mixregT function

Robust Mixture Regression with T-distribution

`mixregT' provides a robust estimation for a mixture of linear regression models by assuming that the error terms follow the t-distribution (Yao et al., 2014). The degrees of freedom is adaptively estimated.

mixregT(x, y, C = 2, maxdf = 30, nstart = 20, tol = 1e-05)

Arguments

• x: an n by p data matrix where n is the number of observations and p is the number of explanatory variables. The intercept term will automatically be added to the data.
• y: an n-dimensional vector of response variable.
• C: number of mixture components. Default is 2.
• maxdf: maximum degrees of freedom for the t-distribution. Default is 30.
• nstart: number of initializations to try. Default is 20.
• tol: threshold value (stopping criteria) for the EM algorithm. Default is 1e-05.

Returns

A list containing the following elements: - pi: C-dimensional vector of estimated mixing proportions.

• beta: C by (p + 1) matrix of estimated regression coefficients.

• sigma: C-dimensional vector of estimated standard deviations.

• lik: final likelihood.

• df: estimated degrees of freedom of the t-distribution.

• run: total number of iterations after convergence.

Examples

data(tone)
y = tone$tuned
x = tone$stretchratio
k = 160
x[151:k] = 0
y[151:k] = 5
est_t = mixregT(x, y, 2, nstart = 20, tol = 0.1)

References

Yao, W., Wei, Y., and Yu, C. (2014). Robust mixture regression using the t-distribution. Computational Statistics & Data Analysis, 71, 116-127.

See Also

mixregLap for robust estimation with Laplace distribution.