The Cramer-Smirnov Test in the Parametric Case
TLDR
In this paper, the authors extended the Cramer-Smirnov and von Mises test to the parametric case, a suggestion of Cramer [1], see also [2].Abstract:
The "goodness of fit" problem, consisting of comparing the empirical and hypothetical cumulative distribution functions (cdf's), is treated here for the case when an auxiliary parameter is to be estimated. This extends the Cramer-Smirnov and von Mises test to the parametric case, a suggestion of Cramer [1], see also [2]. The characteristic function of the limiting distribution of the test function is found by consideration of a Guassian stochastic process.read more
Citations
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The integral of a symmetric unimodal function over a symmetric convex set and some probability inequalities
Reliability Analysis for Complex, Repairable Systems
TL;DR: In this paper, the authors consider the theoretical and practical implications of the nonhomogeneous Poisson process model for reliability, and give estimation, hypotheses testing, comparison and goodness of fit procedures when the process has a Weilbull intensity function.
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Inference on the Quantile Regression Process
Roger Koenker,Zhijie Xiao +1 more
TL;DR: In this paper, the authors consider an approach to the Durbin problem involving a martingale transformation of the parametric empirical process suggested by Khmaladze (1981) and show that it can be adapted to a wide variety of inference problems involving the quantile regression process.
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Goodness-of-Fit Tests for the Generalized Pareto Distribution
TL;DR: Tests of fit are given for the generalized Pareto distribution (GPD) based on Cramér–von Mises statistics; in general, the GPD provides an adequate fit.
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K-Sample Analogues of the Kolmogorov-Smirnov and Cramer-V. Mises Tests
TL;DR: The main purpose of as discussed by the authors is to obtain the limiting distribution of certain statistics described in the title, which is useful for testing the homogeneity hypothesis $H_1$ that random samples of real random variables have the same continuous probability law.
References
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Book
A Course of Modern Analysis
TL;DR: The volume now gives a somewhat exhaustive account of the various ramifications of the subject, which are set out in an attractive manner and should become indispensable, not only as a textbook for advanced students, but as a work of reference to those whose aim is to extend the knowledge of analysis.
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Asymptotic Theory of Certain "Goodness of Fit" Criteria Based on Stochastic Processes
TL;DR: In this article, 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.
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The $\chi^2$ Test of Goodness of Fit
TL;DR: The chi square test of goodness of fit as discussed by the authors is intended for the student and user of statistical theory rather than for the expert, and it has been used extensively in the application of the test.
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On the composition of elementary errors
TL;DR: In this paper, the authors define a variable V(t) the probability function of a quantity z, which may assume certain real values with certain probabilistic properties, and call V t the probability of z having exactly the value t.
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Heuristic Approach to the Kolmogorov-Smirnov Theorems
TL;DR: In this article, the authors present a heuristic reasoning approach to prove the existence of limiting distributions for large samples of various measures of the discrepancy between empirical and true distribution functions, which are then used for the numerical evaluation of these limiting distributions.