Generalized Information Criterion (GIC)
In this chapter, we describe a general framework for constructing information criteria in the context of functional statistics and introduce a generalized information criterion, GIC [Konishi and Kitagawa (1996)]. The GIC can be applied to evaluate statistical models constructed by various types of estimation procedures including the robust estimation procedure and the maximum penalized likelihood procedure. Section 5.1 describes the fundamentals of a functional approach using a probability model having one parameter. In Section 5.2 and subsequent sections, we introduce the generalized information criterion for evaluating statistical models constructed in various ways. We also discuss the relationship among the AIC, TIC, and GIC. Various applications of the GIC to statistical modeling are shown in Chapter 6. Chapter 7 gives the derivation of information criteria and investigates their asymptotic properties with theoretical and numerical improvements.
KeywordsMaximum Likelihood Estimator True Distribution Empirical Distribution Function Implicit Equation Asymptotic Bias
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