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  • Articles  (393)
  • 2020-2023
  • 2010-2014  (131)
  • 1970-1974  (74)
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  • Mathematics  (393)
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  • Articles  (393)
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  • 1
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    Predictive accuracy of covariates for event times (2012)
    Oxford University Press
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    Publication Date: 2012-08-22
    Description: We propose a graphical measure, the generalized negative predictive function, to quantify the predictive accuracy of covariates for survival time or recurrent event times. This new measure characterizes the event-free probabilities over time conditional on a thresholded linear combination of covariates and has direct clinical utility. We show that this function is maximized at the set of covariates truly related to event times and thus can be used to compare the predictive accuracy of different sets of covariates. We construct nonparametric estimators for this function under right censoring and prove that the proposed estimators, upon proper normalization, converge weakly to zero-mean Gaussian processes. To bypass the estimation of complex density functions involved in the asymptotic variances, we adopt the bootstrap approach and establish its validity. Simulation studies demonstrate that the proposed methods perform well in practical situations. Two clinical studies are presented.
    Print ISSN: 0006-3444
    Electronic ISSN: 1464-3510
    Topics: Biology , Mathematics , Medicine
    Published by Oxford University Press
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  • 2
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    On robust estimation via pseudo-additive information (2012)
    Oxford University Press
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    Publication Date: 2012-04-19
    Description: We consider a robust parameter estimator minimizing an empirical approximation to the q -entropy and show its relationship to minimization of power divergences through a simple parameter transformation. The estimator balances robustness and efficiency through a tuning constant q and avoids kernel density smoothing. We derive an upper bound to the estimator mean squared error under a contaminated reference model and use it as a min-max criterion for selecting q .
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    Electronic ISSN: 1464-3510
    Topics: Biology , Mathematics , Medicine
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  • 3
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    'On measuring the variability of small area estimators under a basic area level model' (2012)
    Oxford University Press
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    Publication Date: 2012-05-22
    Print ISSN: 0006-3444
    Electronic ISSN: 1464-3510
    Topics: Biology , Mathematics , Medicine
    Published by Oxford University Press
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  • 4
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    Nonparametric Bayes dynamic modelling of relational data (2014)
    Oxford University Press
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    Publication Date: 2014-11-25
    Description: Symmetric binary matrices representing relations are collected in many areas. Our focus is on dynamically evolving binary relational matrices, with interest being on inference on the relationship structure and prediction. We propose a nonparametric Bayesian dynamic model, which reduces dimensionality in characterizing the binary matrix through a lower-dimensional latent space representation, with the latent coordinates evolving in continuous time via Gaussian processes. By using a logistic mapping function from the link probability matrix space to the latent relational space, we obtain a flexible and computationally tractable formulation. Employing Pólya-gamma data augmentation, an efficient Gibbs sampler is developed for posterior computation, with the dimension of the latent space automatically inferred. We provide theoretical results on flexibility of the model, and illustrate its performance via simulation experiments. We also consider an application to co-movements in world financial markets.
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    Topics: Biology , Mathematics , Medicine
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  • 5
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    A class of improved hybrid Hochberg-Hommel type step-up multiple test procedures (2014)
    Oxford University Press
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    Publication Date: 2014-11-25
    Description: In this paper we derive a new p -value based multiple testing procedure that improves upon the Hommel procedure by gaining power as well as having a simpler step-up structure similar to the Hochberg procedure. The key to this improvement is that the Hommel procedure can be improved by a consonant procedure. Exact critical constants of this new procedure can be numerically determined. The zeroth-order approximations to the exact critical constants, albeit slightly conservative, are simple to use and need no tabling, and hence are recommended in practice. The proposed procedure is shown to control the familywise error rate under independence among the p -values. Simulations empirically demonstrate familywise error rate control under positive and negative dependence. Power superiority of the proposed procedure over competing ones is also empirically demonstrated. Illustrative examples are given.
