Showing papers on "Semiparametric model published in 1998"

Semiparametric Stochastic Mixed Models for Longitudinal Data

Abstract: We consider inference for a semiparametric stochastic mixed model for longitudinal data. This model uses parametric fixed effects to represent the covariate effects and an arbitrary smooth function to model the time effect and accounts for the within-subject correlation using random effects and a stationary or nonstationary stochastic process. We derive maximum penalized likelihood estimators of the regression coefficients and the nonparametric function. The resulting estimator of the nonparametric function is a smoothing spline. We propose and compare frequentist inference and Bayesian inference on these model components. We use restricted maximum likelihood to estimate the smoothing parameter and the variance components simultaneously. We show that estimation of all model components of interest can proceed by fitting a modified linear mixed model. We illustrate the proposed method by analyzing a hormone dataset and evaluate its performance through simulations.

Practical Nonparametric and Semiparametric Bayesian Statistics

Abstract: I Dirichlet and Related Processes.- 1 Computing Nonparametric Hierarchical Models.- 1.1 Introduction.- 1.2 Notation and Perspectives.- 1.3 Posterior Sampling in Dirichlet Process Mixtures.- 1.4 An Example with Poisson-Gamma Structure.- 1.5 An Example with Normal Structure.- 2 Computational Methods for Mixture of Dirichlet Process Models.- 2.1 Introduction.- 2.2 The Basic Algorithm.- 2.3 More Efficient Algorithms.- 2.4 Non-Conjugate Models.- 2.5 Discussion.- 3 Nonparametric Bayes Methods Using Predictive Updating.- 3.1 Introduction.- 3.2 Onn=1.- 3.3 A Recursive Algorithm.- 3.4 Interval Censoring.- 3.5 Censoring Example.- 3.6 Mixing Example.- 3.7 Onn= 2.- 3.8 Concluding Remarks.- 4 Dynamic Display of Changing Posterior in Bayesian Survival Analysis.- 4.1 Introduction and Summary.- 4.2 A Gibbs Sampler for Censored Data.- 4.3 Proof of Proposition 1.- 4.4 Importance Sampling.- 4.5 The Environment for Dynamic Graphics.- 4.6 Appendix: Completion of the Proof of Proposition 1.- 5 Semiparametric Bayesian Methods for Random Effects Models.- 5.1 Introduction.- 5.2 Normal Linear Random Effects Models.- 5.3 DP priors in the Normal Linear Random Effects Model.- 5.4 Generalized Linear Mixed Models.- 5.5 DP priors in the Generalized Linear Mixed Model.- 5.6 Applications.- 5.7 Discussion.- 6 Nonparametric Bayesian Group Sequential Design.- 6.1 Introduction.- 6.2 The DP Mixing Approach Applied to the Group Sequential Framework.- 6.3 Model Fitting Techniques.- 6.4 Implementation of the Design.- 6.5 Examples.- II Modeling Random Functions.- 7 Wavelet-Based Nonparametric Bayes Methods.- 7.1 Introduction.- 7.2 Discrete Wavelet Transformations.- 7.3 Bayes and Wavelets.- 7.4 Other Problems.- 8 Nonparametric Estimation of Irregular Functions with Independent or Autocorrelated Errors.- 8.1 Introduction.- 8.2 Nonparametric Regression for Independent Errors.- 8.3 Nonparametric Regression for Data with Autocorrelated Errors.- 9 Feedforward Neural Networks for Nonparametric Regression.- 9.1 Introduction.- 9.2 Feed Forward Neural Networks as Nonparametric Regression Models.- 9.3 Variable Architecture FFNNs.- 9.4 Posterior Inference with the FFNN Model.- 9.5 Examples.- 9.6 Discussion.- III Levy and Related Processes.- 10 Survival Analysis Using Semiparametric Bayesian Methods.- D. Sinha.- D. Dey.- 10.1 Introduction.