ProbabilityIntegralTransformTest.java
package org.drip.validation.hypothesis;
/*
* -*- mode: java; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
*/
/*!
* Copyright (C) 2020 Lakshmi Krishnamurthy
* Copyright (C) 2019 Lakshmi Krishnamurthy
*
* This file is part of DROP, an open-source library targeting analytics/risk, transaction cost analytics,
* asset liability management analytics, capital, exposure, and margin analytics, valuation adjustment
* analytics, and portfolio construction analytics within and across fixed income, credit, commodity,
* equity, FX, and structured products. It also includes auxiliary libraries for algorithm support,
* numerical analysis, numerical optimization, spline builder, model validation, statistical learning,
* and computational support.
*
* https://lakshmidrip.github.io/DROP/
*
* DROP is composed of three modules:
*
* - DROP Product Core - https://lakshmidrip.github.io/DROP-Product-Core/
* - DROP Portfolio Core - https://lakshmidrip.github.io/DROP-Portfolio-Core/
* - DROP Computational Core - https://lakshmidrip.github.io/DROP-Computational-Core/
*
* DROP Product Core implements libraries for the following:
* - Fixed Income Analytics
* - Loan Analytics
* - Transaction Cost Analytics
*
* DROP Portfolio Core implements libraries for the following:
* - Asset Allocation Analytics
* - Asset Liability Management Analytics
* - Capital Estimation Analytics
* - Exposure Analytics
* - Margin Analytics
* - XVA Analytics
*
* DROP Computational Core implements libraries for the following:
* - Algorithm Support
* - Computation Support
* - Function Analysis
* - Model Validation
* - Numerical Analysis
* - Numerical Optimizer
* - Spline Builder
* - Statistical Learning
*
* Documentation for DROP is Spread Over:
*
* - Main => https://lakshmidrip.github.io/DROP/
* - Wiki => https://github.com/lakshmiDRIP/DROP/wiki
* - GitHub => https://github.com/lakshmiDRIP/DROP
* - Repo Layout Taxonomy => https://github.com/lakshmiDRIP/DROP/blob/master/Taxonomy.md
* - Javadoc => https://lakshmidrip.github.io/DROP/Javadoc/index.html
* - Technical Specifications => https://github.com/lakshmiDRIP/DROP/tree/master/Docs/Internal
* - Release Versions => https://lakshmidrip.github.io/DROP/version.html
* - Community Credits => https://lakshmidrip.github.io/DROP/credits.html
* - Issues Catalog => https://github.com/lakshmiDRIP/DROP/issues
* - JUnit => https://lakshmidrip.github.io/DROP/junit/index.html
* - Jacoco => https://lakshmidrip.github.io/DROP/jacoco/index.html
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
*
* You may obtain a copy of the License at
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
*
* See the License for the specific language governing permissions and
* limitations under the License.
*/
/**
* <i>ProbabilityIntegralTransformTest</i> implements Comparison Tests post a PIT Transform on the Hypothesis
* and/or Test Sample.
*
* <br><br>
* <ul>
* <li>
* Bhattacharya, B., and D. Habtzghi (2002): Median of the p-value under the Alternate Hypothesis
* American Statistician 56 (3) 202-206
* </li>
* <li>
* Head, M. L., L. Holman, R, Lanfear, A. T. Kahn, and M. D. Jennions (2015): The Extent and
* Consequences of p-Hacking in Science PLoS Biology 13 (3) e1002106
* </li>
* <li>
* Wasserstein, R. L., and N. A. Lazar (2016): The ASA’s Statement on p-values: Context, Process,
* and Purpose American Statistician 70 (2) 129-133
* </li>
* <li>
* Wetzels, R., D. Matzke, M. D. Lee, J. N. Rouder, G, J, Iverson, and E. J. Wagenmakers (2011):
* Statistical Evidence in Experimental Psychology: An Empirical Comparison using 855 t-Tests
* Perspectives in Psychological Science 6 (3) 291-298
* </li>
* <li>
* Wikipedia (2019): p-value https://en.wikipedia.org/wiki/P-value
* </li>
* </ul>
*
* <br><br>
* <ul>
* <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ComputationalCore.md">Computational Core Module</a></li>
* <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ModelValidationAnalyticsLibrary.md">Model Validation Analytics Library</a></li>
* <li><b>Project</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/validation/README.md">Risk Factor and Hypothesis Validation, Evidence Processing, and Model Testing</a></li>
