Information and Asymptotic Efficiency in Parametric-Nonparametric Models

Begun, Janet M.; Hall, William J.; Huang, Weimin; Wellner, Jon A.

doi:10.1214/aos/1176346151

Cited by 347 publications

(238 citation statements)

References 40 publications

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“…where is the score operator (Begun et al, 1983) for based on the truncation likelihood T = log L T and H is a infinite-dimensional class of direction h from which paths of onedimensional submodels for may approach the true parameter. We use P n to denote the empirical measure, and use P for the probability measures.…”

Section: ·4 Efficiency Considerationsmentioning

confidence: 99%

A maximum pseudo-profile likelihood estimator for the Cox model under length-biased sampling

Huang¹,

Qin²,

Follmann³

2012

Biometrika

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SUMMARYThis paper considers semiparametric estimation of the Cox proportional hazards model for right-censored and length-biased data arising from prevalent sampling. To exploit the special structure of length-biased sampling, we propose a maximum pseudo-profile likelihood estimator, which can handle time-dependent covariates and is consistent under covariate-dependent censoring. Simulation studies show that the proposed estimator is more efficient than its competitors. A data analysis illustrates the methods and theory.

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Section: ·4 Efficiency Considerationsmentioning

confidence: 99%

A maximum pseudo-profile likelihood estimator for the Cox model under length-biased sampling

Huang¹,

Qin²,

Follmann³

2012

Biometrika

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“…Stein (1956), Bickel (1982), and Begun, Hall, Huang, and Wellner (1983)] that a necessary condition for asymptotically fully efficient adaptive estimation to be possible is that the two estimation problems--that of e for known n and that of n for known 8--are, in a sense, asymptotically orthogonal. Since ~(X 1 ; 8) is sufficient with respect to n for known 8 , and T(X 1 ; n, 8 ) contains the information about e locally for known n. assumption (1.16) is indeed an asymptotic orthogonality condition of this kind.…”

Section: Lim ---------------------mentioning

confidence: 99%

“…Stein (1956) and Begun et al (1983) define a class of score functions for n as the class of all limits, in the ordinary sense or in for all n' in the set Hne where In Section 2 we shall provide the proofs of Theorems 1.1 and 1.2.…”

Section: Lim ---------------------mentioning

confidence: 99%

On Estimating a Parameter and Its Score Function

Klaassen

Zwet

2011

Selected Works of Willem Van Zwet

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ABSTRACT:We consider the problem of estimating a real-valued parameter 8 in the presence of an abstract nuisance parameter n, such as an unknown distributional shape. Attention is restricted to the case in which the score functions for 8 and n are orthogonal, so that fully a symptotica lly efficient estimation is not a priori impossible. For fixed sample size, we provide a bound of Cramer-Rao type. The bound dif f ers from the classical one for known n by a term involving the integrated mean square error of an estimator of a multiple of the score function for 8 for the case where 8 is known. This implies that an estimator of 8 can only perform well over a class of shapes n if it is possible to e stimate the score function for 8 accurately over this cl a ss.

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“…As mentioned in Begun, Hall, Huang, and Wellner (1983), v * f corresponds to a worst possible direction of approach to ¡ η 0 , f x|x * , f x * |z ¢ for the problem of estimating b 0 . In the language of Stein (1956), v * f yields the most difficult one-dimensional sub-problem.…”

Section: Asymptotic Normalitymentioning

confidence: 99%

Identification and estimation of nonclassical nonlinear errors-in-variables models with continuous distributions using instruments

Schennach

2006

Working Paper Series

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Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in AbstractWhile the literature on nonclassical measurement error traditionally relies on the availability of an auxiliary dataset containing correctly measured observations, we establish that the availability of instruments enables the identification of a large class of nonclassical nonlinear errors-in-variables models with continuously distributed variables. Our main identifying assumption is that, conditional on the value of the true regressors, some "measure of location" of the distribution of the measurement error (e.g. its mean, mode or median) is equal to zero. The proposed approach relies on the eigenvalue-eigenfunction decomposition of an integral operator associated with specific joint probability densities. The main identifying assumption is used to "order" the eigenfunctions so that the decomposition is unique. We propose a convenient sievebased estimator, derive its asymptotic properties and investigate its finite-sample behavior through Monte Carlo simulations. An example of application to the relationship between earnings and divorce rates is also provided.

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Information and Asymptotic Efficiency in Parametric-Nonparametric Models

Cited by 347 publications

References 40 publications

A maximum pseudo-profile likelihood estimator for the Cox model under length-biased sampling

A maximum pseudo-profile likelihood estimator for the Cox model under length-biased sampling

On Estimating a Parameter and Its Score Function

Identification and estimation of nonclassical nonlinear errors-in-variables models with continuous distributions using instruments

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