- 10.2 Models.- 10.3 Prior Processes.- 10.4 Bayesian Analysis.- 10.5 Further Readings.- 11 Bayesian Nonparametric and Covariate Analysis of Failure Time Data.- 11.1 Introduction.- 11.2 Cox Model with Beta Process Prior.- 11.3 The Computational Model.- 11.4 Illustrative Analysis.- 11.5 Conclusion.- 12 Simulation of Levy Random Fields.- 12.1 Introduction and Overview.- 12.2 Increasing Independent-Increment Processes: A New Look at an Old Idea.- 12.3 Example: Gamma Variates, Processes, and Fields.- 12.4 Inhomogeneous Levy Random Fields.- 12.5 Comparisons with Other Methods.- 12.6 Conclusions.- 13 Sampling Methods for Bayesian Nonparametric Inference Involving Stochastic Processes.- 13.1 Introduction.- 13.2 Neutral to the Right Processes.- 13.3 Mixtures of Dirichlet Processes.- 13.4 Conclusions.- 14 Curve and Surface Estimation Using Dynamic Step Functions.- 14.1 Introduction.- 14.2 Some Statistical Problems.- 14.3 Some Spatial Statistics.- 14.4 Prototype Prior.- 14.5 Posterior Inference.- 14.6 Example in Intensity Estimation.- 14.7 Discussion.- IV Prior Elicitation and Asymptotic Properties 15 Prior Elicitation for Semiparametric Bayesian Survival Analysis.- 15.1 Introduction.- 15.2 The Method.- 15.3 Sampling from the Joint Posterior Distribution of(ss? ao).- 15.4 Applications to Variable Selection.- 15.5 Myeloma Data.- 15.6 Discussion.- 16 Asymptotic Properties of Nonparametric Bayesian Procedures.- 16.1 Introduction.- 16.2 Frequentist or Bayesian Asymptotics?.- 16.3 Consistency.- 16.4 Consistency in Bellinger Distance.- 16.5 Other Asymptotic Properties.- 16.6 The Robins-Ritov Paradox.- 16.7 Conclusion.- V Case Studies.- 17 Modeling Travel Demand in Portland, Oregon.- 17.1 Introduction.- 17.2 The Data.- 17.3 Poisson/Gamma Random Field Models.- 17.4 The Computational Scheme.- 17.5 Posterior Analysis.- 17.6 Discussion.- 18 Semiparametric PK/PD Models.- 18.1 Introduction.- 18.2 A Semiparametric Population Model.- 18.3 Meta-analysis Over Related Studies.- 18.4 Discussion.- 19 A Bayesian Model for Fatigue Crack Growth.- 19.1 Introduction.- 19.2 The Model.- 19.3 A Markov Chain Monte Carlo Method.- 19.4 An Example: Growth of Crack Lengths.- 19.5 Discussion.- 20 A Semiparametric Model for Labor Earnings Dynamics.- 20.1 Introduction.- 20.2 Longitudinal Earnings Data.- 20.3 A Parametric Random Effects Model.- 20.4 A Semiparametric Model.- 20.5 Predictive Distributions.- 20.6 Conclusion.

Semiparametric estimation and consumer demand

Abstract: This paper considers the implementation of semiparametric methods in the empirical analysis of consumer demand. The application is to the estimation of the Engel curve relationship and uses the British Family Expenditure Survey. Household composition is modelled using an extended partially linear framework. This is shown to provide a useful method for pooling non-parametric Engel curves across households of different demographic composition. (C) 1998 John Wiley & Sons, Ltd.

A Semiparametric Bayesian Approach to the Random Effects Model

Abstract: In longitudinal random effects models, the random effects are typically assumed to have a normal distribution in both Bayesian and classical models. We provide a Bayesian model that allows the random effects to have a nonparametric prior distribution. We propose a Dirichlet process prior for the distribution of the random effects; computation is made possible by the Gibbs sampler. An example using marker data from an AIDS study is given to illustrate the methodology.

