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117
Semiparametric Bayesian Analysis Of Survival Data
 Journal of the American Statistical Association
, 1996
"... this paper are motivated and aimed at analyzing some common types of survival data from different medical studies. We will center our attention to the following topics. ..."
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Cited by 44 (1 self)
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this paper are motivated and aimed at analyzing some common types of survival data from different medical studies. We will center our attention to the following topics.
Finding Salient Regions in Images: NonParametric Clustering for Image Segmentation and Grouping
, 1998
"... A major problem in ContentBased Image Retrieval (CBIR) is the unsupervised identification of perceptually salient regions in images. We contend that this problem can be tackled by mapping the pixels into various featurespaces, whereupon they are subjected to a groupingalgorithm. In this paper ..."
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Cited by 24 (0 self)
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A major problem in ContentBased Image Retrieval (CBIR) is the unsupervised identification of perceptually salient regions in images. We contend that this problem can be tackled by mapping the pixels into various featurespaces, whereupon they are subjected to a groupingalgorithm. In this paper we develop a robust and versatile nonparametric clustering algorithm that is able to handle the unbalanced and highly irregular clusters encountered in such CBIRapplications. The strength of our approach lies not so much in the clustering itself, but rather in the definition and use of two clustervalidity indices that are independent of the clustertopology. By combining them, an optimal clustering can be identified, and experiments confirm that the associated clusters do indeed correspond to perceptually salient imageregions. Contents 1 Intermediatelevel processing for ContentBased Image Retrieval 3 2 Brief overview of classical clusteringmethodology 4 3 Nonparametric cluste...
A fuzzy, nonparametric segmentation framework for
 DTI and MRI analysis,” in Proc. Inf. Process. Med. Imag. (IPMl), 2007
"... Abstract—This paper presents a novel fuzzysegmentation method for diffusion tensor (DT) and magnetic resonance (MR) images. Typical fuzzysegmentation schemes, e.g., those based on fuzzy C means (FCM), incorporate Gaussian class models that are inherently biased towards ellipsoidal clusters charact ..."
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Cited by 22 (2 self)
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Abstract—This paper presents a novel fuzzysegmentation method for diffusion tensor (DT) and magnetic resonance (MR) images. Typical fuzzysegmentation schemes, e.g., those based on fuzzy C means (FCM), incorporate Gaussian class models that are inherently biased towards ellipsoidal clusters characterized by a mean element and a covariance matrix. Tensors in fiber bundles, however, inherently lie on specific manifolds in Riemannian spaces. Unlike FCMbased schemes, the proposed method represents these manifolds using nonparametric datadriven statistical models. The paper describes a statisticallysound (consistent) technique for nonparametric modeling in Riemannian DT spaces. The proposed method produces an optimal fuzzy segmentation by maximizing a novel informationtheoretic energy in a Markovrandomfield framework. Results on synthetic and real, DT and MR images, show that the proposed method provides information about the uncertainties in the segmentation decisions, which stem from imaging artifacts including noise, partial voluming, and inhomogeneity. By enhancing the nonparametric model to capture the spatial continuity and structure of the fiber bundle, we exploit the framework to extract the cingulum fiber bundle. Typical tractography methods for tract delineation, incorporating thresholds on fractional anisotropy and fiber curvature to terminate tracking, can face serious problems arising from partial voluming and noise. For these reasons, tractography often fails to extract thin tracts with sharp changes in orientation, such as the cingulum. The results demonstrate that the proposed method extracts this structure significantly more accurately as compared to tractography. Index Terms—Diffusion tensor imaging (DTI), fuzzy sets, image segmentation, information theory, magnetic resonance imaging (MRI), Markov random fields, nonparametric modeling, Riemannian statistics.
Penalized Maximum Likelihood Estimator for Normal Mixtures
, 2000
"... The estimation of the parameters of a mixture of Gaussian densities is considered, within the framework of maximum likelihood. Due to unboundedness of the likelihood function, the maximum likelihood estimator fails to exist. We adopt a solution to likelihood function degeneracy which consists in pen ..."
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Cited by 22 (3 self)
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The estimation of the parameters of a mixture of Gaussian densities is considered, within the framework of maximum likelihood. Due to unboundedness of the likelihood function, the maximum likelihood estimator fails to exist. We adopt a solution to likelihood function degeneracy which consists in penalizing the likelihood function. The resulting penalized likelihood function is then bounded over the parameter space and the existence of the penalized maximum likelihood estimator is granted. As original contribution we provide asymptotic properties, and in particular a consistency proof, for the penalized maximum likelihood estimator. Numerical examples are provided in the finite data case, showing the performances of the penalized estimator compared to the standard one.
A nonparametric EM algorithm for multiscale Hawkes processes.
 Journal of Nonparametric Statistics,
, 2011
"... Estimating the conditional intensity of a selfexciting point process is particularly challenging when both exogenous and endogenous effects play a role in clustering. We propose maximum penalized likelihood estimation as a method for simultaneously estimating the background rate and the triggering ..."
