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

Class PattonPolitisWhite2009ForObject<X>

java.lang.Object

dev.nm.stat.random.sampler.resampler.bootstrap.block.PattonPolitisWhite2009ForObject<X>

All Implemented Interfaces:

ObjectResampler<X>, Seedable

public class PattonPolitisWhite2009ForObject<X>
extends Object
implements ObjectResampler<X>

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

Nested Class Summary

Nested Classes

Modifier and Type	Class	Description
static interface	PattonPolitisWhite2009ForObject.AutoCorrelationForObject
static interface	PattonPolitisWhite2009ForObject.AutoCovarianceForObject
static enum	PattonPolitisWhite2009ForObject.Type

Field Summary

Fields

Modifier and Type	Field	Description
static final int	DEFAULT_CACHE_SIZE	The default cache size = the number of available processors × 1000.

Constructor Summary

Constructors

Constructor	Description
PattonPolitisWhite2009ForObject(X[] sample, Class<X> clazz, long blockLength, PattonPolitisWhite2009ForObject.Type type, ConcurrentCachedRLG rlg, ConcurrentCachedRNG rng)	Constructs a block bootstrap sample generator.
PattonPolitisWhite2009ForObject(X[] sample, Class<X> clazz, long blockLength, PattonPolitisWhite2009ForObject.Type type, RandomLongGenerator uniform, RandomNumberGenerator rng)	Constructs a block bootstrap sample generator.
PattonPolitisWhite2009ForObject(X[] sample, Class<X> clazz, PattonPolitisWhite2009ForObject.AutoCorrelationForObject autoCorrelation, PattonPolitisWhite2009ForObject.AutoCovarianceForObject autoCovariance)	Constructs a block bootstrap sample generator.
PattonPolitisWhite2009ForObject(X[] sample, Class<X> clazz, PattonPolitisWhite2009ForObject.AutoCorrelationForObject autoCorrelation, PattonPolitisWhite2009ForObject.AutoCovarianceForObject autoCovariance, PattonPolitisWhite2009ForObject.Type type)	Constructs a block bootstrap sample generator.
PattonPolitisWhite2009ForObject(X[] sample, Class<X> clazz, PattonPolitisWhite2009ForObject.AutoCorrelationForObject autoCorrelation, PattonPolitisWhite2009ForObject.AutoCovarianceForObject autoCovariance, PattonPolitisWhite2009ForObject.Type type, RandomLongGenerator uniform, RandomNumberGenerator rng)	Constructs a block bootstrap sample generator.

Method Summary

Modifier and Type	Method	Description
static long	getOptimalBlockLength(Object[] x, PattonPolitisWhite2009ForObject.AutoCorrelationForObject autoCorrelation, PattonPolitisWhite2009ForObject.AutoCovarianceForObject autoCovariance, PattonPolitisWhite2009ForObject.Type type)	Computes the optimal of block length.
static long	getOptimalLag(Object[] x, PattonPolitisWhite2009ForObject.AutoCorrelationForObject R)	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.
X[]	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

Field Details

DEFAULT_CACHE_SIZE

public static final int DEFAULT_CACHE_SIZE

The default cache size = the number of available processors × 1000.

Constructor Details

PattonPolitisWhite2009ForObject

public PattonPolitisWhite2009ForObject(X[] sample,
 Class<X> clazz,
 PattonPolitisWhite2009ForObject.AutoCorrelationForObject autoCorrelation,
 PattonPolitisWhite2009ForObject.AutoCovarianceForObject autoCovariance)

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

clazz - the class of the sample objects

autoCorrelation - the autocorrelation function for the sample objects

autoCovariance - the autocovariance function for the sample objects

PattonPolitisWhite2009ForObject

public PattonPolitisWhite2009ForObject(X[] sample,
 Class<X> clazz,
 PattonPolitisWhite2009ForObject.AutoCorrelationForObject autoCorrelation,
 PattonPolitisWhite2009ForObject.AutoCovarianceForObject autoCovariance,
 PattonPolitisWhite2009ForObject.Type type)

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

Parameters:

sample - the original sample

clazz - the class of the sample objects

autoCorrelation - the autocorrelation function for the sample objects

autoCovariance - the autocovariance function for the sample objects

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

PattonPolitisWhite2009ForObject

public PattonPolitisWhite2009ForObject(X[] sample,
 Class<X> clazz,
 PattonPolitisWhite2009ForObject.AutoCorrelationForObject autoCorrelation,
 PattonPolitisWhite2009ForObject.AutoCovarianceForObject autoCovariance,
 PattonPolitisWhite2009ForObject.Type type,
 RandomLongGenerator uniform,
 RandomNumberGenerator rng)

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

Parameters:

sample - the original sample

clazz - the class of the sample objects

autoCorrelation - the autocorrelation function for the sample objects

autoCovariance - the autocovariance function for the sample objects

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

PattonPolitisWhite2009ForObject

public PattonPolitisWhite2009ForObject(X[] sample,
 Class<X> clazz,
 long blockLength,
 PattonPolitisWhite2009ForObject.Type type,
 RandomLongGenerator uniform,
 RandomNumberGenerator rng)

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

Parameters:

sample - the original sample

clazz - the class of the sample objects

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

PattonPolitisWhite2009ForObject

public PattonPolitisWhite2009ForObject(X[] sample,
 Class<X> clazz,
 long blockLength,
 PattonPolitisWhite2009ForObject.Type type,
 ConcurrentCachedRLG rlg,
 ConcurrentCachedRNG rng)

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

Parameters:

sample - the original sample

clazz - the class of the sample objects

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

Method Details

getOptimalBlockLength

public static long getOptimalBlockLength(Object[] x,
 PattonPolitisWhite2009ForObject.AutoCorrelationForObject autoCorrelation,
 PattonPolitisWhite2009ForObject.AutoCovarianceForObject autoCovariance,
 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(Object[] x,
 PattonPolitisWhite2009ForObject.AutoCorrelationForObject R)

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 X[] newResample()

Description copied from interface: ObjectResampler

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 ObjectResampler<X>

Returns:

a resample, e.g., a bootstrap sample