Testing Parametric Versus Semiparametric Modeling in Generalized Linear Models

Abstract: We consider a generalized partially linear model E(Y|X, T) = G{X T β + m(T)}, where G is a known function, β is an unknown parameter vector, and m is an unknown function. We introduce a test statistic that allows one to decide between a parametric and a semiparametric model: (a) m is linear (i.e., m(t) = t T γ for a parameter vector γ), and (b) m is a smooth (nonlinear) function. Under linearity (a), we show that the test statistic is asymptotically normal. Moreover, we prove that the bootstrap works asymptotically. Simulations suggest that (in small samples) the bootstrap outperforms the calculation of critical values from the normal approximation. The practical performance of the test is demonstrated in applications to data on East–West German migration and credit scoring.

Bayesian goodness-of-fit testing using infinite-dimensional exponential families

Abstract: We develop a nonparametric Bayes factor for testing the fit of a parametric model. We begin with a nominal parametric family which we then embed into an infinite-dimensional exponential family. The new model then has a parametric and nonparametric component. We give the log density of the nonparametric component a Gaussian process prior. An asymptotic consistency requirement puts a restriction on the form of the prior, leaving us with a single hyperparameter for which we suggest a default value based on simulation experience. Then we construct a Bayes factor to test the nominal model versus the semiparametric alternative. Finally, we show that the Bayes factor is consistent. The proof of the consistency is based on approximating the model by a sequence of exponential families.

Land Value and Parcel Size: A Semiparametric Analysis

Abstract: We use a semiparametric estimator to analyze the relationship between land values and parcel size in a sample of 158 undeveloped parcels in the Portland, Oregon, metropolitan area. The semiparametric estimator combines the benefits of parametric and nonparametric estimation. The value-size relationship is estimated nonparametrically, which permits the function to be linear, convex, and concave in different regions. A simple log-linear parametric relationship is assumed for the rest of the model, which conserves degrees of freedom and simplifies hypothesis testing. Our semiparametric estimates do not reject log-linearity for the value-size relationship.

Quasi-Likelihood Regression with Unknown Link and Variance Functions

Abstract: We consider the multiple regression model E(y) = μ, μ = g(x T β), var(y) — [sgrave]2(μ) with predictors x, link function g, and variance function [sgrave]2(·). The aim is to reduce the assumptions in a fully parametric generalized linear model or a quasi-likelihood model by allowing the link and the variance functions to be unknown but smooth. These functions are then estimated nonparametrically, and the estimates are substituted into the quasi-likelihood function. We propose a three-stage approach to identify this semiparametric model by estimating the link function, the variance function, and the vector of regression coefficients in the linear predictor of the model. Consistency results for the link and the variance function estimators, as well as the asymptotic limiting distribution of the regression coefficients, are obtained. We show that the resulting parameter estimates are asymptotically efficient, as compared to the quasi-likelihood parameter estimates obtained for the case where link an...

Semiparametric efficient estimation in the generalized odds-rate class of regression models for right-censored time-to-event data.

Abstract: The generalized odds-rate class of regression models for time to event data is indexed by a non-negative constant ρ and assumes that

On a semiparametric survival model with flexible covariate effect

Abstract: A semiparametric hazard model with parametrized time but general covariate dependency is formulated and analyzed inside the framework of counting process theory. A profile likelihood principle is introduced for estimation of the parameters: the resulting estimator is $n^{1/2}$-consistent, asymptotically normal and achieves the semiparametric efficiency bound. An estimation procedure for the nonparametric part is also given and its asymptotic properties are derived. We provide an application to mortality data.

Bayesian Method of Moments (BMOM) Analysis of Parametric and Semiparametric Regression Models

Abstract: The Bayesian Method of Moments is applied to semiparametric regression models using alternative series expansions of an unknown regression function. We describe estimation loss functions, predictive loss functions and posterior odds as techniques to determine how many terms in a particular expansion to keep and how to choose among different types of expansions. The developed theory is then applied in a Monte-Carlo experiment to data generated from a CES production function.

