StandardNormalSignificanceTest.java

package org.drip.sample.hypothesistest;

import org.drip.measure.gaussian.R1UnivariateNormal;
import org.drip.numerical.common.FormatUtil;
import org.drip.service.env.EnvManager;
import org.drip.validation.hypothesis.SignificanceTestSetting;
import org.drip.validation.evidence.Ensemble;
import org.drip.validation.evidence.Sample;
import org.drip.validation.evidence.TestStatisticEvaluator;
import org.drip.validation.hypothesis.SignificanceTestOutcome;
import org.drip.validation.hypothesis.ProbabilityIntegralTransformTest;

/*
 * -*- mode: java; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
 */

/*!
 * Copyright (C) 2019 Lakshmi Krishnamurthy
 * 
 *  This file is part of DROP, an open-source library targeting risk, transaction costs, exposure, margin
 *      calculations, and portfolio construction within and across fixed income, credit, commodity, equity,
 *      FX, and structured products.
 *  
 *      https://lakshmidrip.github.io/DROP/
 *  
 *  DROP is composed of three main modules:
 *  
 *  - DROP Analytics Core - https://lakshmidrip.github.io/DROP-Analytics-Core/
 *  - DROP Portfolio Core - https://lakshmidrip.github.io/DROP-Portfolio-Core/
 *  - DROP Numerical Core - https://lakshmidrip.github.io/DROP-Numerical-Core/
 * 
 *  DROP Analytics Core implements libraries for the following:
 *  - Fixed Income Analytics
 *  - Asset Backed Analytics
 *  - XVA Analytics
 *  - Exposure and Margin Analytics
 * 
 *  DROP Portfolio Core implements libraries for the following:
 *  - Asset Allocation Analytics
 *  - Transaction Cost Analytics
 * 
 *  DROP Numerical Core implements libraries for the following:
 *  - Statistical Learning Library
 *  - Numerical Optimizer Library
 *  - Machine Learning Library
 *  - Spline Builder Library
 * 
 *  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
 *  - 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>StandardNormalSignificanceTest</i> illustrates Significance Test for a Standard Normal Ensemble.
 *
 *  <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/AnalyticsCore.md">Analytics 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">Model Validation Suite</a></li>
 *      <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/validation/core">Core Model Validation Support Utilities</a></li>
 *  </ul>
 * <br><br>
 *
 * @author Lakshmi Krishnamurthy
 */

public class StandardNormalSignificanceTest
{

    private static final double UnivariateRandom()
        throws Exception
    {
        return R1UnivariateNormal.Standard().random();
    }

    private static final Sample GenerateSample (
        final int drawCount)
        throws Exception
    {
        double[] univariateRandomArray = new double[drawCount];

        for (int drawIndex = 0; drawIndex < drawCount; ++drawIndex)
        {
            univariateRandomArray[drawIndex] = UnivariateRandom();
        }

        return new Sample (univariateRandomArray);
    }

    private static final Sample[] GenerateSampleArray (
        final int drawCount,
        final int sampleCount)
        throws Exception
    {
        Sample[] sampleArray = new Sample[sampleCount];

        for (int sampleIndex = 0; sampleIndex < sampleCount; ++sampleIndex)
        {
            sampleArray[sampleIndex] = GenerateSample (drawCount);
        }

        return sampleArray;
    }

    private static final TestStatisticEvaluator[] MakeTestStatisticEvaluatorArray()
        throws Exception
    {
        return new TestStatisticEvaluator[]
        {
            new TestStatisticEvaluator()
            {
                public double evaluate (
                    final double[] drawArray)
                    throws Exception
                {
                    double mean = 0.;
                    int drawCount = drawArray.length;

                    for (int drawIndex = 0; drawIndex < drawCount; ++drawIndex)
                    {
                        mean += drawArray[drawIndex];
                    }

                    return mean / drawCount;
                }
            }
        };
    }

    private static final void SignificanceTest (
        final ProbabilityIntegralTransformTest test,
        final int drawCount,
        final TestStatisticEvaluator testStatisticEvaluator,
        final SignificanceTestSetting pTestSetting)
        throws Exception
    {
        Sample testSample = GenerateSample (drawCount);

        SignificanceTestOutcome significanceTest = test.significanceTest (
            testSample.applyTestStatistic (testStatisticEvaluator),
            pTestSetting
        );

