Geodesic
Asymptotic confidence interval for a discontinuity point of a probability density function
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 24 (2018) no. 2, pp. 194-199 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider the problem of interval estimation of an unknown parameter $\theta\in\Theta\subset R$ of a distribution density $f(x,\theta)$ (with respect to the Lebesgue measure) for a sample $X_1,\dots,X_n$ of large size. It is assumed that the density has a discontinuity of the first kind at the point $x=\theta$. We construct a confidence interval based on a known maximum likelihood estimator $\theta_n^*$ and the distribution function $G(x,\theta)$ found by the authors earlier, which is the limit of the sequence of distribution functions of normalized maximum likelihood estimators\linebreak $n(\theta_n^*-\theta)$. It is proved that the resulting confidence interval is asymptotically exact. We also describe a method for the “fast” calculation of maximum likelihood estimators for a discontinuity point of a density.
Keywords: estimation of a discontinuity point of a probability density, maximum likelihood estimators, asymptotic confidence interval, limiting distributions of statistical estimators. 
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V. E. Mosyagin; N. A. Shvemler. Asymptotic confidence interval for a discontinuity point of a probability density function. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 24 (2018) no. 2, pp. 194-199. http://geodesic.mathdoc.fr/item/TIMM_2018_24_2_a17/

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