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    Topics: Biology , Mathematics , Medicine
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  • 6
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    Robust estimators for nondecomposable elliptical graphical models (2014)
    Oxford University Press
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    Publication Date: 2014-11-25
    Description: Robust estimators of the restricted covariance matrices associated with elliptical graphical models are studied. General asymptotic results, which apply to both decomposable and nondecomposable graphical models, are presented for robust plug-in type estimators. These extend results previously established only for the decomposable case. Furthermore, a class of graphical M -estimators for the restricted covariance matrices is introduced and compared with the corresponding plug-in M -estimators. The two approaches are shown to be asymptotically equivalent under random sampling from an elliptical distribution. A simulation study demonstrates the superiority of the graphical M -estimators for small samples.
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    Topics: Biology , Mathematics , Medicine
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  • 7
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    Controlling the bias of robust small-area estimators (2013)
    Oxford University Press
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    Publication Date: 2013-11-27
    Description: Sinha & Rao (2009) proposed estimation procedures designed for small-area means, based on robustified maximum likelihood estimators and robust empirical best linear unbiased predictors. Their methods are of the plug-in type and may be biased. Bias-corrected estimators have been proposed by Chambers et al. (2013). Here, we investigate two new approaches: one relying on the work of Chambers (1986), and the second using the concept of conditional bias to measure the influence of units in the population. These two classes of estimators also include correction terms for the bias but are both fully bias-corrected, in the sense that the corrections account for the potential impact of the other domains on the small area of interest. Monte Carlo simulations suggest that the Sinha–Rao method and the bias-adjusted estimator of Chambers et al. (2013) may exhibit a large bias, while the new procedures often offer lower bias and mean squared error. A parametric bootstrap procedure is considered for constructing confidence intervals.
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    Topics: Biology , Mathematics , Medicine
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  • 8
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    Distances and inference for covariance operators (2014)
    Oxford University Press
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    Publication Date: 2014-05-24
    Description: A framework is developed for inference concerning the covariance operator of a functional random process, where the covariance operator itself is an object of interest for statistical analysis. Distances for comparing positive-definite covariance matrices are either extended or shown to be inapplicable to functional data. In particular, an infinite-dimensional analogue of the Procrustes size-and-shape distance is developed. Convergence of finite-dimensional approximations to the infinite-dimensional distance metrics is also shown. For inference, a Fréchet estimator of both the covariance operator itself and the average covariance operator is introduced. A permutation procedure to test the equality of the covariance operators between two groups is also considered. Additionally, the use of such distances for extrapolation to make predictions is explored. As an example of the proposed methodology, the use of covariance operators has been suggested in a philological study of cross-linguistic dependence as a way to incorporate quantitative phonetic information. It is shown that distances between languages derived from phonetic covariance functions can provide insight into the relationships between the Romance languages.
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    Topics: Biology , Mathematics , Medicine
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  • 9
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    Testing equality of a large number of densities (2014)
    Oxford University Press
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    Publication Date: 2014-05-24
    Description: The problem of testing equality of a large number of densities is considered. The classical k -sample problem compares a small, fixed number of distributions and allows the sample size from each distribution to increase without bound. In our asymptotic analysis the number of distributions tends to infinity but the size of individual samples remains fixed. The proposed test statistic is motivated by the simple idea of comparing kernel density estimators from the various samples to the average of all density estimators. However, a novel interpretation of this familiar type of statistic arises upon centring it. The asymptotic distribution of the statistic under the null hypothesis of equal densities is derived, and power against local alternatives is considered. It is shown that a consistent test is attainable in many situations where all but a vanishingly small proportion of densities are equal to each other. The test is studied via simulation, and an illustration involving microarray data is provided.
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    Topics: Biology , Mathematics , Medicine
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  • 10
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    Distances and inference for covariance operators (2014)
    Oxford University Press
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    Publication Date: 2014-04-17
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    Topics: Biology , Mathematics , Medicine
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