Diagnosing Homoscedasticity with the Power-weighted Smoothing Spline

DOI Web Site 2 Citations 30 References

Bibliographic Information

Other Title
  • ベキ重み付き平滑化スプラインによる分散均一性の診断
  • ベ キ オモミツキ ヘイカツカ スプライン ニ ヨル ブンサン キンイツセイ ノ シンダン

Search this article

Abstract

In nonparametric regression models, the requirements of homoscedasticity and so on are implicitly assumed, which leads to poor estimation of regression functions. A power weighted smoothing spline (PWSS) model, whose objective is to diagnose homoscedasticity as well as to estimate unknown nonlinear regression structure, is assumed. The responses in an additive regression model are power-transformed, and then their variances after transformation are assumed to be constant. Smoothing splines are obtained as estimated functions by maximizing the penalized likelihood, and a reweighted version of a backfitting algorithm is constructed. A power-transformation parameter and smoothing parameters, which control smoothness of the functions, are estimated by maximizing the marginal likelihood, based on Bayesian approaches to smoothing splines. A form of the marginal likelihood, which yields comparatively easy computation, is derived using the property that smoothing splines are the best linear unbiased predictor of a linear mixed model. Examination of some data sets from the literature and a simulation experiment show that the power transformation estimated with the PWSS model attains homoscedasticity while taking nonlinear structure into account.

Journal

  • Ouyou toukeigaku

    Ouyou toukeigaku 33 (1), 27-49, 2004

    Japanese Society of Applied Statistics

Citations (2)*help

See more

References(30)*help

See more

Related Projects

See more

Keywords

Details 詳細情報について

Report a problem

Back to top