Wavelet-PLS Regression: Application to Oil Production Data Salwa Benammou 1 , Kacem Zied 1 , Hedi Kortas 1 , and Dhifaoui Zouhaier 1 1 Computational Mathematical Laboratory, saloua.benammou@yahoo.fr 2 ZiedKacem2004@yahoo.fr 3 kortashedi@yahoo.fr 4 dh.zouhaier@yahoo.fr Abstract. This paper is devoted to the study of PLS regression in the presence of noise that could affect the quality of the results. To solve this problem, we suggest a hybrid approach which combines PLS regression and wavelet-based thresholding techniques. The proposed method is validated via a simulation study and subse- quently applied to petroleum data. Empirical results show the relevance of the selected approach and contribute to a better modelling of the series of study. Keywords: PLS regression, thresholding, minimax, wavelet-PLS 1 Introduction In numerous data analysis applications, statisticians are confronted with sev- eral problems such as missing or incomplete data, the presence of a strong collinearity between the explanatory variables or the case where the number of variables exceeds the number of observations. To cope with these problems, several statistical approaches have been developed, among them, a data anal- ysis method initially proposed by Wold and al. (1983). It is known as Partial Least Squares (PLS) regression. Although PLS regression has proven to be of great performance in a wide range of applications, the model variables are usually corrupted by noise which may adversely affect the results drawn from the PLS regression in terms of modelling and prediction accuracy (Tenenhaus and al. (1995)). To deal with this problem, we discuss, in this paper, a hybrid data analysis method based on the combination of wavelet thresholding techniques and PLS regression. 2 The Wavelet-PLS method The Wavelet-PLS regression entails several steps. As a first step, we pre- process the variables in the following manner: if the explanatory data vectors are not of dyadic lengths (i.e. powers of 2), we extend the data samples by applying a so called ”zero-padding” method. This method consists in adding