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Parametric Assumptions (parametric + assumption)

Distribution by Scientific Domains
Mathematics and Statistics81%

Selected Abstracts

Bayesian nonparametric hierarchical modeling

BIOMETRICAL JOURNAL, Issue 2 2009
David B. Dunson
Abstract In biomedical research, hierarchical models are very widely used to accommodate dependence in multivariate and longitudinal data and for borrowing of information across data from different sources. A primary concern in hierarchical modeling is sensitivity to parametric assumptions, such as linearity and normality of the random effects. Parametric assumptions on latent variable distributions can be challenging to check and are typically unwarranted, given available prior knowledge. This article reviews some recent developments in Bayesian nonparametric methods motivated by complex, multivariate and functional data collected in biomedical studies. The author provides a brief review of flexible parametric approaches relying on finite mixtures and latent class modeling. Dirichlet process mixture models are motivated by the need to generalize these approaches to avoid assuming a fixed finite number of classes. Focusing on an epidemiology application, the author illustrates the practical utility and potential of nonparametric Bayes methods. [source]

A Semi-Parametric Shared Parameter Model to Handle Nonmonotone Nonignorable Missingness

BIOMETRICS, Issue 1 2009
Roula Tsonaka
Summary Longitudinal studies often generate incomplete response patterns according to a missing not at random mechanism. Shared parameter models provide an appealing framework for the joint modelling of the measurement and missingness processes, especially in the nonmonotone missingness case, and assume a set of random effects to induce the interdependence. Parametric assumptions are typically made for the random effects distribution, violation of which leads to model misspecification with a potential effect on the parameter estimates and standard errors. In this article we avoid any parametric assumption for the random effects distribution and leave it completely unspecified. The estimation of the model is then made using a semi-parametric maximum likelihood method. Our proposal is illustrated on a randomized longitudinal study on patients with rheumatoid arthritis exhibiting nonmonotone missingness. [source]

Flexible Maximum Likelihood Methods for Bivariate Proportional Hazards Models

BIOMETRICS, Issue 4 2003
Wenqing He
Summary. This article presents methodology for multivariate proportional hazards (PH) regression models. The methods employ flexible piecewise constant or spline specifications for baseline hazard functions in either marginal or conditional PH models, along with assumptions about the association among lifetimes. Because the models are parametric, ordinary maximum likelihood can be applied; it is able to deal easily with such data features as interval censoring or sequentially observed lifetimes, unlike existing semiparametric methods. A bivariate Clayton model (1978, Biometrika65, 141,151) is used to illustrate the approach taken. Because a parametric assumption about association is made, efficiency and robustness comparisons are made between estimation based on the bivariate Clayton model and "working independence" methods that specify only marginal distributions for each lifetime variable. [source]

Optimal Nonparametric Estimation of First-price Auctions

ECONOMETRICA, Issue 3 2000
Emmanuel Guerre
This paper proposes a general approach and a computationally convenient estimation procedure for the structural analysis of auction data. Considering first-price sealed-bid auction models within the independent private value paradigm, we show that the underlying distribution of bidders' private values is identified from observed bids and the number of actual bidders without any parametric assumptions. Using the theory of minimax, we establish the best rate of uniform convergence at which the latent density of private values can be estimated nonparametrically from available data. We then propose a two-step kernel-based estimator that converges at the optimal rate. [source]

The bootstrap and cross-validation in neuroimaging applications: Estimation of the distribution of extrema of random fields for single volume tests, with an application to ADC maps

