errorrate {EMMIXSSL}

Error rate of the Bayes rule for two-class Gaussian homoscedastic model

Description

The optimal error rate of Bayes rule for two-class Gaussian homoscedastic model

Usage

errorrate(beta0, beta, pi, mu, sigma)

Arguments

beta0

An n\times p matrix where each row represents an individual observation

beta

Number of observations.

pi

A g-dimensional vector for the initial values of the mixing proportions.

mu

A p \times g matrix for the initial values of the location parameters.

sigma

A p\times p covariance matrix if ncov=1, or a list of g covariance matrices with dimension p\times p \times g if ncov=2.

Details

The optimal error rate of Bayes rule for two-class Gaussian homoscedastic model can be expressed as

err(y_j;\theta)=\pi_1\phi\{-\frac{\beta_0+\beta_1^T\mu_1}{(\beta_1^T\Sigma\beta_1)^{\frac{1}{2}}}\}+\pi_2\phi\{\frac{\beta_0+\beta_1^T\mu_2}{(\beta_1^T\Sigma\beta_1)^{\frac{1}{2}}}\}

where \phi is a normal probability function with mean \mu_i and covariance matrix \Sigma_i.

Value

errval

A vector of error rate.