@Override
public List<java.lang.Double> parameters() {
List<Double> parameters = new ArrayList<Double>((n + 1) * (h) + (h + 1) * n);
for (int i : series(h)) // to
for (int j : series(n + 1)) // from
parameters.add(weights0.getEntry(i, j));
for (int i : series(n)) // to
for (int j : series(h + 1)) // from
parameters.add(weights1.getEntry(i, j));
return parameters;
}
/**
* Derives a correlation matrix from a covariance matrix.
*
* <p>Uses the formula <br>
* <code>r(X,Y) = cov(X,Y)/s(X)s(Y)</code> where <code>r(·,·)</code> is the
* correlation coefficient and <code>s(·)</code> means standard deviation.
*
* @param covarianceMatrix the covariance matrix
* @return correlation matrix
*/
public RealMatrix covarianceToCorrelation(RealMatrix covarianceMatrix) {
int nVars = covarianceMatrix.getColumnDimension();
RealMatrix outMatrix = new BlockRealMatrix(nVars, nVars);
for (int i = 0; i < nVars; i++) {
double sigma = Math.sqrt(covarianceMatrix.getEntry(i, i));
outMatrix.setEntry(i, i, 1d);
for (int j = 0; j < i; j++) {
double entry =
covarianceMatrix.getEntry(i, j) / (sigma * Math.sqrt(covarianceMatrix.getEntry(j, j)));
outMatrix.setEntry(i, j, entry);
outMatrix.setEntry(j, i, entry);
}
}
return outMatrix;
}
/**
* Returns a matrix of standard errors associated with the estimates in the correlation matrix.
* <br>
* <code>getCorrelationStandardErrors().getEntry(i,j)</code> is the standard error associated with
* <code>getCorrelationMatrix.getEntry(i,j)</code>
*
* <p>The formula used to compute the standard error is <br>
* <code>SE<sub>r</sub> = ((1 - r<sup>2</sup>) / (n - 2))<sup>1/2</sup></code> where <code>r
* </code> is the estimated correlation coefficient and <code>n</code> is the number of
* observations in the source dataset.
*
* @return matrix of correlation standard errors
*/
public RealMatrix getCorrelationStandardErrors() {
int nVars = correlationMatrix.getColumnDimension();
double[][] out = new double[nVars][nVars];
for (int i = 0; i < nVars; i++) {
for (int j = 0; j < nVars; j++) {
double r = correlationMatrix.getEntry(i, j);
out[i][j] = Math.sqrt((1 - r * r) / (nObs - 2));
}
}
return new BlockRealMatrix(out);
}
public void print(RealMatrix matrix, PrintWriter output, NumberFormat format, int width) {
for (int row = 0; row < matrix.getRowDimension(); row++) {
for (int column = 0; column < matrix.getColumnDimension(); column++) {
String number = format.format(matrix.getEntry(row, column));
int padding = Math.max(1, width - number.length());
for (int p = 0; p < padding; p++) output.print(' ');
output.print(number);
}
output.println();
}
}
/**
* Returns a matrix of p-values associated with the (two-sided) null hypothesis that the
* corresponding correlation coefficient is zero.
*
* <p><code>getCorrelationPValues().getEntry(i,j)</code> is the probability that a random variable
* distributed as <code>t<sub>n-2</sub></code> takes a value with absolute value greater than or
* equal to <br>
* <code>|r|((n - 2) / (1 - r<sup>2</sup>))<sup>1/2</sup></code>
*
* <p>The values in the matrix are sometimes referred to as the <i>significance</i> of the
* corresponding correlation coefficients.
*
* @return matrix of p-values
* @throws MathException if an error occurs estimating probabilities
*/
public RealMatrix getCorrelationPValues() throws MathException {
TDistribution tDistribution = new TDistributionImpl(nObs - 2);
int nVars = correlationMatrix.getColumnDimension();
double[][] out = new double[nVars][nVars];
for (int i = 0; i < nVars; i++) {
for (int j = 0; j < nVars; j++) {
if (i == j) {
out[i][j] = 0d;
} else {
double r = correlationMatrix.getEntry(i, j);
double t = Math.abs(r * Math.sqrt((nObs - 2) / (1 - r * r)));
out[i][j] = 2 * (1 - tDistribution.cumulativeProbability(t));
}
}
}
return new BlockRealMatrix(out);
}