HUMAN BRAIN MAPPING, Issue 10 2007
Roberto Viviani
Abstract We discuss the assessment of signal change in single magnetic resonance images (MRI) based on quantifying significant departure from a reference distribution estimated from a large sample of normal subjects. The parametric approach is to build a test based on the expected distribution of extrema in random fields. However, in conditions where the variance is not uniform across the volume and the smoothness of the images is moderate to low, this test may be rather conservative. Furthermore, parametric tests are limited to datasets for which distributional assumptions hold. This paper investigates resampling methods that improve statistical tests for signal changes in single images in such adverse conditions, and that can be used for the assessment of images taken for clinical purposes. Two methods, the bootstrap and cross-validation, are compared. It is shown that the bootstrap may fail to provide a good estimate of the distribution of extrema of parametric maps. In contrast, calibration of the significance threshold by means of cross-validation (or related sampling without replacement techniques) address three issues at once: improved power, better voxel-by-voxel estimate of variance by local pooling, and adaptation to departures from ideal distributional assumptions on the signal. We apply the cross-validated tests to apparent diffusion coefficient maps, a type of MRI capable of detecting changes in the microstructural organization of brain parenchyma. We show that deviations from parametric assumptions are strong enough to cast doubt on the correctness of parametric tests for these images. As case studies, we present parametric maps of lesions in patients suffering from stroke and glioblastoma at different stages of evolution. Hum Brain Mapp 2007. © 2007 Wiley-Liss, Inc. [source]

Application of Markov chain Monte Carlo methods to projecting cancer incidence and mortality

JOURNAL OF THE ROYAL STATISTICAL SOCIETY: SERIES C (APPLIED STATISTICS), Issue 2 2002
Isabelle Bray
Summary. Projections based on incidence and mortality data collected by cancer registries are important for estimating current rates in the short term, and public health planning in the longer term. Classical approaches are dependent on questionable parametric assumptions. We implement a Bayesian age,period,cohort model, allowing the inclusion of prior belief concerning the smoothness of the parameters. The model is described by a directed acyclic graph. Computations are carried out by using Markov chain Monte Carlo methods (implemented in BUGS) in which the degree of smoothing is learnt from the data. Results and convergence diagnostics are discussed for an exemplary data set. We then compare the Bayesian projections with other methods in a range of situations to demonstrate its flexibility and robustness. [source]

Two-part regression models for longitudinal zero-inflated count data

THE CANADIAN JOURNAL OF STATISTICS, Issue 2 2010
Marco Alfò
Abstract Two-part models are quite well established in the economic literature, since they resemble accurately a principal-agent type model, where homogeneous, observable, counted outcomes are subject to a (prior, exogenous) selection choice. The first decision can be represented by a binary choice model, modeled using a probit or a logit link; the second can be analyzed through a truncated discrete distribution such as a truncated Poisson, negative binomial, and so on. Only recently, a particular attention has been devoted to the extension of two-part models to handle longitudinal data. The authors discuss a semi-parametric estimation method for dynamic two-part models and propose a comparison with other, well-established alternatives. Heterogeneity sources that influence the first level decision process, that is, the decision to use a certain service, are assumed to influence also the (truncated) distribution of the positive outcomes. Estimation is carried out through an EM algorithm without parametric assumptions on the random effects distribution. Furthermore, the authors investigate the extension of the finite mixture representation to allow for unobservable transition between components in each of these parts. The proposed models are discussed using empirical as well as simulated data. The Canadian Journal of Statistics 38: 197,216; 2010 © 2010 Statistical Society of Canada Les modèles en deux parties sont bien établis dans la littérature économique puisqu'ils sont très similaires à un modèle principal-agent pour lequel les résultats homogènes, observables et dénombrables sont sujets à un critère de sélection (exogène et a priori). La première décision est représentée à l'aide un modèle de choix binaire et une fonction de lien probit ou logit tandis que la seconde peut être analysée à l'aide d'une loi discrète tronquée telle que la loi de Poisson tronquée, la loi binomiale négative, etc. Depuis peu, une attention particulière a été portée à la généralisation du modèle en deux parties pour prendre en compte les données longitudinales. Les auteurs présentent une méthode d'estimation semi-paramétrique pour les modèles en deux parties dynamiques et ils les comparent avec d'autres modèles alternatifs bien connus. Les sources hétérogènes qui influencent le premier niveau du processus de décision, c'est-à-dire la décision d'utiliser un certain service, sont censées influencer aussi la distribution (tronquée) des résultats positifs. L'estimation est faite à l'aide de l'algorithme EM sans présupposés paramétriques sur la distribution des effets aléatoires. De plus, les auteurs considèrent une généralisation à une représentation en mélange fini afin de permettre une transition non observable entre les différentes composantes de chacune des parties. Une discussion est faite sur les modèles présentés en utilisant des données empiriques ou simulées. La revue canadienne de statistique 38: 197,216; 2010 © 2010 Société statistique du Canada [source]

