共查询到20条相似文献,搜索用时 15 毫秒
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We show that there is an intimate connection between the theory of nonparametric (smoothed) maximum likelihood estimators for certain inverse problems and integral equations. This is illustrated by estimators for interval censoring and deconvolution problems. We also discuss the asymptotic efficiency of the MLE for smooth functionals in these models. 相似文献
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Stefan Sperlich 《Journal of the Korean Statistical Society》2009,38(2):111-113
This is a discussion of the paper “Nonparametric estimation of noisy integral equations of the second kind” by Enno Mammen and Kyusang Yu. 相似文献
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In this overview we will show that many statistical estimation problems can be considered as empirical solutions of noisy integral equations of the second kind. We illustrate this by giving a series of examples and we will discuss a general nonparametric approach based on plugging-in nonparametric estimates of the integral kernel and of the intercept of the integral equation. 相似文献
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Nonparametric likelihood and doubly robust estimating equations for marginal and nested structural models 总被引:1,自引:0,他引:1
Zhiqiang Tan 《Revue canadienne de statistique》2010,38(4):609-632
This article considers Robins's marginal and nested structural models in the cross‐sectional setting and develops likelihood and regression estimators. First, a nonparametric likelihood method is proposed by retaining a finite subset of all inherent and modelling constraints on the joint distributions of potential outcomes and covariates under a correctly specified propensity score model. A profile likelihood is derived by maximizing the nonparametric likelihood over these joint distributions subject to the retained constraints. The maximum likelihood estimator is intrinsically efficient based on the retained constraints and weakly locally efficient. Second, two regression estimators, named hat and tilde, are derived as first‐order approximations to the likelihood estimator under the propensity score model. The tilde regression estimator is intrinsically and weakly locally efficient and doubly robust. The methods are illustrated by data analysis for an observational study on right heart catheterization. The Canadian Journal of Statistics 38: 609–632; 2010 © 2010 Statistical Society of Canada 相似文献
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The receiver operating characteristic (ROC) curve is a graphical representation of the relationship between false positive and true positive rates. It is a widely used statistical tool for describing the accuracy of a diagnostic test. In this paper we propose a new nonparametric ROC curve estimator based on the smoothed empirical distribution functions. We prove its strong consistency and perform a simulation study to compare it with some other popular nonparametric estimators of the ROC curve. We also apply the proposed method to a real data set. 相似文献
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Peter C. Smith 《Journal of the Royal Statistical Society. Series A, (Statistics in Society)》2002,165(3):405-434
Summary. The single-input case of the 'technical efficiency' theory of M. J. Farrell is reformulated geometrically and algebraically. Its linear programming developments as 'data envelopment analysis' are critically reviewed, as are the related techniques of 'stochastic frontier analysis'. The sense and realism of using data envelopment analysis or stochastic frontier analysis techniques, rather than some value-based method, for the assessment of police force efficiency are questioned with reference to the Spottiswoode report and related studies. 相似文献
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Shota Takeishi 《Scandinavian Journal of Statistics》2023,50(3):1503-1531
The change-plane Cox model is a popular tool for the subgroup analysis of survival data. Despite the rich literature on this model, there has been limited investigation into the asymptotic properties of the estimators of the finite-dimensional parameter. Particularly, the convergence rate, not to mention the asymptotic distribution, has not been fully characterized for the general model where classification is based on multiple covariates. To bridge this theoretical gap, this study proposes a maximum smoothed partial likelihood estimator and establishes the following asymptotic properties. First, it shows that the convergence rate for the classification parameter can be arbitrarily close to up to a logarithmic factor under a certain condition on covariates and the choice of tuning parameter. Given this convergence rate result, it also establishes the asymptotic normality for the regression parameter. 相似文献
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Statistics and Computing - 相似文献
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Nonparametric maximum likelihood estimation of population size based on the counting distribution 总被引:1,自引:0,他引:1
Dankmar Böhning Dieter Schön 《Journal of the Royal Statistical Society. Series C, Applied statistics》2005,54(4):721-737
Summary. The paper discusses the estimation of an unknown population size n . Suppose that an identification mechanism can identify n obs cases. The Horvitz–Thompson estimator of n adjusts this number by the inverse of 1− p 0 , where the latter is the probability of not identifying a case. When repeated counts of identifying the same case are available, we can use the counting distribution for estimating p 0 to solve the problem. Frequently, the Poisson distribution is used and, more recently, mixtures of Poisson distributions. Maximum likelihood estimation is discussed by means of the EM algorithm. For truncated Poisson mixtures, a nested EM algorithm is suggested and illustrated for several application cases. The algorithmic principles are used to show an inequality, stating that the Horvitz–Thompson estimator of n by using the mixed Poisson model is always at least as large as the estimator by using a homogeneous Poisson model. In turn, if the homogeneous Poisson model is misspecified it will, potentially strongly, underestimate the true population size. Examples from various areas illustrate this finding. 相似文献
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Vasant P. Bhapkar 《统计学通讯:理论与方法》2013,42(4):945-952
A counter-example shows that the proof of optimality of the marginal likelihood estimating function for parameter of interest, under the conditions assumed in Lloyd (1987), contains a gap and is, thus, invalid. The same comment applies to the generalized version of Lloyd’s Theorem given by Bhapkar and Srinivasan (1993). In the light of known results concerning Fisher information for parameter of interest and partial sufficiency of a suitable statistic, the counter-example reveals a similar gap in the proof of corollary 3.2 of Bhapkar (1991). 相似文献
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Min Xie 《统计学通讯:模拟与计算》2013,42(1):281-293
A simple method (here called the RS-method) established for solving renewal-type integral equations based on direct numerical Riemann-Stieltjes integration is presented and evaluated. In almost all situations it has shown surprisingly good results in terms of simplicity, convergence and applicability compared with the other known methods. The RS-method is particularly useful when the probability density function has singularities. 相似文献
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Christian P. Robert Xiao-Li Meng Jesper Møller Jeffrey S Rosenthal C Jennison M. A Hurn F Al-Awadhi Peter McCullagh Christophe Andrieu Arnaud Doucet Petros Dellaportas Ioulia Papageorgiou Ricardo S Ehlers Elena A Erosheva Stephen E Fienberg Jonathan J Forster Roger C Gill Nial Friel Peter Green David Hastie R King Hans R Künsch N. A. Lazar C Osinski 《Journal of the Royal Statistical Society. Series B, Statistical methodology》2003,65(1):39-55