Transformed empirical processes and modified Kolmogorov-Smirnov tests for multivariate distributions

Cabaña, Alejandra; Cabaña, Enrique M.

doi:10.1214/aos/1030741078

Cited by 22 publications

(11 citation statements)

References 11 publications

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“…Using a simple partial linear model, we performed Monte Carlo simulations to compare their size and power. We found that neither of the two approaches dominated the other: along a certain direction of alternatives, the martingale transform showed a conspicuously greater power than 1 See Cabaña and Cabaña (1997) for a general class of isometric nonorthogonal projections that encompasses the martingale transform of Khmaladze. 2 Phillips and Sun (2002), in a brief note, considered two detrending methods of semimartingale processes and showed that an efficient detrending is a nonorthogonal projection with respect to the inner product Z 1 , Z 2 = Z 1 (t)Z 2 (t)dt.…”

Section: For Example)mentioning

confidence: 96%

Testing semiparametric conditional moment restrictions using conditional martingale transforms

Song¹

2010

Journal of Econometrics

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Section: For Example)mentioning

confidence: 96%

Testing semiparametric conditional moment restrictions using conditional martingale transforms

Song¹

2010

Journal of Econometrics

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“…Then {ξ i (v, β)} ∞ i=1 , for any v ∈ R + and any β ∈ R p , is a sequence of independently distributed r.v.'s. Finally, Equations (18), (19) and (21) …”

Section: Approximation Of Empirical Df Under Heteroscedasticitymentioning

confidence: 99%

“…Attention was also paid to the problem of large deviations of the K-S statistic [17]. Later, some results of a more general approach via empirical processes (requiring naturally stronger assumptions) started to appear [18][19][20]. We are going to prove an analogous result to Equation (1) for the regression framework for the situation when the error terms are heteroscedastic and a supremum is assumed over the argument of d.f.…”

Section: Introductionmentioning

confidence: 98%

Empirical distribution function under heteroscedasticity

Víšek

2011

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Neglecting heteroscedasticity of error terms may imply the wrong identification of a regression model (see appendix). Employment of (heteroscedasticity resistent) White's estimator of covariance matrix of estimates of regression coefficients may lead to the correct decision about the significance of individual explanatory variables under heteroscedasticity. However, White's estimator of covariance matrix was established for least squares (LS)-regression analysis (in the case when error terms are normally distributed, LSand maximum likelihood (ML)-analysis coincide and hence then White's estimate of covariance matrix is available for ML-regression analysis, too). To establish White's-type estimate for another estimator of regression coefficients requires Bahadur representation of the estimator in question, under heteroscedasticity of error terms. The derivation of Bahadur representation for other (robust) estimators requires some tools. As the key tool proved to be a tight approximation of the empirical distribution function (d.f.) of residuals by the theoretical d.f. of the error terms of the regression model. We need the approximation to be uniform in the argument of d.f. as well as in regression coefficients. The present paper offers this approximation for the situation when the error terms are heteroscedastic.

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“…We mention Strasser (1985), Bickel, Klaassen, Ritov, and Wellner (1993), Cabana and Cabana ( 1997) and Bose, Gangopadhyay, and Goswami (2007). The results are explicitly used in e.g.…”

Section: A Note On Contiguity and Hellinger Distancementioning

confidence: 99%