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

In fastmatrix: Fast Computation of some Matrices Useful in Statistics

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)

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.

Value

A list containing the following named components:

mean	an estimate for the center (mean) of the data.
cov	the estimated covariance matrix.

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

fastmatrix documentation built on Sept. 11, 2024, 7:22 p.m.