Variance function estimation in regression by wavelet methods

Christian Lavergne (1) , Anestis Antoniadis (1)

1 LMC - IMAG - Laboratoire de Modélisation et Calcul

The objective of this paper is to contribute to the methodology available for dealing with a very common statistical problem, the estimation of the variance function in heteroscedastic multiple linear regression problems. The variance function is recovered by means of a smoothing nonparametric method, based on wavelet decompositions. The proposed method does not require preliminary or simultaneous estimation of the mean function. The resulting wavelet estimator is shown to be consistent, and is used to improve the estimation of the mean function itself. The method is illustrated with real and simulated data.

Domaines: Statistiques [math.ST]

Christian Lavergne, Anestis Antoniadis. Variance function estimation in regression by wavelet methods. Anestis Antoniadis; Georges Oppenheim. Wavelets and Statistics, 103, Springer, pp.31-42, 1995, Lecture Notes in Statitsics, ⟨10.1007/978-1-4612-2544-7_3⟩. ⟨hal-00196101⟩