Prediction of Percent Change in Linear Regression by Correlated Variables

Prediction of Percent Change in Linear Regression by Correlated Variables

Identifying the time of a step change in AR(1) auto-correlated simple linear profiles

Assuming a first-order auto-regressive model for the auto-correlation structure between observations, in this paper, a transformation method is first employed to eliminate the effect of auto-correlation. Then, a maximum likelihood estimator (MLE) of a step change in the parameters of the transformed model is derived and three separate EWMA control charts are used to monitor the parameters of th...

Prediction in Functional Linear Regression

There has been substantial recent work on methods for estimating the slope function in linear regression for functional data analysis. However, as in the case of more conventional finite-dimensional regression, much of the practical interest in the slope centers on its application for the purpose of prediction, rather than on its significance in its own right. We show that the problems of slope...

Discussion of ‘ Correlated variables in regression : clustering and sparse estimation

We would like to begin by congratulating the authors on their fine paper. Handling highly correlated variables is one of the most important issues facing practitioners in highdimensional regression problems, and in some ways it is surprising that it has not received more attention up to this point. The authors have made substantial progress towards practical methodological proposals, however, a...

Discussion of “correlated Variables in Regression: Clustering and Sparse Estimation”

Y = Xβ + ε. Here Y is the response vector in Rn, X is an n × p matrix, β0 ∈ Rp is the vector of coefficients, and finally ε ∈ Rn is assumed to be multivariate normal with mean zero and covariance matrix σ2I. While it has been shown that the lasso, and its many variants, “work” in terms of variable selection and prediction, they work best for near orthogonal cases of X. However, if p > n, correl...