رگرسیون خوشه هوشمند "حداقل مربعات جزئی" در یک فرایند تصادفی

The clusterwise linear regression is studied when the set of predictor variables forms a L2L2-continuous stochastic process. For each cluster the estimators of the regression coefficients are given by partial least square regression. The number of clusters is treated as unknown and the convergence of the clusterwise algorithm is discussed. The approach is compared with other methods via an application on stock-exchange data.

In this paper, we propose to use the PLS estimators for regression coefficients of each cluster in the particular case where the set of explanatory variables forms a stochastic process X=(Xt)t∈[0,T]X=(Xt)t∈[0,T], T>0T>0. Thus, clusterwise PLS regression on a stochastic process is an extension of the global PLS approach given in Preda and Saporta (2002). The paper is divided into three parts. In the first part we introduce some tools for linear regression on a stochastic process (PCR, PLS) and justify the choice of the PLS approach. The clusterwise linear regression algorithm adapted to PLS regression as well as aspects related to the prediction problem are discussed in the second part. In the last part we present an application of the clusterwise PLS regression to stock-exchange data and compare the results with those obtained by other methods such asAguilera et al. (1997) and Preda and Saporta (2002).

The clusterwise PLS regression on a stochastic process offers an interesting alternative to classical methods of clusterwise analysis. It is particularly adapted to solve multicollinearity problems for regression and also when the number of observations is smaller than the number of predictor variables, which is often the case in the context of the clusterwise linear regression.