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Minimum contrast estimators on sieves: Exponential bounds and rates of convergence. (English) Zbl 0954.62033
The paper is dedicated to Lucien Le Cam for his seventieth birthday. The authors develop further the theory of minimum contrast estimators elaborated in their work, Probab. Theory Relat. Fields 97, No. 1-2, 113-150 (1993; Zbl 0805.62037). They derived an upper bound for a mean quadratic loss for minimum contrast estimators on sieves that include maximum likelihood estimators for densities and least-squares estimators for regression. They gathered, in a section, useful information on linear and nonlinear sieves.
Reviewer: M.Huškova (Praha)

MSC:
62G05 Nonparametric estimation
62G20 Asymptotic properties of nonparametric inference
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