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Cited by 21 (1 self)
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Estimating the conditional intensity of a selfexciting point process is particularly challenging when both exogenous and endogenous effects play a role in clustering. We propose maximum penalized likelihood estimation as a method for simultaneously estimating the background rate and the triggering density of Hawkes process intensities that vary over multiple time scales. We compare the accuracy of the algorithm with the recently introduced Model Independent Stochastic Declustering (MISD) algorithm and then use the model to examine selfexcitation in Iraq IED event patterns.
Minimum variance in biased estimation: Bounds and asymptotically optimal estimators
 IEEE Trans. Signal Processing
, 2004
"... Abstract—We develop a uniform Cramér–Rao lower bound (UCRLB) on the total variance of any estimator of an unknown vector of parameters, with bias gradient matrix whose norm is bounded by a constant. We consider both the Frobenius norm and the spectral norm of the bias gradient matrix, leading to two ..."
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Cited by 18 (6 self)
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Abstract—We develop a uniform Cramér–Rao lower bound (UCRLB) on the total variance of any estimator of an unknown vector of parameters, with bias gradient matrix whose norm is bounded by a constant. We consider both the Frobenius norm and the spectral norm of the bias gradient matrix, leading to two corresponding lower bounds. We then develop optimal estimators that achieve these lower bounds. In the case in which the measurements are related to the unknown parameters through a linear Gaussian model, Tikhonov regularization is shown to achieve the UCRLB when the Frobenius norm is considered, and the shrunken estimator is shown to achieve the UCRLB when the spectral norm is considered. For more general models, the penalized maximum likelihood (PML) estimator with a suitable penalizing function is shown to asymptotically achieve the UCRLB. To establish the asymptotic optimality of the PML estimator, we first develop the asymptotic mean and variance of the PML estimator for any choice of penalizing function satisfying certain regularity constraints and then derive a general condition on the penalizing function under which the resulting PML estimator asymptotically achieves the UCRLB. This then implies that from all linear and nonlinear estimators with bias gradient whose norm is bounded by a constant, the proposed PML estimator asymptotically results in the smallest possible variance. Index Terms—Asymptotic optimality, biased estimation, bias gradient norm, Cramér–Rao lower bound, penalized maximum likelihood, Tikhonov regularization.
Penalized Likelihood
 In Encyclopedia of Statistical Sciences, Update Volume 2
, 1996
"... this article. The scope for the application of penalized likelihood is greatest in nonparametric and semiparametric regression, interpreting the term very broadly, and such applications will be emphasised here. A brief discussion of application to density estimation will also be given. The emphasis ..."
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Cited by 17 (0 self)
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this article. The scope for the application of penalized likelihood is greatest in nonparametric and semiparametric regression, interpreting the term very broadly, and such applications will be emphasised here. A brief discussion of application to density estimation will also be given. The emphasis in this article is on methodology, not theory; for careful and illuminating accounts of the asymptotic theory of penalized likelihood estimators, we refer the reader to Cox and O'Sullivan [3], and Gu and Qiu [10]. 1.1 Nonparametric regression
QUASICONCAVE DENSITY ESTIMATION
"... Abstract. Maximum likelihood estimation of a logconcave probability density is formulated as a convex optimization problem and shown to have an equivalent dual formulation as a constrained maximum Shannon entropy problem. Closely related maximum Renyi entropy estimators that impose weaker concavity ..."
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Cited by 13 (1 self)
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Abstract. Maximum likelihood estimation of a logconcave probability density is formulated as a convex optimization problem and shown to have an equivalent dual formulation as a constrained maximum Shannon entropy problem. Closely related maximum Renyi entropy estimators that impose weaker concavity restrictions on the fitted density are also considered, notably a minimum Hellinger discrepancy estimator that constrains the reciprocal of the squareroot of the density to be concave. A limiting form of these estimators constrains solutions to the class of quasiconcave densities. 1.
Penalized likelihood density estimation: direct crossvalidation and scalabe approximation.
 Statistica Sinica,
, 2003
"... Abstract: For smoothing parameter selection in penalized likelihood density estimation, a direct crossvalidation strategy is illustrated. The strategy is as effective as the indirect crossvalidation developed earlier but is much easier to implement in multivariate settings. Also studied is the pr ..."
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Cited by 13 (7 self)
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Abstract: For smoothing parameter selection in penalized likelihood density estimation, a direct crossvalidation strategy is illustrated. The strategy is as effective as the indirect crossvalidation developed earlier but is much easier to implement in multivariate settings. Also studied is the practical implementation of certain lowdimensional approximations of the estimate, with the dimension of the model space selected to achieve both asymptotic efficiency and numerical scalability. The greatly reduced computational burden allows the routine use of the technique for the analysis of large data sets. Related practical issues concerning multivariate numerical integration are also briefly addressed.
Penalized likelihood hazard estimation: a general procedure
 Statistica Sinica
, 1996
"... Abstract: A general penalized likelihood hazard estimation procedure is formulated and an asymptotic theory developed. The life time data may be lefttruncated, partly rightcensored, and may come with a covariate. In the presence of a covariate, the modular model construction via tensorproduct sp ..."
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Cited by 12 (4 self)
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Abstract: A general penalized likelihood hazard estimation procedure is formulated and an asymptotic theory developed. The life time data may be lefttruncated, partly rightcensored, and may come with a covariate. In the presence of a covariate, the modular model construction via tensorproduct splines provides rich collections of hazard models, of which the proportional hazard model and a model of