1. Asymptotic properties of nonlinear estimates in stochastic models with finite design space
- Author
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Luc Pronzato, Laboratoire d'Informatique, Signaux, et Systèmes de Sophia-Antipolis (I3S) / Equipe SYSTEMES, Signal, Images et Systèmes (Laboratoire I3S - SIS), Laboratoire d'Informatique, Signaux, et Systèmes de Sophia Antipolis (I3S), Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Laboratoire d'Informatique, Signaux, et Systèmes de Sophia Antipolis (I3S), and COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)
- Subjects
Statistics and Probability ,Stochastic modelling ,Bernoulli trials ,stochastic regressors ,asymptotic normality ,0211 other engineering and technologies ,Asymptotic distribution ,02 engineering and technology ,01 natural sciences ,010104 statistics & probability ,Probability theory ,[MATH.MATH-ST]Mathematics [math]/Statistics [math.ST] ,Calculus ,Applied mathematics ,0101 mathematics ,MSC 62L05, 62P10 ,Mathematics ,021103 operations research ,Strong consistency ,Estimator ,[STAT.TH]Statistics [stat]/Statistics Theory [stat.TH] ,16. Peace & justice ,sequential design ,Nonlinear system ,Sequential analysis ,strong consistency ,Statistics, Probability and Uncertainty ,Nonlinear regression - Abstract
available online at http://dx.doi.org/10.1016/j.spl.2009.07.025; International audience; Under the condition that the design space is finite, new sufficient conditions for the strong consistency and asymptotic normality of the least-squares estimator in nonlinear stochastic regression models are derived. Similar conditions are obtained for the maximum-likelihood estimator in Bernoulli type experiments. Consequences on the sequential design of experiments are pointed out.
- Published
- 2009
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