Transformations of the empirical measure and Kolmogorov-Smirnov tests
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چکیده
منابع مشابه
A The Power of Alternative Kolmogorov-Smirnov Tests Based on Transformations of the Data
The Kolmogorov-Smirnov (KS) statistical test is commonly used to determine if data can be regarded as a sample from a sequence of i.i.d. random variables with specified continuous cdf F , but with small samples it can have insufficient power, i.e., its probability of rejecting natural alternatives can be too low. However, Durbin [1961] showed that the power of the KS test often can be increased...
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A test for goodness of fit usually involves examining a random sample from some unknown distribution in order to test the null hypothesis that the unknown distribution function is in fact a known, specified function. The Chi-square test can be applied to any univariate distribution for which you can calculate the cumulative distribution function. The Chi-square test does not have good propertie...
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15 صفحه اولSmall Improvement to the Kolmogorov-Smirnov Test
The Kolmogorov-Smirnov (K-S) test is widely used as a goodness-of-fit test. This thesis consists of two parts to describe ways to improve the classical K-S test in both 1-dimensional and 2-dimensional data. The first part is about how to improve the accuracy of the classical K-S goodness-of-fit test in 1-dimensional data. We replace the p-values estimated by the asymptotic distribution with nea...
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1 Some Basic Theory 1 1.1 Consistency and Unbiasedness at a Point . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 The Kolmogorov–Smirnov Statistic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.3 Order Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.4 Proof of the Kolmogorov–Smirnov Theorem . . ....
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ژورنال
عنوان ژورنال: The Annals of Statistics
سال: 1996
ISSN: 0090-5364
DOI: 10.1214/aos/1069362307