Semiparametric Regression Smoothing of Non‐linear Time Series

Abstract: In this paper, we consider using a semiparametric regression approach to modelling non-linear autoregressive time series. Based on a finite series approximation to non-parametric components, an adaptive selection procedure for the number of summands in the series approximation is proposed. Meanwhile, a large sample study is detailed and a small sample simulation for the Mackey-Glass system is presented to support the large sample study.

Semi-parametric statistical approaches for space-time process prediction

Abstract: The problem of estimation and prediction of a spatial-temporal stochastic process, observed at regular times and irregularly in space, is considered. A mixed formulation involving a non- parametric component, accounting for a deterministic trend and the effect of exogenous variables, and a parametric component representing the purely spatio-temporal random variation is proposed. Correspondingly, a two-step procedure, first addressing the estimation of the non- parametric component, and then the estimation of the parametric component is developed from the residual series obtained, with spatial-temporal prediction being performed in terms of suitable spatial interpolation of the temporal variation structure. The proposed model formula-tion, together with the estimation and prediction procedure, are applied using a Gaussian ARMA structure for temporal modelling to space-time forecasting from real data of air pollution concentration levels in the region surrounding a power station in northwest Spain.

Semiparametric estimation of major gene effects for age of onset.

Abstract: Analysis of age of onset is a key factor in the segregation and linkage analysis of some complex genetic traits Previous work in the genetics literature has used parametric distributional assumptions on age of onset In this paper, a Cox model with latent major gene effects is used: a semiparametric model with unspecified baseline hazard A Monte Carlo EM procedure is used to obtain maximum likelihood estimates Markov chain Monte Carlo is used to realize genotypic configurations from the posterior distribution given the current model and the observed data, and these genotypic configurations are used to estimate the expectations in the EM algorithm Simulated data sets indicate that the parameters can be estimated well, and one real data set shows the practical applicability of the proposed method

Estimating a Distribution Function in the Presence of Auxiliary Information

Abstract: For estimating the distribution function F of a population, the empirical or sample distribution function Fn has been studied extensively. Qin and Lawless (1994) have proposed an alternative estimator Fn for estimating F in the presence of auxiliary information under a semiparametric model. They have also proved the point-wise asymptotic normality of Fn. In this paper, we establish the weak convergence of Fn to a Gaussian process and show that the asymptotic variance function of Fn is uniformly smaller than that of Fn. As an application of Fn, we propose to employ the mean X and variance (formula) of Fn to estimate the population mean and variance in the presence of auxiliary information. A simulation study is presented to assess the finite sample performance of the proposed estimators Fn, X, and S (formula).

Efficient semiparametric scoring estimation of sample selection models

Abstract: A semiparametric likelihood method is proposed for the estimation of sample selection models. The method is a two-step semiparametric scoring estimation procedure based on an index restriction and kernel estimation. Under some regularity conditions, the estimator is square-root n -consistent and asymptotically normal. The estimator is also asymptotically efficient in the sense that its asymptotic covariance matrix attains the semiparametric efficiency bound under the index restriction. For the binary choice sample selection model, it also attains the efficiency bound under the independence assumption. This method can be applied to the estimation of general sample selection models.

Survival Analysis Using Semiparametric Bayesian Methods

Abstract: This article presents the scope of nonparametric and semi-parametric Bayesian methods for the analysis of survival data using models based on either the hazard or the intensity function. The nonparametric part of every model is assumed to have a suitable prior process. The parametric part, which may include a regression parameter or a parameter quantifying the heterogeneity of a population, is assumed to have a prior distribution with possibly unknown hyperparameters. Careful applications of some recently popular computational tools, including MCMC algorithms, are available to perform sophisticated Bayesian analyses even when we are dealing with complex models and unusual data structures.

