A review of selected techniques in inverse problem nonparametric probability distribution estimation

Abstract

Techniques for the nonparametric estimation of probability distributions are reviewed. Methods are divided into two categories for estimation problems: those applied to situations in which individual data is available, and those where only aggregate data is available. For each technique, the general ideas, strengths, and weaknesses of the corresponding methodology are discussed. In addition, the generation of estimates of not only the parameter distributions but also any structural parameters that are constant across the population is outlined. When discussing various techniques, particular consideration is given to the theory behind finite dimensional approximations (since the space of measures on a viable parameter space ‚ is an infinite dimensional space) in the development of computational methodologies. Additional issues, such as consistency of the estimation procedure, are considered when appropriate. Various sample problems on which the methods can be applied are referenced throughout the review.

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