        System.out.println (
            "\t| " + FormatUtil.FormatDouble (significanceTest.testStatistic(), 1, 8, 1.) +
            " | " + FormatUtil.FormatDouble (significanceTest.rightTailPValue(), 1, 8, 1.) +
            " | " + FormatUtil.FormatDouble (significanceTest.leftTailPValue(), 1, 8, 1.) +
            " | " + significanceTest.pass()
        );
    }

    public static final void main (
        final String[] argumentArray)
        throws Exception
    {
        EnvManager.InitEnv ("");

        int drawCount = 10000;
        int sampleCount = 100;
        int significanceTestCount = 20;

        TestStatisticEvaluator[] testStatisticEvaluatorArray = MakeTestStatisticEvaluatorArray();

        Ensemble ensemble = new Ensemble (
            GenerateSampleArray (
                drawCount,
                sampleCount
            ),
            testStatisticEvaluatorArray
        );

        ProbabilityIntegralTransformTest test = ensemble.significanceTest()[0];

        SignificanceTestSetting significanceTestSettingRightTail = SignificanceTestSetting.FisherRightTail();

        System.out.println ("\t|-------------------------------------------------||");

        System.out.println ("\t|      ENSEMBLE SIGNIFICANCE RIGHT TAIL TEST      ||");

        System.out.println ("\t|-------------------------------------------------||");

        System.out.println ("\t|    L -> R:                                      ||");

        System.out.println ("\t|        - Test Statistic                         ||");

        System.out.println ("\t|        - Right Tail p-Value                     ||");

        System.out.println ("\t|        - Left Tail p-Value                      ||");

        System.out.println ("\t|        - Significance Test Status               ||");

        System.out.println ("\t|-------------------------------------------------||");

        for (int significanceTest = 0; significanceTest < significanceTestCount; ++significanceTest)
        {
            SignificanceTest (
                test,
                drawCount,
                testStatisticEvaluatorArray[0],
                significanceTestSettingRightTail
            );
        }

        System.out.println ("\t|-------------------------------------------------||");

        SignificanceTestSetting significanceTestSettingLeftTail = SignificanceTestSetting.FisherLeftTail();

        System.out.println ("\t|-------------------------------------------------||");

        System.out.println ("\t|      ENSEMBLE SIGNIFICANCE RIGHT TAIL TEST      ||");

        System.out.println ("\t|-------------------------------------------------||");

        System.out.println ("\t|    L -> R:                                      ||");

        System.out.println ("\t|        - Test Statistic                         ||");

        System.out.println ("\t|        - Right Tail p-Value                     ||");

        System.out.println ("\t|        - Left Tail p-Value                      ||");

        System.out.println ("\t|        - Significance Test Status               ||");

        System.out.println ("\t|-------------------------------------------------||");

        for (int significanceTest = 0; significanceTest < significanceTestCount; ++significanceTest)
        {
            SignificanceTest (
                test,
                drawCount,
                testStatisticEvaluatorArray[0],
                significanceTestSettingLeftTail
            );
        }

        System.out.println ("\t|-------------------------------------------------||");

        SignificanceTestSetting significanceTestSettingDoubleTail = SignificanceTestSetting.FisherDoubleTail();

        System.out.println ("\t|-------------------------------------------------||");

        System.out.println ("\t|      ENSEMBLE SIGNIFICANCE DOUBLE TAIL TEST     ||");

        System.out.println ("\t|-------------------------------------------------||");

        System.out.println ("\t|    L -> R:                                      ||");

        System.out.println ("\t|        - Test Statistic                         ||");

        System.out.println ("\t|        - Right Tail p-Value                     ||");

        System.out.println ("\t|        - Left Tail p-Value                      ||");

        System.out.println ("\t|        - Significance Test Status               ||");

        System.out.println ("\t|-------------------------------------------------||");

        for (int significanceTest = 0; significanceTest < significanceTestCount; ++significanceTest)
        {
            SignificanceTest (
                test,
                drawCount,
                testStatisticEvaluatorArray[0],
                significanceTestSettingDoubleTail
            );
        }

        System.out.println ("\t|-------------------------------------------------||");

        EnvManager.TerminateEnv();
    }
}