на главную поиск contacts

Asymptotic Theory of Certain "Goodness of Fit" Criteria Based on Stochastic Processes

Опубликовано на портале: 31-03-2004
Annals of Mathematical Statistics. 1952.  Vol. 23. No. 2. P. 193-212. 
Тематический раздел:
The statistical problem treated is that of testing the hypothesis that $n$ independent, identically distributed random variables have a specified continuous distribution function F(x). If F_n(x) is the empirical cumulative distribution function and \psi(t) is some nonnegative weight function (0 \leqq t \leqq 1), we consider n^{\frac{1}{2}} \sup_{-\infty and n\int^\infty_{-\infty}\lbrack F(x) - F_n(x) \rbrack^2 \psi\lbrack F(x)\rbrack dF(x). A general method for calculating the limiting distributions of these criteria is developed by reducing them to corresponding problems in stochastic processes, which in turn lead to more or less classical eigenvalue and boundary value problems for special classes of differential equations. For certain weight functions including \psi = 1 and \psi = 1/\lbrack t(1 - t) \rbrack we give explicit limiting distributions. A table of the asymptotic distribution of the von Mises \omega^2 criterion is given.

текст статьи в формате pdf на сайте JSTORE:
Ключевые слова

См. также:
Sandor Csorgo, Julian Faraway
Journal of the Royal Statistical Society. Series B (Methodological). 1996.  Vol. 58. No. 1.
Александр Дмитриевич Смирнов
Экономический журнал ВШЭ. 2000.  Т. 4. № 2. С. 157-183. 
David J. Hand
Journal of the Royal Statistical Society. Series A (Statistics in Society). 1996.  Vol. 159. No. 3. P. 445-492. 
Александр Дмитриевич Смирнов
Экономический журнал ВШЭ. 1998.  Т. 2. № 1. С. 3-30. 
Ernst R. Berndt, David O. Wood
Review of Economics and Statistics. 1975.  Vol. 57. No. 3. P. 259-268.