taperingEst: Tapering Estimator

In cvCovEst: Cross-Validated Covariance Matrix Estimation

Tapering Estimator

Description

taperingEst() estimates the covariance matrix of a data.frame-like object with ordered variables by gradually shrinking the bands of the sample covariance matrix towards zero. The estimator is defined as the Hadamard product of the sample covariance matrix and a weight matrix. The amount of shrinkage is dictated by the weight matrix and is specified by a hyperparameter k. This estimator is attributed to \insertCitecai2010;textualcvCovEst.

The weight matrix is a Toeplitz matrix with entries defined as follows. Let i and j index the rows and columns of the weight matrix, respectively. If abs(i - j) <= k / 2, then entry {i, j} in the weight matrix is equal to 1. If k / 2 < abs(i - j) < k, then entry {i, j} is equal to 2 - 2 * abs(i - j) / k. Otherwise, entry {i, j} is equal to 0.

Usage

taperingEst(dat, k)

Arguments

dat	A numeric data.frame, matrix, or similar object.
k	A non-negative, even numeric integer.

Value

A matrix corresponding to the estimate of the covariance matrix.

References

\insertAllCited

Examples

taperingEst(dat = mtcars, k = 0.1)

cvCovEst documentation built on May 29, 2024, 5:51 a.m.