Non‐parametric Estimation of the Residual Distribution

Akritas, Michaël G.; Keilegom, Ingrid Van

doi:10.1111/1467-9469.00254

Cited by 168 publications

(173 citation statements)

References 15 publications

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“…1 ii) the ability to nonparametrically estimate the error distribution at a √ n-rate (Akritas & Van Keilegom 2001, Escanciano & Jacho-Chávez 2012, and iii) more efficient estimation of the conditional distribution of Y given X than its unstructured counterpart.…”

Section: Methodsmentioning

confidence: 99%

“…Akritas & Van Keilegom (2001) and Li & Racine (forthcoming)), particularly in Econometrics, it might be too strong, hence a testing procedure having high power is particularly appealing.…”

Section: Methodsmentioning

confidence: 99%

“…A variety of tests have been proposed for assessing the appropriateness of the location-scale assumption that is often invoked in applied settings; see by way of illustration Akritas & Van Keilegom (2001) and Li & Racine (forthcoming), who adopt the location-scale framework, see Einmahl & Van Keilegom (2008), Birke, Neumeyer & Volgushev (2017) and Neumeyer, Noh & Van Keilegom (2016) for various approaches that have been proposed to test the location-scale assumption in a range of settings, and see Neumeyer (2009) for a bootstrap procedure for the error distribution in these models. These approaches employ test statistics that are based on conditional mean models, in particular, the difference between the joint distribution of the predictor and error and the product of the marginal distributions of the predictor and error, and include the KolmogorovSmirnov (Kolmogorov 1933, Smirnov 1948), Cramér-von-Mises (Cramér 1928, von Mises 1928 and Anderson-Darling (Anderson & Darling 1952) statistics, among others.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A Smooth Nonparametric, Multivariate, Mixed-Data Location-Scale Test

Racine¹,

Keilegom

2017

SSRN Journal

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A number of tests have been proposed for assessing the location-scale assumption that is often invoked by practitioners. Existing approaches include Kolmogorov-Smirnov and Cramér-von-Mises statistics that each involve measures of divergence between unknown joint distribution functions and products of marginal distributions. In practice, the unknown distribution functions embedded in these statistics are approximated using non-smooth empirical distribution functions. We demonstrate how replacing the non-smooth distributions with their kernel-smoothed counter-parts can lead to substantial power improvements. In so doing we extend existing approaches to the smooth multivariate and mixed continuous and discrete data setting thereby extending the reach of existing approaches. Theoretical underpinnings are provided, Monte Carlo simulations are undertaken to assess finite-sample performance, and illustrative applications are provided. I N S T I T U T D E S T A T I S T I Q U E B I O S T A T I S T I Q U E E T S C I E N C E S A C T U A R I E L L E S ( I S B INGRID VAN KEILEGOMORSTAT, KU Leuven, Naamsestraat 69, B-3000 Leuven, Belgium.Abstract. A number of tests have been proposed for assessing the location-scale assumption that is often invoked by practitioners. Existing approaches include Kolmogorov-Smirnov and Cramér-von-Mises statistics that each involve measures of divergence between unknown joint distribution functions and products of marginal distributions. In practice, the unknown distribution functions embedded in these statistics are approximated using non-smooth empirical distribution functions. We demonstrate how replacing the non-smooth distributions with their kernel-smoothed counterparts can lead to substantial power improvements. In so doing we extend existing approaches to the smooth multivariate and mixed continuous and discrete data setting thereby extending the reach of existing approaches. Theoretical underpinnings are provided, Monte Carlo simulations are undertaken to assess finite-sample performance, and illustrative applications are provided.

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Section: Methodsmentioning

confidence: 99%

“…Akritas & Van Keilegom (2001) and Li & Racine (forthcoming)), particularly in Econometrics, it might be too strong, hence a testing procedure having high power is particularly appealing.…”

Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A Smooth Nonparametric, Multivariate, Mixed-Data Location-Scale Test

Racine¹,

Keilegom

2017

SSRN Journal

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“…For kernel regression estimators corresponding results can be found in Mack and Silverman (1982), see also Einmahl and Mason (2000). Rates of uniform almost sure convergence for variance function estimators in nonparametric regression models are a by-product of Akritas and Van Keilegom (2001). Further, there is a vast literature about uniform consistency of wavelet estimators for densities and regression functions based on iid or time series or censored data, respectively, see, e. g., Masry (1997), Massiani (2003), Zhang, Sha and Cheng (1999) or Xue (2002).…”

Section: Monotone Modifications Of Function Estimatorsmentioning

confidence: 99%

A note on uniform consistency of monotone function estimators

Neumeyer

2007

Statistics & Probability Letters

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Recently, Dette, Neumeyer and Pilz (2005a) proposed a new monotone estimator for strictly increasing nonparametric regression functions and proved asymptotic normality. We explain two modifications of their method that can be used to obtain monotone versions of any nonparametric function estimators, for instance estimators of densities, variance functions or hazard rates. The method is appealing to practitioners because they can use their favorite method of function estimation (kernel smoothing, wavelets, orthogonal series,. . . ) and obtain a monotone estimator that inherits desirable properties of the original estimator. In particular, we show that both monotone estimators share the same rates of uniform convergence (almost sure or in probability) as the original estimator.MSC 2000: 62G05

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“…Efromovich (2005) proposed an adaptive estimator of the error density, based on a density estimator proposed by Pinsker (1980). Finally, Samb (2010) also considered the estimation of the error density, but his approach is more closely related to the one in Akritas and Van Keilegom (2001).…”

Section: Introductionmentioning

confidence: 99%

Estimation of the error density in a semiparametric transformation model

et al. 2014

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Consider the semiparametric transformation model Λ θo (Y ) = m(X) + ε, where θo is an unknown finite dimensional parameter, the functions Λ θo and m are smooth, ε is independent of X, and E(ε) = 0.We propose a kernel-type estimator of the density of the error ε, and prove its asymptotic normality. The estimated errors, which lie at the basis of this estimator, are obtained from a profile likelihood estimator of θo and a nonparametric kernel estimator of m. The practical performance of the proposed density estimator is evaluated in a simulation study.

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Non‐parametric Estimation of the Residual Distribution

Cited by 168 publications

References 15 publications

A Smooth Nonparametric, Multivariate, Mixed-Data Location-Scale Test

A Smooth Nonparametric, Multivariate, Mixed-Data Location-Scale Test

A note on uniform consistency of monotone function estimators

Estimation of the error density in a semiparametric transformation model

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