KernelDensityEstimationL1.java

package org.drip.sequence.custom;

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

/*!
 * Copyright (C) 2019 Lakshmi Krishnamurthy
 * Copyright (C) 2018 Lakshmi Krishnamurthy
 * Copyright (C) 2017 Lakshmi Krishnamurthy
 * Copyright (C) 2016 Lakshmi Krishnamurthy
 * Copyright (C) 2015 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>KernelDensityEstimationL1</i> implements the L1 Error Scheme Estimation for a Multivariate Kernel
 * Density Estimator with Focus on establishing targeted Variate-Specific and Agnostic Bounds.
 * 
 * <br><br>
 *  <ul>
 *      <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/NumericalCore.md">Numerical Core Module</a></li>
 *      <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/StatisticalLearningLibrary.md">Statistical Learning Library</a></li>
 *      <li><b>Project</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/sequence">Sequence</a></li>
 *      <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/sequence/custom">Custom</a></li>
 *  </ul>
 * <br><br>
 *
 * @author Lakshmi Krishnamurthy
 */

public class KernelDensityEstimationL1 extends org.drip.sequence.functional.BoundedMultivariateRandom {
    private int _iSampleSize = -1;
    private double _dblSmoothingParameter = java.lang.Double.NaN;
    private org.drip.function.definition.R1ToR1 _auKernel = null;
    private org.drip.function.definition.R1ToR1 _auResponse = null;

    /**
     * KernelDensityEstimationL1 Constructor
     * 
     * @param auKernel The Kernel Function
     * @param dblSmoothingParameter The Smoothing Parameter
     * @param iSampleSize The Sample Size
     * @param auResponse The Response Function
     * 
     * @throws java.lang.Exception Thrown if Inputs are Invalid
     */

    public KernelDensityEstimationL1 (
        final org.drip.function.definition.R1ToR1 auKernel,
        final double dblSmoothingParameter,
        final int iSampleSize,
        final org.drip.function.definition.R1ToR1 auResponse)
        throws java.lang.Exception
    {
        if (null == (_auKernel = auKernel) || !org.drip.numerical.common.NumberUtil.IsValid
            (_dblSmoothingParameter = dblSmoothingParameter) || 0 >= (_iSampleSize = iSampleSize) || null ==
                (_auResponse = auResponse))
            throw new java.lang.Exception ("KernelDensityEstimationL1 Constructor => Invalid Inputs!");
    }

    /**
     * Retrieve the Kernel Function
     * 
     * @return The Kernel Function
     */

    public org.drip.function.definition.R1ToR1 kernelFunction()
    {
        return _auKernel;
    }

    /**
     * Retrieve the Smoothing Parameter
     * 
     * @return The Smoothing Parameter
     */

    public double smoothingParameter()
    {
        return _dblSmoothingParameter;
    }

    /**
     * Retrieve the Sample Size
     * 
     * @return The Sample Size
     */

    public int sampleSize()
    {
        return _iSampleSize;
    }

    /**
     * Retrieve the Response Function
     * 
     * @return The Response Function
     */

    public org.drip.function.definition.R1ToR1 responseFunction()
    {
        return _auResponse;
    }

    @Override public int dimension()
    {
        return org.drip.function.definition.RdToR1.DIMENSION_NOT_FIXED;
    }

    @Override public double evaluate (
        final double[] adblVariate)
        throws java.lang.Exception
    {
        double dblMinVariate = org.drip.numerical.common.NumberUtil.Minimum (adblVariate);

        double dblMaxVariate = org.drip.numerical.common.NumberUtil.Maximum (adblVariate);

        double dblKernelIntegral = 0.;
        int iNumVariate = adblVariate.length;

        for (int i = 0; i < iNumVariate; ++i)
            dblKernelIntegral += _auKernel.integrate ((dblMinVariate - adblVariate[i]) /
                _dblSmoothingParameter, (dblMaxVariate - adblVariate[i]) / _dblSmoothingParameter);

        return dblKernelIntegral / (_iSampleSize * _dblSmoothingParameter) - _auResponse.integrate
            (dblMinVariate, dblMaxVariate);
    }

    @Override public double targetVariateVarianceBound (
        final int iTargetVariateIndex)
        throws java.lang.Exception
    {
        return 4. / (_iSampleSize * _iSampleSize);
    }
}