Testing for normal errors in designs with many blocks

Meester, S. G.; Lockhart, Richard

doi:10.1093/biomet/75.3.569

Cited by 6 publications

(4 citation statements)

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“…Consequently, statistics based on the sample process of residuals have the same asymptotic null distribution as in the location-scale model. Related findings were obtained independently by Loynes (1980) and Mukantseva (1977); see also Meester and Lockhart (1988) for a discussion of the case of designs with many blocks. These conclusions are based on finite dimensional asymptotics.…”

supporting

confidence: 67%

Simulation‐based finite sample normality tests in linear regressions

Dufour

Farhat

Gardiol

et al. 1998

The Econometrics Journal

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In the literature on tests of normality, much concern has been expressed over the problems associated with residual‐based procedures. Indeed, the specialized tables of critical points which are needed to perform the tests have been derived for the location‐scale model; hence, reliance on available significance points in the context of regression models may cause size distortions. We propose a general solution to the problem of controlling the size of normality tests for the disturbances of standard linear regressions, which is based on using the technique of Monte Carlo tests. We study procedures based on 11 well‐known test statistics: the Kolmogorov–Smirnov, Anderson–Darling, Cramér–von Mises, Shapiro–Wilk, Jarque–Bera and D’Agostino criteria. Evidence from a simulation study is reported showing that the usual critical values lead to severe size problems (over‐rejections or under‐rejections). In contrast, we show that Monte Carlo tests achieve perfect size control for any design matrix and have good power.

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confidence: 67%

Simulation‐based finite sample normality tests in linear regressions

Dufour

Farhat

Gardiol

et al. 1998

The Econometrics Journal

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“…This problem can sometimes be corrected by consideration of the process n −1/2 1 w i εi ≤ t − t using the exact probability integral transform; Meester and Lockhart (1988) for example, give weak convergence results for this process for highly structured designs with p/n → c ∈ 0 1 . This prompts us to consider a slightly more general empirical process,…”

Section: Counterexamplesmentioning

confidence: 99%

Weak convergence of the empirical process of residuals in linear models with many parameters

Chen¹,

Lockhart²

2001

Ann. Statist.

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When fitting, by least squares, a linear model (with an intercept term) with p parameters to n data points, the asymptotic behavior of the residual empirical process is shown to be the same as in the single sample problem provided p 3 log 2 p /n → 0 for any error density having finite variance and a bounded first derivative. No further conditions are imposed on the sequence of design matrices. The result is extended to more general estimates with the property that the average error and average squared error in the fitted values are on the same order as for least squares.

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“…Residuals are used instead of the non-observable errors terms to construct empirical distribution functions for goodness-of-fit tests, prediction intervals, and so on. Empirical processes built from residuals received considerable attention lately; see for example Loynes (1980), Shorack (1984), Meester and Lockhart (1988), Koul and Ossiander (1994), Koul (1996), Kulperger (1996) and Mammen (1996).…”

Section: Introductionmentioning

confidence: 99%

Empirical processes based on pseudo-observations II: The multivariate case

Ghoudi¹,

Rémillard²

2004

Asymptotic Methods in Stochastics

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One often needs to estimate the distribution functions of a random vector E = H(X), where the H is unknown and might depend on the law of X . When H is estimated by some H,, using a sample XI,. . . , X,, the H,,(X,)'s are termed pseudeobservations. In a semiparametric context, one often wants to estimate parameters related to the law of the non-observable E . The transformed data Hn(X1), . . ., Hn(Xn) are then naturally used, introducing dependence. Classical techniques do not apply and hard work is needed to get the asymptotic behaviour of estimators and empirical processes.The aim of this paper is to give a unified treatment of inference procedures based on pseudeobservations in the multivariate setting. Exaniples of applications are given.

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Testing for normal errors in designs with many blocks

Cited by 6 publications

References 0 publications

Simulation‐based finite sample normality tests in linear regressions

Simulation‐based finite sample normality tests in linear regressions

Weak convergence of the empirical process of residuals in linear models with many parameters

Empirical processes based on pseudo-observations II: The multivariate case

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