Penalized partial least squares for pleiotropy

Penalized Least Squares and Penalized Likelihood

where pλ(·) is the penalty function. Best subset selection corresponds to pλ(t) = (λ/2)I(t 6= 0). If we take pλ(t) = λ|t|, then (1.2) becomes the Lasso problem (1.1). Setting pλ(t) = at + (1 − a)|t| with 0 ≤ a ≤ 1 results in the method of elastic net. With pλ(t) = |t| for some 0 < q ≤ 2, it is called bridge regression, which includes the ridge regression as a special case when q = 2. Some penal...

Classification using partial least squares with penalized logistic regression

MOTIVATION One important aspect of data-mining of microarray data is to discover the molecular variation among cancers. In microarray studies, the number n of samples is relatively small compared to the number p of genes per sample (usually in thousands). It is known that standard statistical methods in classification are efficient (i.e. in the present case, yield successful classifiers) partic...

Penalized Partial Least Squares Based on B-Splines Transformations

Penalized least squares for single index models

The single index model is a useful regression model. In this paper, we propose a nonconcave penalized least squaresmethod to estimate both the parameters and the link function of the single index model. Compared to other variable selection and estimation methods, the proposed method can estimate parameters and select variables simultaneously.When the dimension of parameters in the single indexm...

Partial Least Squares for Discrimination

Partial least squares (PLS) was not originally designed as a tool for statistical discrimination. In spite of this, applied scientists routinely use PLS for classification and there is substantial empirical evidence to suggest that it performs well in that role. The interesting question is: why can a procedure that is principally designed for overdetermined regression problems locate and emphas...