BLA {mixAK} | R Documentation

## Best linear approximation with respect to the mean square error (theoretical linear regression).

### Description

For a random vector X = (X[1], ..., X[p])' for which a mean and a covariance matrix are given computes coefficients of the best linear approximations with respect to the mean square error of each component of X given the remaining components of X.

### Usage

    BLA(mean=c(0, 0),  Sigma=diag(2))

### Arguments

`mean` | a numeric vector of means.
`Sigma` | a covariance matrix.

### Value

A list with the following components:

`beta` | computed regression coefficients
`sigmaR2` | residual variances

### Author(s)

Arnošt Komárek arnost.komarek[AT]mff.cuni.cz

### References

Anděl, J. (2007, odd. 2.5). Základy matematické statistiky. Praha: MATFYZPRESS.

### Examples

    ##### X = (U(1), U(2), U(3))'
    ##### * U(1) <= U(2) <= U(3)
    ##### * ordered uniform Unif(0, 1) variates
    EX <- (1:3)/4
    varX <- matrix(c(3,2,1, 2,4,2, 1,2,3), ncol=3)/80
    BLA(EX, Sigma=varX)

    ##### Uroda sena
    ##### * Y1 = uroda sena [cent/akr]
    ##### * Y2 = jarni srazky [palce]
    ##### * Y3 = kumulovana teplota nad 42 F
    EY <- c(28.02, 4.91, 28.7)
    varY <- matrix(c(19.54, 3.89, -3.76,  3.89, 1.21, -1.31,  -3.76, -1.31, 4.52), ncol=3)
    BLA(EY, Sigma=varY)

    ##### Z=(X, Y) ~ uniform distribution on a triangle
    ##### M = {(x,y): x>=0, y>=0, x+y<=3}
    EZ <- c(1, 1)
    varZ <- matrix(c(2, -1,  -1, 2), nrow=2)/4
    BLA(EZ, Sigma=varZ)

    ##### W=(X, Y) ~ uniform distribution on
    ##### M = {(x,y): x>=0, 0<=y<=1, y<=x<=y+1}
    EW <- c(1, 1/2)
    varW <- matrix(c(2, 1,  1, 1), nrow=2)/12
    BLA(EW, Sigma=varW)

[Package mixAK version 0.6 Index]