Details

Autor(en) / Beteiligte

• Leng, Chenlei

Titel

Some problems in model selection

Ort / Verlag

ProQuest Dissertations & Theses

Erscheinungsjahr

2004

Link zum Volltext

• ProQuest

Quelle

ProQuest Dissertations & Theses A&I

Beschreibungen/Notizen

• This dissertation consists of three parts: the first two parts are related to smoothing spline ANOVA models; the third part concerns the Lasso and its related procedures in model selection. In Part I, we propose a novel nonparametric model selection technique to analyze time to event data, within the framework of smoothing spline ANOVA models. Instead of the usual squared norms in the traditional smoothing spline ANOVA, our method employs a regularization with the penalty functional being the sum of the component norms. This method shrinks functional components and produces some components that are exactly zeros. To compute the estimate when the smoothing parameter is fixed, we develop an efficient algorithm based on a reformulation of the penalized partial likelihood. Approximations to the leave-out-one likelihood cross validation score are derived to choose the smoothing parameters. Both simulations and real examples suggest that our proposal is very powerful for model selection and component estimation. Part II of the thesis concerns penalized likelihood density estimation. We introduce a randomized Generalized Approximate Cross Validation score to estimate the smoothing parameters. Part III studies the consistency of several recent linear model selection proposals. The Lasso, the Forward Stagewise regression and the Lars are closely related procedures recently proposed for linear regression problems. Each of them can produce sparse models and can be used both for estimation and variable selection. We show, however, that the dual goal of accurate estimation and consistent variable selection can not be achieved simultaneously: when the tuning parameter is chosen to minimize the prediction error, in general these procedures are not consistent in terms of variable selection. In particular, we show that for any sample size n, when there are superfluous variables in the linear regression model and the design matrix is orthogonal, the probability of the procedures correctly identifying the true set of important variables is less than a constant (smaller than one) not depending on n.