Bayesian nonparametric hierarchical modeling

BIOMETRICAL JOURNAL, Issue 2 2009
David B. Dunson
Abstract In biomedical research, hierarchical models are very widely used to accommodate dependence in multivariate and longitudinal data and for borrowing of information across data from different sources. A primary concern in hierarchical modeling is sensitivity to parametric assumptions, such as linearity and normality of the random effects. Parametric assumptions on latent variable distributions can be challenging to check and are typically unwarranted, given available prior knowledge. This article reviews some recent developments in Bayesian nonparametric methods motivated by complex, multivariate and functional data collected in biomedical studies. The author provides a brief review of flexible parametric approaches relying on finite mixtures and latent class modeling. Dirichlet process mixture models are motivated by the need to generalize these approaches to avoid assuming a fixed finite number of classes. Focusing on an epidemiology application, the author illustrates the practical utility and potential of nonparametric Bayes methods. [source]

Order-Restricted Semiparametric Inference for the Power Bias Model

BIOMETRICS, Issue 2 2010
Ori Davidov
Summary The power bias model, a generalization of length-biased sampling, is introduced and investigated in detail. In particular, attention is focused on order-restricted inference. We show that the power bias model is an example of the density ratio model, or in other words, it is a semiparametric model that is specified by assuming that the ratio of several unknown probability density functions has a parametric form. Estimation and testing procedures under constraints are developed in detail. It is shown that the power bias model can be used for testing for, or against, the likelihood ratio ordering among multiple populations without resorting to any parametric assumptions. Examples and real data analysis demonstrate the usefulness of this approach. [source]

Area under the Free-Response ROC Curve (FROC) and a Related Summary Index

BIOMETRICS, Issue 1 2009
Andriy I. Bandos
Summary Free-response assessment of diagnostic systems continues to gain acceptance in areas related to the detection, localization, and classification of one or more "abnormalities" within a subject. A free-response receiver operating characteristic (FROC) curve is a tool for characterizing the performance of a free-response system at all decision thresholds simultaneously. Although the importance of a single index summarizing the entire curve over all decision thresholds is well recognized in ROC analysis (e.g., area under the ROC curve), currently there is no widely accepted summary of a system being evaluated under the FROC paradigm. In this article, we propose a new index of the free-response performance at all decision thresholds simultaneously, and develop a nonparametric method for its analysis. Algebraically, the proposed summary index is the area under the empirical FROC curve penalized for the number of erroneous marks, rewarded for the fraction of detected abnormalities, and adjusted for the effect of the target size (or "acceptance radius"). Geometrically, the proposed index can be interpreted as a measure of average performance superiority over an artificial "guessing" free-response process and it represents an analogy to the area between the ROC curve and the "guessing" or diagonal line. We derive the ideal bootstrap estimator of the variance, which can be used for a resampling-free construction of asymptotic bootstrap confidence intervals and for sample size estimation using standard expressions. The proposed procedure is free from any parametric assumptions and does not require an assumption of independence of observations within a subject. We provide an example with a dataset sampled from a diagnostic imaging study and conduct simulations that demonstrate the appropriateness of the developed procedure for the considered sample sizes and ranges of parameters. [source]