A generalized risk criterion for variable selection.

• Other Authors: Zuo, Guoxin.
• Format: Others
• Language: English; Chinese
• Published: 2007
• Subjects: Mathematical statistics; Regression analysis; Variables (Mathematics)
• Online Access: http://library.cuhk.edu.hk/record=b6074358; http://repository.lib.cuhk.edu.hk/en/item/cuhk-343987

In general model selection so far considered in literature, the parameter estimation loss and the prediction loss from the model selected are considered to be the same. In this thesis, the methods of parameter estimation may vary with different estimation loss, and the model selection may be based on different prediction loss. Under some regularized conditions, a model selection criterion, called generalized risk criterion (GRC), is proposed with a closed form. For multivariate linear regression model, and Cox regression model for ranking data, our studies that this criterion is an extension of the model selection criterion AIC. We also demonstrate that GRC performs better than AIC in a practical semi-parametric regression problem involving investments on horse racing. === Keywords: Variable selection; Model selection criterion; AIC; GRC; Loss function; Risk function; Multinomial Choice Model; Cox model for ranking data. === Searching for the true model based on the limited data is usually an impossible task. More and more attention in research has been focused on how to find an optimal model based on some special objective, such as focused information criterion (FIC, Hjort and Claeskens, 2003 [15]), Subspace Information criterion (Sugiyama and Ogawa, 2001 [43]) in statistical learning, etc. These ideas also motivate us to find an optimal subset of variables based on some objective. Different objectives may result in different choices of subset of variables. === Variable selection, an important aspect of model selection, is applied widely in real practices to explore the latent relationship between the random phenomena and various factors. Many model selection criteria, such as Mallow's Cp (Mallows, 1964 [28]). PRESS (Allen, 1971 [3]). AIC (Akaike, 1973 [2]), are proposed for seeking the optimal subset of the variables. Most of them try to find a criterion based on the observed data such that the selected models perform well both for fitting and for prediction. === Zuo, Guo Xin. === "July 2007." === Adviser: Ming Gao Gu. === Source: Dissertation Abstracts International, Volume: 69-01, Section: B, page: 0402. === Thesis (Ph.D.)--Chinese University of Hong Kong, 2007. === Includes bibliographical references (p. 71-75) === Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. === Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. === Abstracts in English and Chinese. === School code: 1307.