAR

rlg - a concurrent random long generator

rng - a concurrent random exponential generator

PattonPolitisWhite2009

public PattonPolitisWhite2009(double[] sample,
 long blockLength,
 PattonPolitisWhite2009ForObject.Type type,
 RandomLongGenerator uniform,
 RandomNumberGenerator rng)

Constructs a block bootstrap sample generator.

Parameters:

sample - the original sample

blockLength - the block length

type - the type of block bootstrap, either PattonPolitisWhite2009ForObject.Type.STATIONARY or PattonPolitisWhite2009ForObject.Type.CIRCULAR

uniform - a uniform random number generator

rng - a random exponential generator

PattonPolitisWhite2009

public PattonPolitisWhite2009(double[] sample,
 PattonPolitisWhite2009ForObject.Type type,
 RandomLongGenerator uniform,
 RandomNumberGenerator rng)

Constructs a block bootstrap sample generator. The block length is automatically selected.

Parameters:

sample - the original sample

type - the type of block bootstrap, either PattonPolitisWhite2009ForObject.Type.STATIONARY or PattonPolitisWhite2009ForObject.Type.CIRCULAR

uniform - a concurrent random long generator

rng - a concurrent random exponential generator

PattonPolitisWhite2009

public PattonPolitisWhite2009(double[] sample,
 PattonPolitisWhite2009ForObject.Type type)

Constructs a block bootstrap sample generator. The block length is automatically selected.

Parameters:

sample - the original sample

type - the type of block bootstrap, either PattonPolitisWhite2009ForObject.Type.STATIONARY or PattonPolitisWhite2009ForObject.Type.CIRCULAR

PattonPolitisWhite2009

public PattonPolitisWhite2009(double[] sample)

Constructs a block bootstrap sample generator. The default method is PattonPolitisWhite2009ForObject.Type.STATIONARY block bootstrapping. The block length is automatically selected.

Parameters:

sample - the original sample

Method Details

getOptimalBlockLength

public static long getOptimalBlockLength(double[] x,
 PattonPolitisWhite2009ForObject.Type type)

Computes the optimal of block length. For stationary block bootstrap, the length of each block follows the geometric distribution with mean equal to the computed optimal length; for circular block bootstrap, the length of each block is fixed to the computed optimal length.

Parameters:

x - the data

type - the type of block bootstrap method

Returns:

the optimal block length \(b_{opt} = \sqrt[3]{\frac{2\hat{G}^2N}{\hat{D}}}\)

getOptimalLag

public static long getOptimalLag(double[] x)

Finds the smallest lag \(\hat{m}\) such that the autocorrelation for lags \((\hat{m} + k),~k=1,\dots,K_N\) are all insignificant regarding to the critical value.

Parameters:

x - the data

Returns:

\(M = 2\hat{m}\)

See Also:

• "footnote c, p. 59, Politis and etc. 2004"

seed

public void seed(long... seeds)

Description copied from interface: Seedable

Seed the random number/vector/scenario generator to produce repeatable experiments.

Specified by:

seed in interface Seedable

Parameters:

seeds - the seeds

newResample

public double[] newResample()

Description copied from interface: Resampler

Gets a resample from the original sample. It is very important this method is thread-safe so resampling can be run in parallel.

Specified by:

newResample in interface Resampler

Returns:

a resample, e.g., a bootstrap sample