fastmatrix (version 0.5-7721)

cov.MSSD: Mean Square Successive Difference (MSSD) estimator of the covariance matrix

Description

Returns a list containing the mean and covariance matrix of the data.

Usage

cov.MSSD(x)

Value

A list containing the following named components:

mean

an estimate for the center (mean) of the data.

cov

the estimated covariance matrix.

Arguments

x

a matrix or data frame. As usual, rows are observations and columns are variables.

Details

This procedure uses the Holmes-Mergen method using the difference between each successive pairs of observations also known as Mean Square Successive Method (MSSD) to estimate the covariance matrix, which is given by $$\bold{S}_{HD} = \frac{1}{2(n-1)} \sum\limits_{i=2}^n (\bold{x}_i - \bold{x}_{i-1})(\bold{x}_i - \bold{x}_{i-1})^T.$$

References

Holmes, D.S., Mergen, A.E. (1993). Improving the performance of the \(T^2\) control chart. Quality Engineering 5, 619-625.

See Also

cov and var.

Examples

x <- cbind(1:10, c(1:3, 8:5, 8:10))
z0 <- cov(x)
z0
z1 <- cov.MSSD(x)
z1