org.apache.commons.math.stat.correlation.Covariance Java Examples

/**
 * Generate an error covariance matrix and sample data representing models
 * with this error structure. Then verify that GLS estimated coefficients,
 * on average, perform better than OLS.
 */
@Test
public void testGLSEfficiency() throws Exception {
    RandomGenerator rg = new JDKRandomGenerator();
    rg.setSeed(200);  // Seed has been selected to generate non-trivial covariance
    
    // Assume model has 16 observations (will use Longley data).  Start by generating
    // non-constant variances for the 16 error terms.
    final int nObs = 16;
    double[] sigma = new double[nObs];
    for (int i = 0; i < nObs; i++) {
        sigma[i] = 10 * rg.nextDouble();
    }
    
    // Now generate 1000 error vectors to use to estimate the covariance matrix
    // Columns are draws on N(0, sigma[col])
    final int numSeeds = 1000;
    RealMatrix errorSeeds = MatrixUtils.createRealMatrix(numSeeds, nObs);
    for (int i = 0; i < numSeeds; i++) {
        for (int j = 0; j < nObs; j++) {
            errorSeeds.setEntry(i, j, rg.nextGaussian() * sigma[j]);
        }
    }
    
    // Get covariance matrix for columns
    RealMatrix cov = (new Covariance(errorSeeds)).getCovarianceMatrix();
      
    // Create a CorrelatedRandomVectorGenerator to use to generate correlated errors
    GaussianRandomGenerator rawGenerator = new GaussianRandomGenerator(rg);
    double[] errorMeans = new double[nObs];  // Counting on init to 0 here
    CorrelatedRandomVectorGenerator gen = new CorrelatedRandomVectorGenerator(errorMeans, cov,
     1.0e-12 * cov.getNorm(), rawGenerator);
    
    // Now start generating models.  Use Longley X matrix on LHS
    // and Longley OLS beta vector as "true" beta.  Generate
    // Y values by XB + u where u is a CorrelatedRandomVector generated
    // from cov.
    OLSMultipleLinearRegression ols = new OLSMultipleLinearRegression();
    ols.newSampleData(longley, nObs, 6);
    final RealVector b = ols.calculateBeta().copy();
    final RealMatrix x = ols.X.copy();
    
    // Create a GLS model to reuse
    GLSMultipleLinearRegression gls = new GLSMultipleLinearRegression();
    gls.newSampleData(longley, nObs, 6);
    gls.newCovarianceData(cov.getData());
    
    // Create aggregators for stats measuring model performance
    DescriptiveStatistics olsBetaStats = new DescriptiveStatistics();
    DescriptiveStatistics glsBetaStats = new DescriptiveStatistics();
    
    // Generate Y vectors for 10000 models, estimate GLS and OLS and
    // Verify that OLS estimates are better
    final int nModels = 10000;
    for (int i = 0; i < nModels; i++) {
        
        // Generate y = xb + u with u cov
        RealVector u = MatrixUtils.createRealVector(gen.nextVector());
        double[] y = u.add(x.operate(b)).getData();
        
        // Estimate OLS parameters
        ols.newYSampleData(y);
        RealVector olsBeta = ols.calculateBeta();
        
        // Estimate GLS parameters
        gls.newYSampleData(y);
        RealVector glsBeta = gls.calculateBeta();
        
        // Record deviations from "true" beta
        double dist = olsBeta.getDistance(b);
        olsBetaStats.addValue(dist * dist);
        dist = glsBeta.getDistance(b);
        glsBetaStats.addValue(dist * dist);
        
    }
    
    // Verify that GLS is on average more efficient, lower variance
    assert(olsBetaStats.getMean() > 1.5 * glsBetaStats.getMean());
    assert(olsBetaStats.getStandardDeviation() > glsBetaStats.getStandardDeviation());  
}
 

/**
 * Generate an error covariance matrix and sample data representing models
 * with this error structure. Then verify that GLS estimated coefficients,
 * on average, perform better than OLS.
 */
@Test
public void testGLSEfficiency() throws Exception {
    RandomGenerator rg = new JDKRandomGenerator();
    rg.setSeed(200);  // Seed has been selected to generate non-trivial covariance
    
    // Assume model has 16 observations (will use Longley data).  Start by generating
    // non-constant variances for the 16 error terms.
    final int nObs = 16;
    double[] sigma = new double[nObs];
    for (int i = 0; i < nObs; i++) {
        sigma[i] = 10 * rg.nextDouble();
    }
    
    // Now generate 1000 error vectors to use to estimate the covariance matrix
    // Columns are draws on N(0, sigma[col])
    final int numSeeds = 1000;
    RealMatrix errorSeeds = MatrixUtils.createRealMatrix(numSeeds, nObs);
    for (int i = 0; i < numSeeds; i++) {
        for (int j = 0; j < nObs; j++) {
            errorSeeds.setEntry(i, j, rg.nextGaussian() * sigma[j]);
        }
    }
    
    // Get covariance matrix for columns
    RealMatrix cov = (new Covariance(errorSeeds)).getCovarianceMatrix();
      
    // Create a CorrelatedRandomVectorGenerator to use to generate correlated errors
    GaussianRandomGenerator rawGenerator = new GaussianRandomGenerator(rg);
    double[] errorMeans = new double[nObs];  // Counting on init to 0 here
    CorrelatedRandomVectorGenerator gen = new CorrelatedRandomVectorGenerator(errorMeans, cov,
     1.0e-12 * cov.getNorm(), rawGenerator);
    
