The Limiting Log-Likelihood Process for Discontinuous Multiparameter Density Families

Georg Ch. Pflug
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Georg Ch. Pflug: University of Vienna, Institute of Statistics

A chapter in Probability and Statistical Inference, 1982, pp 287-295 from Springer

Abstract: Abstract Let $${\{ f(\theta ,x)\} _{\theta \in \Theta }}$$ be a family of probability densities on a measure space (X,A,μ) with multidimensional parameter $$\theta \in \Theta \subseteq {\mathbb{R}^k}$$ . Let $${\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{X} _n} = ({X_1}, \ldots ,{X_n})$$ be a i. i. d. sample in Xn, distributed according to f(θ,.). We study the asymptotic distribution of the log-likelihood process $${Y_n}(t) = \sum\limits_{i = 1}^n {\log } \frac{{f(\theta + t.1/n,{X_i})}}{{f(\theta ,{X_i})}}{\text{ }}t \in {\mathbb{R}^k}$$ under the special assumption, that the densities have — as function of θ — discontinuities of the first kind.

Keywords: Asymptotic Distribution; Special Assumption; Discontinuous Density; Multidimensional Parameter; Density Family (search for similar items in EconPapers)
Date: 1982
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-009-7840-9_27

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DOI: 10.1007/978-94-009-7840-9_27

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