Semiparametric smoothing for discrete data

Abstract: A method for semiparametric smoothing of discrete data is proposed. The method consists of the repeated application of a Markov chain transition matrix constructed so as to have a given standard discrete parametric vehicle model as its stationary distribution. Theory and practical examples suggest that the approach yields improved performance over fully nonparametric methods when the vehicle model is a good one and otherwise provides a method comparable to fully nonparametric smoothers. An automatic choice of the amount of smoothing is proposed and used.

Asymptotic normality in a Semiparametric partially linear model with right–censored data

Abstract: The effect of incomplete observation characteristics in a semiparametric partiaEly linear model is examined. To construct estimate of interest–inparameter, synthetic data and generalized profile likelihood, are employed. It is shown that the resulting estimator as asymptotic normal under mild assumptions. Simulations are also presented to explain the behavior of the estimate in the case of small–samples.

Parametric versus semi-parametric models for the analysis of correlated survival data: A case study in veterinary epidemiology

Abstract: Correlated survival data arise frequently in biomedical and epidemiologic research, because each patient may experience multiple events or because there exists clustering of patients or subjects, such that failure times within the cluster are correlated. In this paper, we investigate the appropriateness of the semi-parametric Cox regression and of the generalized estimating equations as models for clustered failure time data that arise from an epidemiologic study in veterinary medicine. The semi-parametric approach is compared with a proposed fully parametric frailty model. The frailty component is assumed to follow a gamma distribution. Estimates of the fixed covariates effects were obtained by maximizing the likelihood function, while an estimate of the variance component ( frailty parameter) was obtained from a profile likelihood construction.

A Semiparametric Model for Labor Earnings Dynamics

Abstract: We apply semiparametric Bayesian methodology to produce predictive distributions for labor earnings of individuals in the U.S., based on longitudinal data from the Panel Study of Income Dynamics. We generalize conventional models for earnings dynamics, by allowing the model disturbances to have an arbitrary distribution. This distribution is modelled as having a mixture of normals representation, where the mixing distribution is given a Dirichlet process prior. The semiparametric models for earnings result in predictive distributions that are quite different from those produced by conventional parametric models. In particular, the predictive distributions appear to be heavy-tailed and have different persistence properties.

Semiparametric Estimation of Censored Transformation Models

Abstract: Many widely used models, including proportional hazards models with un- observed heterogeneity, can be written in the form (Y ) = min[ 0 X + U; C], where is an unknown increasing function, the error term U has unknown distribution function and is independent of X, C is a random censoring threshold, and U and C are conditionally independent given X. Thispaper develops new n 1=2 -consistent and asymptotically normal semiparametric esti- mators of and which are easier to use than existing estimators. Moreover, Monte Carlo results suggest that the mean integrated squared error of predic- tions based on the new estimators is lower than for existing estimators.

Prior Elicitation for Semiparametric Bayesian Survival Analysis

Abstract: The quantification of prior information is a very important problem in a Bayesian analysis. In many situations, especially in clinical trials, the investigator has historical data from past studies which are similar to the current study. In this chapter, we discuss a class of informative prior distributions for Cox’s proportional hazards model. A novel construction of the prior is developed for this semiparametric model based on the notion of the availability of historical data. The prior specifications focus on the observables in that the elicitation is based on a prior prediction yo for the response vector and a quantity ao quantifying the uncertainty in yo. Then, yo and ao are used to specify a prior for the regression coefficients in a semi-automatic fashion. One of the main applications of our proposed priors is for model selection. Efficient computational methods are proposed for sampling from the posterior distribution and computing posterior model probabilities. A real data set is used to demonstrate our methodology.

Bayesian identification of semi-parametric binary response models

Abstract: In this paper, minimal conditions under which a semi-parametric binary response model is identified in a Bayesian framework are presented and compared to the conditions usually required in a sampling theory framework.

A Model Specification Test

Abstract: A general model specification test of a parametric model against a nonparametric or semiparametric alternative is studied. The test statistic employs a fixed kernel, not varying by a bandwidth. This test is proved to be consistent, the asymptotic distribution is derived and shown to be approximated by a bootstrap procedure.