A one-sample test for normality with kernel methods

Kellner, Jérémie; Célisse, Alain

doi:10.3150/18-bej1037

Cited by 18 publications

(20 citation statements)

References 28 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Our paper fills an important gap in the literature by proposing the first set of kernel-based composite hypothesis tests applicable to a wide range of parametric models. These are in contrast to previously introduced composite tests which are limited to very specific parametric families (Kellner et al 2019;Fernandez et al 2020). To devise these new tests, we make use of recently developed minimum distance estimators based on the KSD (Barp et al 2019).…”

Section: Introductionmentioning

confidence: 87%

Composite Goodness-of-fit Tests with Kernels

Key¹,

Fernández²,

Gretton³

et al. 2021

Preprint

View full text Add to dashboard Cite

Model misspecification can create significant challenges for the implementation of probabilistic models, and this has led to development of a range of inference methods which directly account for the issue. However, these method tend to lose efficiency and should only be used when the model is really misspecified. Unfortunately, there is a lack of generally applicable methods to test whether this is the case or not. One set of tools which can help are goodness-of-fit tests, which can test whether a dataset has been generated from a fixed distribution. Kernel-based tests have been developed to for this problem, and these are popular due to their flexibility, strong theoretical guarantees and ease of implementation in a wide range of scenarios. In this paper, we extend this line of work to the more challenging composite goodness-of-fit problem, where we are instead interested in whether the data comes from any distribution in some parametric family.

show abstract

Section: Introductionmentioning

confidence: 87%

Composite Goodness-of-fit Tests with Kernels

Key¹,

Fernández²,

Gretton³

et al. 2021

Preprint

View full text Add to dashboard Cite

show abstract

“…Here we assume μ 1 = 1, σ 1 = 1 and σ 2 = 1 and analyze the power of the test by changing the μ 2 parameter. As it is explained in the Appendix, there is one to one correspondence between the μ 2 parameter and the excess kurtosis of the mixed Gaussian distribution (see formula (16)). Therefore, in Fig 8 we present the power of the test with respect to the excess kurtosis and compare it with the power of the common tests for normality.…”

Section: Plos Onementioning

confidence: 94%

“…There have been also attempts in the literature to provide a one-sample statistical test of normality for data in a broader setting like in a general Hilbert space [16]. Despite this verity, there have been continuing efforts to develop tests for the departure of a random sample from normality that could be considered omnibus, [17,18,19,20,21,22], that is, to be able to reject the null hypothesis of normality with high power for a wide range of alternatives.…”

Section: Introductionmentioning

confidence: 99%

Omnibus test for normality based on the Edgeworth expansion

Wyłomańska

Iskander²,

Burnecki

2020

PLoS ONE

View full text Add to dashboard Cite

Statistical inference in the form of hypothesis tests and confidence intervals often assumes that the underlying distribution is normal. Similarly, many signal processing techniques rely on the assumption that a stationary time series is normal. As a result, a number of tests have been proposed in the literature for detecting departures from normality. In this article we develop a novel approach to the problem of testing normality by constructing a statistical test based on the Edgeworth expansion, which approximates a probability distribution in terms of its cumulants. By modifying one term of the expansion, we define a test statistic which includes information on the first four moments. We perform a comparison of the proposed test with existing tests for normality by analyzing different platykurtic and leptokurtic distributions including generalized Gaussian, mixed Gaussian, α-stable and Student's t distributions. We show for some considered sample sizes that the proposed test is superior in terms of power for the platykurtic distributions whereas for the leptokurtic ones it is close to the best tests like those of D'Agostino-Pearson, Jarque-Bera and Shapiro-Wilk. Finally, we study two real data examples which illustrate the efficacy of the proposed test.

show abstract

“…For a survey of classical methods see del Barrio et al (2000), section 3, and Henze (1994), and for comparative simulation studies, see Baringhaus et al (1989); Farrell and Rogers-Stewart (2006); Landry and Lepage (1992); Pearson et al (1977); Romão et al (2010); Shapiro et al (1968); Yap and Sim (2011). For a survey on tests of multivariate normality see Henze (2002), for recent multivariate tests see , and for new developments on normality tests for Hilbert space valued random elements, see Henze and Jiménez-Gamero (2021); Kellner and Celisse (2019).…”

Section: Introductionmentioning

confidence: 99%

On combining the zero bias transform and the empirical characteristic function to test normality

Ebner¹

2021

ALEA

View full text Add to dashboard Cite

We propose a new powerful family of tests of univariate normality. These tests are based on an initial value problem in the space of characteristic functions originating from the fixed point property of the normal distribution in the zero bias transform. Limit distributions of the test statistics are provided under the null hypothesis, as well as under contiguous and fixed alternatives. Using the covariance structure of the limiting Gaussian process from the null distribution, we derive explicit formulas for the first four cumulants of the limiting random element and apply the results by fitting a distribution from the Pearson system. A comparative Monte Carlo power study shows that the new tests are serious competitors to the strongest well established tests.

show abstract

A one-sample test for normality with kernel methods

Cited by 18 publications

References 28 publications

Composite Goodness-of-fit Tests with Kernels

Composite Goodness-of-fit Tests with Kernels

Omnibus test for normality based on the Edgeworth expansion

On combining the zero bias transform and the empirical characteristic function to test normality

Contact Info

Product

Resources

About