Distance-based Regression Research Articles

Implementing PLS for distance-based regression: computational issues

Distance-based regression allows for a neat implementation of the partial least squares recurrence. In this paper, we address practical issues arising when dealing with moderately large datasets (n ~ 104) such as those typical of automobile insurance premium calculations.

Selection of Predictors in Distance-Based Regression

Distance-based regression is a prediction method consisting of two steps: from distances between observations we obtain latent variables which, in turn, are the regressors in an ordinary least squares linear model. Distances are computed from actually observed predictors by means of a suitable dissimilarity function. Being generally nonlinearly related with the response, their selection by the usual F tests is unavailable. In this article, we propose a solution to this predictor selection problem by defining generalized test statistics and adapting a nonparametric bootstrap method to estimate their p-values. We include a numerical example with automobile insurance data.

A family of matrices, the discretized brownian bridge, and distance-based regression

The investigation of a distance-based regression model, using a one-dimensional set of equally spaced points as regressor values and √| x − y| as a distance function, leads to the study of a family of matrices which is closely related to a discrete analog of the Brownian-bridge stochastic process. We describe its eigenstructure and several properties, recovering in particular well-known results on tridiagonal Toeplitz matrices and related topics.