* <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/validation/hypothesis/README.md">Statistical Hypothesis Validation Test Suite</a></li>
* </ul>
* <br><br>
*
* @author Lakshmi Krishnamurthy
*/
public class ProbabilityIntegralTransformTest
{
private org.drip.validation.hypothesis.ProbabilityIntegralTransform _probabilityIntegralTransform = null;
/**
* ProbabilityIntegralTransformTest Constructor
*
* @param probabilityIntegralTransform The Probability Integral Transform Instance
*
* @throws java.lang.Exception Thrown if the Inputs are Invalid
*/
public ProbabilityIntegralTransformTest (
final org.drip.validation.hypothesis.ProbabilityIntegralTransform probabilityIntegralTransform)
throws java.lang.Exception
{
if (null == (_probabilityIntegralTransform = probabilityIntegralTransform))
{
throw new java.lang.Exception ("ProbabilityIntegralTransformTest Constructor => Invalid Inputs");
}
}
/**
* Retrieve the ProbabilityIntegralTransform Instance
*
* @return The ProbabilityIntegralTransform Instance
*/
public org.drip.validation.hypothesis.ProbabilityIntegralTransform probabilityIntegralTransform()
{
return _probabilityIntegralTransform;
}
/**
* Run the Significance Test for the Realized Test Statistic
*
* @param testStatistic The Realized Test Statistic
* @param pTestSetting The P-Test Setting
*
* @return The Significance Test Result for the Realized Test Statistic
*/
public org.drip.validation.hypothesis.SignificanceTestOutcome significanceTest (
final double testStatistic,
final org.drip.validation.hypothesis.SignificanceTestSetting pTestSetting)
{
if (!org.drip.numerical.common.NumberUtil.IsValid (testStatistic) || null == pTestSetting)
{
return null;
}
double pValue = java.lang.Double.NaN;
try
{
pValue = _probabilityIntegralTransform.pValue (testStatistic);
}
catch (java.lang.Exception e)
{
e.printStackTrace();
return null;
}
int tailCheck = pTestSetting.tailCheck();
double threshold = pTestSetting.threshold();
if (org.drip.validation.hypothesis.SignificanceTestSetting.LEFT_TAIL_CHECK == tailCheck)
{
try
{
return new SignificanceTestOutcome (
testStatistic,
1. - pValue,
pValue,
pValue > threshold
);
}
catch (java.lang.Exception e)
{
e.printStackTrace();
return null;
}
}
if (org.drip.validation.hypothesis.SignificanceTestSetting.RIGHT_TAIL_CHECK == tailCheck)
{
try
{
return new SignificanceTestOutcome (
testStatistic,
1. - pValue,
pValue,
1. - pValue > threshold
);
}
catch (java.lang.Exception e)
{
e.printStackTrace();
return null;
}
}
try
{
return new SignificanceTestOutcome (
testStatistic,
1. - pValue,
pValue,
2. * java.lang.Math.min (
pValue,
1. - pValue
) > threshold
);
}
catch (java.lang.Exception e)
{
e.printStackTrace();
}
return null;
}
/**
* Run a Distance Gap Test between the Hypothesis and the Sample
*
* @param samplePIT The Sample Probability Integral Transform
* @param gapTestSetting The Distance Gap Test Setting
*
* @return The Distance Gap Test Outcome
*/
public org.drip.validation.distance.GapTestOutcome distanceTest (
final org.drip.validation.hypothesis.ProbabilityIntegralTransform samplePIT,
final org.drip.validation.distance.GapTestSetting gapTestSetting)
{
if (null == samplePIT || null == gapTestSetting)
{
return null;
}
double distance = 0.;
double hypothesisPValueLeft = 0.;
org.drip.validation.distance.GapLossFunction gapLossFunction = gapTestSetting.lossFunction();
org.drip.validation.distance.GapLossWeightFunction gapLossWeightFunction =
gapTestSetting.lossWeightFunction();
org.drip.validation.evidence.TestStatisticAccumulator weightedGapLossAccumulator = new
org.drip.validation.evidence.TestStatisticAccumulator();
org.drip.validation.evidence.TestStatisticAccumulator unweightedGapLossAccumulator = new
org.drip.validation.evidence.TestStatisticAccumulator();
for (java.util.Map.Entry<java.lang.Double, java.lang.Double> testStatisticPValueEntry :
samplePIT.testStatisticPValueMap().entrySet())
{
try
{
double hypothesisPValueRight = _probabilityIntegralTransform.pValue
(testStatisticPValueEntry.getKey());
double gapLoss = gapLossFunction.loss (testStatisticPValueEntry.getValue() -
hypothesisPValueRight);
double weightedGapLoss = gapLoss * gapLossWeightFunction.weight (hypothesisPValueRight);
