The Asymptotic Inadmissibility of the Sample Distribution Function

Read, Robert R.

doi:10.1214/aoms/1177692704

Cited by 27 publications

(11 citation statements)

References 3 publications

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“…For example, see Read (1972) for an estimator based on linear interpolation and Azzalini (1981) for the case of kernel estimators.…”

Section: Some Basic Resultsmentioning

confidence: 99%

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On estimating distribution functions using Bernstein polynomials

Leblanc

2011

Ann Inst Stat Math

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It is a known fact that some estimators of smooth distribution functions can outperform the empirical distribution function in terms of asymptotic (integrated) mean-squared error. In this paper, we show that this is also true of Bernstein polynomial estimators of distribution functions associated with densities that are supported on a closed interval. Specifically, we introduce a higher order expansion for the asymptotic (integrated) mean-squared error of Bernstein estimators of distribution functions and examine the relative deficiency of the empirical distribution function with respect to these estimators. Finally, we also establish the (pointwise) asymptotic normality of these estimators and show that they have highly advantageous boundary properties, including the absence of boundary bias.

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“…For example, see Read (1972) for an estimator based on linear interpolation and Azzalini (1981) for the case of kernel estimators.…”

Section: Some Basic Resultsmentioning

confidence: 99%

“…Similarly, Read (1972) was the first to exhibit a continuous estimator of smooth distribution functions that dominates the empirical estimator F n in terms of MSE. Note that both of these authors did not discuss deficiency in their work.…”

Section: Corollarymentioning

confidence: 99%

On estimating distribution functions using Bernstein polynomials

Leblanc

2011

Ann Inst Stat Math

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“…Until now, and as far as we can judge, comparison of these simple estimators with the classical edf has not been studied deeply. To our knowledge, the single reference is Read (1972) where a continuous estimator of F , namely joining the points (X * i , i n+1 ), with X * 1 , . .…”

Section: Introductionmentioning

confidence: 99%

Polygonal smoothing of the empirical distribution function

Blanke

Bosq

2018

Stat Inference Stoch Process

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We present two families of polygonal estimators of the distribution function: the first family is based on the knowledge of the support while the second addresses the case of an unknown support. Polygonal smoothing is a simple and natural method for regularizing the empirical distribution function Fn but its properties have not been studied deeply. First, consistency and exponential type inequalities are derived from well-known convergence properties of Fn. Then, we study their mean integrated squared error (MISE) and we establish that polygonal estimators may improve the MISE of Fn. We conclude by some numerical results to compare these estimators globally, and also together with the integrated kernel distribution estimator.

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“…For instance, Dvoretzky et al (1956) studied the asymptotical minimaxity property of the best invariant estimator for some loss function; and Read (1972) considered the asymptotical admissibility property of the best invariant estimator. However, this method does not describe the decision theoretic properties when the sample size n is finite.…”

Section: L(f A) = F(f(t) -A(t))2h(f(t))df(t) mentioning

confidence: 99%

Methodology for the invariant estimation of a continuous distribution function

1989

Ann Inst Stat Math

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The Asymptotic Inadmissibility of the Sample Distribution Function

Cited by 27 publications

References 3 publications

On estimating distribution functions using Bernstein polynomials

On estimating distribution functions using Bernstein polynomials

Polygonal smoothing of the empirical distribution function

Methodology for the invariant estimation of a continuous distribution function

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