    // Now start generating models.  Use Longley X matrix on LHS
    // and Longley OLS beta vector as "true" beta.  Generate
    // Y values by XB + u where u is a CorrelatedRandomVector generated
    // from cov.
    OLSMultipleLinearRegression ols = new OLSMultipleLinearRegression();
    ols.newSampleData(longley, nObs, 6);
    final RealVector b = ols.calculateBeta().copy();
    final RealMatrix x = ols.X.copy();
    
    // Create a GLS model to reuse
    GLSMultipleLinearRegression gls = new GLSMultipleLinearRegression();
    gls.newSampleData(longley, nObs, 6);
    gls.newCovarianceData(cov.getData());
    
    // Create aggregators for stats measuring model performance
    DescriptiveStatistics olsBetaStats = new DescriptiveStatistics();
    DescriptiveStatistics glsBetaStats = new DescriptiveStatistics();
    
    // Generate Y vectors for 10000 models, estimate GLS and OLS and
    // Verify that OLS estimates are better
    final int nModels = 10000;
    for (int i = 0; i < nModels; i++) {
        
        // Generate y = xb + u with u cov
        RealVector u = MatrixUtils.createRealVector(gen.nextVector());
        double[] y = u.add(x.operate(b)).getData();
        
        // Estimate OLS parameters
        ols.newYSampleData(y);
        RealVector olsBeta = ols.calculateBeta();
        
        // Estimate GLS parameters
        gls.newYSampleData(y);
        RealVector glsBeta = gls.calculateBeta();
        
        // Record deviations from "true" beta
        double dist = olsBeta.getDistance(b);
        olsBetaStats.addValue(dist * dist);
        dist = glsBeta.getDistance(b);
        glsBetaStats.addValue(dist * dist);
        
    }
    
    // Verify that GLS is on average more efficient, lower variance
    assert(olsBetaStats.getMean() > 1.5 * glsBetaStats.getMean());
    assert(olsBetaStats.getStandardDeviation() > glsBetaStats.getStandardDeviation());  
}
 

/**
 * Generate an error covariance matrix and sample data representing models
 * with this error structure. Then verify that GLS estimated coefficients,
 * on average, perform better than OLS.
 */
@Test
public void testGLSEfficiency() throws Exception {
    RandomGenerator rg = new JDKRandomGenerator();
    rg.setSeed(200);  // Seed has been selected to generate non-trivial covariance
    
    // Assume model has 16 observations (will use Longley data).  Start by generating
    // non-constant variances for the 16 error terms.
    final int nObs = 16;
    double[] sigma = new double[nObs];
    for (int i = 0; i < nObs; i++) {
        sigma[i] = 10 * rg.nextDouble();
    }
    
    // Now generate 1000 error vectors to use to estimate the covariance matrix
    // Columns are draws on N(0, sigma[col])
    final int numSeeds = 1000;
    RealMatrix errorSeeds = MatrixUtils.createRealMatrix(numSeeds, nObs);
    for (int i = 0; i < numSeeds; i++) {
        for (int j = 0; j < nObs; j++) {
            errorSeeds.setEntry(i, j, rg.nextGaussian() * sigma[j]);
        }
    }
    
    // Get covariance matrix for columns
    RealMatrix cov = (new Covariance(errorSeeds)).getCovarianceMatrix();
      
    // Create a CorrelatedRandomVectorGenerator to use to generate correlated errors
    GaussianRandomGenerator rawGenerator = new GaussianRandomGenerator(rg);
    double[] errorMeans = new double[nObs];  // Counting on init to 0 here
    CorrelatedRandomVectorGenerator gen = new CorrelatedRandomVectorGenerator(errorMeans, cov,
     1.0e-12 * cov.getNorm(), rawGenerator);
    
    // Now start generating models.  Use Longley X matrix on LHS
    // and Longley OLS beta vector as "true" beta.  Generate
    // Y values by XB + u where u is a CorrelatedRandomVector generated
    // from cov.
    OLSMultipleLinearRegression ols = new OLSMultipleLinearRegression();
    ols.newSampleData(longley, nObs, 6);
    final RealVector b = ols.calculateBeta().copy();
    final RealMatrix x = ols.X.copy();
    
    // Create a GLS model to reuse
    GLSMultipleLinearRegression gls = new GLSMultipleLinearRegression();
    gls.newSampleData(longley, nObs, 6);
    gls.newCovarianceData(cov.getData());
    
    // Create aggregators for stats measuring model performance
    DescriptiveStatistics olsBetaStats = new DescriptiveStatistics();
    DescriptiveStatistics glsBetaStats = new DescriptiveStatistics();
    
    // Generate Y vectors for 10000 models, estimate GLS and OLS and
    // Verify that OLS estimates are better
    final int nModels = 10000;
    for (int i = 0; i < nModels; i++) {
        
        // Generate y = xb + u with u cov
        RealVector u = MatrixUtils.createRealVector(gen.nextVector());
        double[] y = u.add(x.operate(b)).getData();
        
        // Estimate OLS parameters
        ols.newYSampleData(y);
        RealVector olsBeta = ols.calculateBeta();
        
        // Estimate GLS parameters
        gls.newYSampleData(y);
        RealVector glsBeta = gls.calculateBeta();
        
        // Record deviations from "true" beta
        double dist = olsBeta.getDistance(b);
        olsBetaStats.addValue(dist * dist);
        dist = glsBeta.getDistance(b);
        glsBetaStats.addValue(dist * dist);
        
    }
    
    // Verify that GLS is on average more efficient, lower variance
    assert(olsBetaStats.getMean() > 1.5 * glsBetaStats.getMean());
    assert(olsBetaStats.getStandardDeviation() > glsBetaStats.getStandardDeviation());  
}
 

public static double cov(Series a, Series b) {
  if(a.hasNull() || b.hasNull())
    return NULL;
  return new Covariance().covariance(a.getDoubles().values(), b.getDoubles().values());
}