distance = distance + weightedGapLoss * (hypothesisPValueRight - hypothesisPValueLeft);
if (!unweightedGapLossAccumulator.addTestStatistic (gapLoss) ||
!weightedGapLossAccumulator.addTestStatistic (weightedGapLoss))
{
return null;
}
hypothesisPValueLeft = hypothesisPValueRight;
}
catch (java.lang.Exception e)
{
e.printStackTrace();
return null;
}
}
try
{
return new org.drip.validation.distance.GapTestOutcome (
unweightedGapLossAccumulator.probabilityIntegralTransform(),
weightedGapLossAccumulator.probabilityIntegralTransform(),
distance
);
}
catch (java.lang.Exception e)
{
e.printStackTrace();
}
return null;
}
/**
* Run a Histogram Test Corresponding to the Test Statistic and its p-Value
*
* @param histogramTestSetting The Histogram Test Setting
*
* @return The Histogram Test Corresponding to the Test Statistic and its p-Value
*/
public org.drip.validation.hypothesis.HistogramTestOutcome histogramTest (
final org.drip.validation.hypothesis.HistogramTestSetting histogramTestSetting)
{
if (null == histogramTestSetting)
{
return null;
}
org.drip.validation.quantile.PlottingPositionGenerator plottingPositionGenerator =
histogramTestSetting.plottingPositionGenerator();
org.drip.validation.quantile.PlottingPosition[] plottingPositionArray =
plottingPositionGenerator.generate();
int qqVertexCount = plottingPositionArray.length + 2;
double[] testStatisticArray = new double[qqVertexCount];
double[] pValueCumulativeArray = new double[qqVertexCount];
double[] pValueIncrementalArray = new double[qqVertexCount];
try
{
pValueIncrementalArray[0] = 0.;
testStatisticArray[0] = _probabilityIntegralTransform.testStatistic
(pValueCumulativeArray[0] = 0.);
testStatisticArray[qqVertexCount - 1] = _probabilityIntegralTransform.testStatistic
(pValueCumulativeArray[qqVertexCount - 1] = 1.);
}
catch (java.lang.Exception e)
{
e.printStackTrace();
return null;
}
for (int qqVertexIndex = 1; qqVertexIndex < qqVertexCount - 1; ++qqVertexIndex)
{
try
{
testStatisticArray[qqVertexIndex] = _probabilityIntegralTransform.testStatistic
(pValueCumulativeArray[qqVertexIndex] =
plottingPositionArray[qqVertexIndex - 1].quantile());
pValueIncrementalArray[qqVertexIndex] = pValueCumulativeArray[qqVertexIndex] -
pValueCumulativeArray[qqVertexIndex - 1];
}
catch (java.lang.Exception e)
{
e.printStackTrace();
return null;
}
}
pValueIncrementalArray[qqVertexCount - 1] = pValueCumulativeArray[qqVertexCount - 1] -
pValueCumulativeArray[qqVertexCount - 2];
try
{
return new org.drip.validation.hypothesis.HistogramTestOutcome (
testStatisticArray,
pValueCumulativeArray,
pValueIncrementalArray,
_probabilityIntegralTransform.testStatistic (histogramTestSetting.pValueThreshold())
);
}
catch (java.lang.Exception e)
{
e.printStackTrace();
}
return null;
}
/**
* Run the Quantile-Quantile Test
*
* @param samplePIT The Sample Probability Integral Transform
* @param plottingPositionGenerator The Quantile-Quantile Test Plotting Position Generator
*
* @return The Quantile-Quantile Test Outcome
*/
public org.drip.validation.quantile.QQTestOutcome qqTest (
final org.drip.validation.hypothesis.ProbabilityIntegralTransform samplePIT,
final org.drip.validation.quantile.PlottingPositionGenerator plottingPositionGenerator)
{
if (null == samplePIT || null == plottingPositionGenerator)
{
return null;
}
org.drip.validation.quantile.PlottingPosition[] plottingPositionArray =
plottingPositionGenerator.generate();
if (null == plottingPositionArray)
{
return null;
}
int orderStatisticCount = plottingPositionArray.length;
org.drip.validation.quantile.QQVertex[] qqVertexArray = new
org.drip.validation.quantile.QQVertex[orderStatisticCount];
for (int orderStatisticIndex = 0; orderStatisticIndex < orderStatisticCount; ++orderStatisticIndex)
{
try
{
double pValue = plottingPositionArray[orderStatisticIndex].quantile();
qqVertexArray[orderStatisticIndex] = new org.drip.validation.quantile.QQVertex (
plottingPositionArray[orderStatisticIndex],
samplePIT.testStatistic (pValue),
_probabilityIntegralTransform.testStatistic (pValue)
);
}
catch (java.lang.Exception e)
{
e.printStackTrace();
return null;
}
}
try
{
return new org.drip.validation.quantile.QQTestOutcome (qqVertexArray);
}
catch (java.lang.Exception e)
{
e.printStackTrace();
}
return null;
}
}