Test subsets of \(\beta\) are zero

Tests the null hypothesis that an arbitrary subset of the \(\beta _{ij}\)'s is zero, based on the least squares estimates, using the \(\chi^2\) test as in Section 7.1. The null and alternative are specified by pattern matrices \(P_0\) and \(P_A\), respectively. If the \(P_A\) is omitted, then the alternative will be taken to be the unrestricted model.

bothsidesmodel.chisquare(
  x,
  y,
  z,
  pattern0,
  patternA = matrix(1, nrow = ncol(x), ncol = ncol(z))
)

Arguments

x

An \(N \times P\) design matrix.

y

The \(N \times Q\) matrix of observations.

z

A \(Q \times L\) design matrix.

pattern0

An \(N \times P\) matrix of 0's and 1's specifying the null hypothesis.

patternA

An optional \(N \times P\) matrix of 0's and 1's specifying the alternative hypothesis.

Value

A `list` with the following components:

Theta

The vector of estimated parameters of interest.

Covtheta

The estimated covariance matrix of the estimated parameter vector.

df

The degrees of freedom in the test.

chisq

\(T^2\) statistic in (7.4).

pvalue

The p-value for the test.

See also

bothsidesmodel, bothsidesmodel.df, bothsidesmodel.hotelling, bothsidesmodel.lrt, and bothsidesmodel.mle.

Examples

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