A Receiver Operating Characteristic (ROC) curve reflects the performance of a system which decides between two competing actions in a test of statistical hypotheses. This paper addresses the inference on ROC curves fo...
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A Receiver Operating Characteristic (ROC) curve reflects the performance of a system which decides between two competing actions in a test of statistical hypotheses. This paper addresses the inference on ROC curves for the following problem: How can one statistically validate the performance of a system with a claimed ROC curve, ROC0 say? Our proposed solution consists of two main components: first, a flexible family of distributions, namely the multivariate binormal mixtures, is proposed to account for intra-sample correlation and non-Gaussianity of the marginal distributions under both the null and alternative hypotheses. Second, a semi-parametric inferential framework is developed for estimating all unknown parameters based on a rank likelihood. Actual inference is carried out by running a Gibbs sampler until convergence, and subsequently, constructing a highest posterior density (HPD) set for the true but unknown ROC curve based on the Gibbs output. The proposed methodology is illustrated on several simulation studies and real data. (C) 2011 The Korean Statistical Society. Published by Elsevier B.V. All rights reserved.
We investigate semi-parametric small area inference in generalized semi-varying coefficient mixed effects models with application to longitudinal data. Combining the generalized profiled likelihood approaches for mixe...
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We investigate semi-parametric small area inference in generalized semi-varying coefficient mixed effects models with application to longitudinal data. Combining the generalized profiled likelihood approaches for mixed effect models with kernel methods, we not only construct semi-parametric small area estimators, but also propose two test statistics for discriminating between a parametric mixed effects model and a generalized semi-varying coefficient mixed effects model. The critical values are estimated by a bootstrap procedure. The asymptotic theory for the methods is provided. Simulations exhibit the finite-sample performance for the proposed estimators and test statistics. These verify the feasibility and the excellent behavior of the methods for moderate sample sizes.
The receiver operating characteristic (ROC) curve is often used to assess the usefulness of a diagnostic test. We present a new method to estimate the parameters of a popular semi-parametric ROC model, called the bino...
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The receiver operating characteristic (ROC) curve is often used to assess the usefulness of a diagnostic test. We present a new method to estimate the parameters of a popular semi-parametric ROC model, called the binormal model. Our method is based on minimization of the functional distance between two estimators of an unknown transformation postulated by the model, and has a simple, closed-form solution. We study the asymptotics of our estimators, show via Simulation that they compare favorably with existing estimators, and illustrate how covariates may be incorporated into the norm minimization framework.
Different from the standard treatment discovery framework which is used for finding single treatments for a homogenous group of patients, personalized medicine involves finding therapies that are tailored to each indi...
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Different from the standard treatment discovery framework which is used for finding single treatments for a homogenous group of patients, personalized medicine involves finding therapies that are tailored to each individual in a heterogeneous group. In this paper, we propose a new semiparametric additive single-index model for estimating individualized treatment strategy. The model assumes a flexible and nonparametric link function for the interaction between treatment and predictive covariates. We estimate the rule via monotone B-splines and establish the asymptotic properties of the estimators. Both simulations and an real data application demonstrate that the proposed method has a competitive performance.
The paper discusses a likelihood based method of estimation which allows for a small amount of misspecification in the assumption of normality. Asymptotic results suggest that the new method can give an estimated mode...
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The paper discusses a likelihood based method of estimation which allows for a small amount of misspecification in the assumption of normality. Asymptotic results suggest that the new method can give an estimated model which is closer to the true model. An application to hearing threshold data is discussed.
We develop methods for analysing the 'interaction' or dependence between points in a spatial point pattern, when the pattern is spatially inhomogeneous. Completely non-parametric study of interactions is possi...
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We develop methods for analysing the 'interaction' or dependence between points in a spatial point pattern, when the pattern is spatially inhomogeneous. Completely non-parametric study of interactions is possible using an analogue of the K-function. Alternatively one may assume a semi-parametric model in which a (parametrically specified) homogeneous Markov point process is subjected to (non-parametric) inhomogeneous independent thinning. The effectiveness of these approaches is tested on datasets representing the positions of trees in forests.
Consider the Gaussian sequence model under the additional assumption that a fixed fraction of the means is known. We study the problem of variance estimation from a frequentist Bayesian perspective. The maximum likeli...
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Consider the Gaussian sequence model under the additional assumption that a fixed fraction of the means is known. We study the problem of variance estimation from a frequentist Bayesian perspective. The maximum likelihood estimator (MLE) for sigma(2) is biased and inconsistent. This raises the question whether the posterior is able to correct the MLE in this case. By developing a new proving strategy that uses refined properties of the posterior distribution, we find that the marginal posterior is inconsistent for any i.i.d. prior on the mean parameters. In particular, no assumption on the decay of the prior needs to be imposed. Surprisingly, we also find that consistency can be retained for a hierarchical prior based on Gaussian mixtures. In this case we also establish a limiting shape result and determine the limit distribution. In contrast to the classical Bernstein-von Mises theorem, the limit is non-Gaussian. We show that the Bayesian analysis leads to new statistical estimators outperforming the correctly calibrated MLE in a numerical simulation study.
This paper introduces a general semi-parametric method for estimating a vector of parameters in multivariate copula models. The proposed approach uses the moments of the multivariate probability integral random variab...
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This paper introduces a general semi-parametric method for estimating a vector of parameters in multivariate copula models. The proposed approach uses the moments of the multivariate probability integral random variable to generalize the inversion of Kendall's tau estimator. What makes the new methodology attractive is the fact that it can be performed as soon as one can simulate from the assumed parametric family of copulas. This feature is especially helpful when explicit expressions are not available for the theoretical moments. The consistency and asymptotic normality of the proposed estimators are established under mild conditions. An extensive simulation study indicates that the price to pay for the estimation of the moments is modest and that the new estimators are almost as accurate as the pseudo-maximum likelihood (PML) estimator. The usefulness of the proposed estimators is illustrated on the modelling of multivariate data with copula models where the PML estimator is hardly computable.
The rank-based association between two variables can be modeled by introducing a latent normal level to ordinal data. We demonstrate how this approach yields Bayesian inference for Kendall's tau, improving on a re...
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The rank-based association between two variables can be modeled by introducing a latent normal level to ordinal data. We demonstrate how this approach yields Bayesian inference for Kendall's tau, improving on a recent Bayesian solution based on its asymptotic properties. (C) 2018 Elsevier B.V. All rights reserved.
Signal reconstruction over graphs arises naturally in diverse science and engineering applications. Existing methods employ either parametric or nonparametric approaches based on graph kernels. Although the former are...
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ISBN:
(纸本)9781509059904
Signal reconstruction over graphs arises naturally in diverse science and engineering applications. Existing methods employ either parametric or nonparametric approaches based on graph kernels. Although the former are adequate when the signals of interest adhere to postulated models, their performance degrades rapidly under model mismatch. Nonparametric alternatives on the other hand are flexible, but not as parsimonious in capturing prior information. Targeting a hybrid "sweet spot," the present contribution advocates an efficient semi-parametric approach capable of incorporating known signal structure without sacrificing the flexibility of the overall model. Numerical tests on synthetic as well as real data corroborate that the novel method leads to markedly improved signal reconstruction performance.
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