In this paper we use the penalized maximum likelihood and information criteria to propose a new boosting algorithm for various statistical models, including linear regression, generalized linear, and multi-class classification models. In contrast to previous studies, where the empirical goodness-of-fit measures were often used for model updating, information criteria, as a predictive measure of a model, are employed to select a model in each iteration of the proposed algorithms. In addition, the proposed algorithms select the smoothing parameter in each iteration whereas previous methods fixed the parameter for all iterations.
We show that the penalized maximum likelihood L₂ boosting is consistent for high-dimensional linear models under the conditions that (a) the true underlying regression function is sparse and (b) the number of predictor variables is allowed to grow exponentially. We then demonstrate the proposed boosting algorithms using both simulated and real data. Comparison with some existing methods shows that the proposed boosting algorithms work well.

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A corporate bond is a contract in which the issuing corporation promises to pay interest and principle on prespecified future dates in exchange for use of cash today. The value of a corporate bond depends on three basic components: the term structure of riskless interest rate, embedded option values for callable bonds, and credit risk. This paper presents a penalized likelihood approaches to handle the corporate bond valuation and the term structure of credit spread using a firms credit rating and financial information. The proposed methods select significant financial variables and estimate coefficients simultaneously. Simulation study is also conducted to confirm the applicability of proposed methods. The methodology is applied to corporate bond valuation and term structure of credit risk spreads in Japanese bond markets.

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We propose a method of parameter estimation and goodness-of-fit test for lifetime analysis based on small censored data. Motivated by lifetime estimation of telecommunication systems, 2-parameter and 3-parameter Weibull distribution are discussed in this paper. The discussion is limited to the case when the censor time is a fixed value. With the application of EIC and bootstrap method, the proposed method enables both parameter estimation and the goodness-of-fit test for the estimated distributions, when the sample size is small and the censored data are included. The discussion also concerns with the evaluation of variation of the esimated bias derived from the small sample size.

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