Goodness-of-fit tests via characterizations. general approach

Morris, K. W.; Szynal, Dominik

doi:10.1007/s10958-013-1339-0

Cited by 2 publications

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“…Other methods are based on skewness and kurtosis, as for instance proposed in [33] (known to lead to inconsistent procedures), the empirical characteristic function, see [13], the Wasserstein distance, see [11,12], the sample entropy, see [44], or correlation and regression tests, as the famous Shapiro-Wilk test, see [40], among others. For a survey of classical existing methods see [11], section 3, and [19], for surveys on goodness-of-fit techniques connected to characterizations of distributions, including the normal, see [29,30,32] and for the problem of testing multivariate normality, we refer to [20,28].…”

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confidence: 99%

Testing normality via a distributional fixed point property in the Stein characterization

Betsch

Ebner

2019

TEST

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We propose two families of tests for the classical goodness-of-fit problem to univariate normality. The new procedures are based on L 2 -distances of the empirical zero-bias transformation to the normal distribution or the empirical distribution of the data, respectively. Weak convergence results are derived under the null hypothesis, under fixed alternatives as well as under contiguous alternatives. Empirical critical values are provided and a comparative finite-sample power study shows the competitiveness to classical procedures. IntroductionTesting normality is commonly known as the most used and discussed goodness-of-fit technique, motivated by the model assumption of normality in classical models. To be specific, let X, X 1 , X 2 , . . . be real valued independent and identically distributed (iid.) random variables.The problem of interest is to test the hypothesisagainst general alternatives. So far, a great variety of goodness-of-fit tests have been proposed and research is of ongoing interest, as witnessed by the recent papers [8, 21, 45] and comparative simulation studies like [35, 46]. Classical procedures in goodness-of-fit methodology as the Kolmogorov-Smirnov and the Cramér-von Mises test approach the testing problem by American Mathematical Society 2010 subject classifications. Primary 62G10 Secondary 60F05

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confidence: 99%

Testing normality via a distributional fixed point property in the Stein characterization

Betsch

Ebner

2019

TEST

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“…Only few of them have been used for construction of goodness-of-fit tests, mainly in the works of Morris and Szynal (see, e.g., [68], [69], [66], [93]), where they essentially used the characterizations based on moments of record values. However, nothing is known about the efficiencies of such tests.…”

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confidence: 99%

Tests based on characterizations, and their efficiencies: a survey

Nikitin

2017

ACUTM

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Abstract. A survey of goodness-of-fit and symmetry tests based on the characterization properties of distributions is presented. This approach became popular in recent years. In most cases the test statistics are functionals of U -empirical processes. The limiting distributions and large deviations of new statistics under the null hypothesis are described. Their local Bahadur efficiency for various parametric alternatives is calculated and compared with each other as well as with diverse previously known tests. We also describe new directions of possible research in this domain.

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Goodness-of-fit tests via characterizations. general approach

Cited by 2 publications

References 5 publications

Testing normality via a distributional fixed point property in the Stein characterization

Testing normality via a distributional fixed point property in the Stein characterization

Tests based on characterizations, and their efficiencies: a survey

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