Download Free Penalized Likelihood For General Semi Parametric Regression Models Book in PDF and EPUB Free Download. You can read online Penalized Likelihood For General Semi Parametric Regression Models and write the review.

This paper examines maximum penalized likelihood estimation in the context of general regression problems, characterized as probability models with composite; likelihood functions. The emphasis is on the common situation where a parametric model is considered satisfactory but for inhomogeneity with respect to a few extra variables. A finite-dimensional formulation is adopted, using a suitable set of basis functions. Appropriate definitions of deviance, degrees of freedom, and residual are provided, and the method of cross-validation for choice of the tuning constant is discussed. Quadratic approximations are derived for all the required statistics. Additional keywords: algorithms; smoothing; goodness of fit tests; nonlinear repression. (Author).
Interval-censored failure time data arise in many areas including demographical, financial, actuarial, medical and sociological studies. By interval censoring we mean that the failure time is not always exactly observed and we can only observe an interval within which the failure event has occurred. The goal of this dissertation is to develop maximum penalized likelihood (MPL) methods for ptoportional hazard (PH), additive hazard (AH) and accelerated failure time (AFT) models with partly interval-censored failure time data, which contains exactly observed, left-censored, finite interval-censored and right-censored data.
This document considers generalized linear models in which the linear predictor is of additive semi-parametric form, linear in most of the explanatory variables but with an arbitrary functional dependence on the remainder. Estimation of the parameters and the non-parametric curve in the model is approached by maximizing a penalized likelihood. Two explicit iterative algorithms are presented. The first, which operates in O(n) time per iteration, applies where there is just one variable entering the model in a non-parametric fashion, and an integrated squared second derivative penalty is used. An example in logistic regression of tumour prevalence is given. The second algorithm is for the much more general case of a regression model specified as an arbitrary composite log-likelihood function, permitting nonlinear dependence and several splined variables. Keywords: Maximum penalized likelihood estimation; Nonlinear regression; Splines. (Author).
In recent years, there has been a great deal of interest and activity in the general area of nonparametric smoothing in statistics. This monograph concentrates on the roughness penalty method and shows how this technique provides a unifying approach to a wide range of smoothing problems. The method allows parametric assumptions to be realized in regression problems, in those approached by generalized linear modelling, and in many other contexts. The emphasis throughout is methodological rather than theoretical, and it concentrates on statistical and computation issues. Real data examples are used to illustrate the various methods and to compare them with standard parametric approaches. Some publicly available software is also discussed. The mathematical treatment is self-contained and depends mainly on simple linear algebra and calculus. This monograph will be useful both as a reference work for research and applied statisticians and as a text for graduate students and other encountering the material for the first time.
This volume consists of the published proceedings of the GLIM 95 Conference, held at Lancaster University, UK, from 16-19 September 1995. This is the second of such proceedings, the first of which was published as No 14 of the Springer-Verlag Lecture Notes in Statistics (Gilchrist, ed,1992). Since the 1992 conference there has been a modest update of the GLIM system, called GLIM 3.77. This incorporates some minor but pleasant enhancements and these are outlined in these proceedings by payne and Webb. With the completion of GLIM 3.77, future developments of the GLIM system are again under active review. Aitkin surveys possible directions for GLIM. one sOlMlWhat different avenue for analysing generalized linear models is provided by the GENSTAT system; Lane and payne discuss the new interactive facilities p ided by version 5 of GENSTAT. On the theory Side, NeIder extends the concept and use of quasi-likelihood, giving useful forms of variance function and a method of introducing a random element into the linear predictor. Longford discusses one approach to the analysis of clustered observations (subjects within groups). Green and Yandell introduce 'semi-parametric modelling', allowing a compromise between parametriC and non-parametriC modelling. They modify the linear predictor by the addition of a ( smooth) curve, and estimate parameters by maximising a penalised log-likelihood. Hastie and Tibshirani introduce generalized additive models, introducing a linear predictor of the form 11 = (X + Efj(xj), with the fj estimated from the data by a weighted average of neighbouring observations.
Even experts on semiparametric regression should find something new here.
This dissertation consists of two chapters: Chapter 1 develops nonparametric and semiparametric regression methodologies which relate the group testing responses to the individual covariates information. In this chapter, we extend the parametric regression model of Xie (2001) for binary group testing data to the nonparametric and semiparametric models. We fit nonparametric and semiparametric models and obtain estimators of the parameters by maximizing penalized likelihood function. For implementation, we apply EM algorithm considering the individual responses as complete data and the group testing responses as observed data. Simulation studies are performed to illustrate the methodologies and to evaluate the finite sample performance of our methods. In general, group testing involves a large number of subjects, hence, the computational aspect is also discussed. The results show that our estimation methods perform well for estimating both the individual probability of positive outcome and the prevalence rate in the population. Chapter 2 studies a partially linear regression model with missing response variable and develops semiparametric efficient inference for the parametric component of the model. The missingness considered here includes a broad range of missing patterns. For the estimation method, we use the concept of least favorable curve, least favorable direction and the generalized profile likelihood in Severini and Wong (1992). Asymptotic distributions for the estimators of the parametric components are obtained. It is shown that the estimators are asymptotically normally distributed under some conditions. Furthermore, we prove that the asymptotic covariance of the estimators achieves the semiparametric lower bound under the regularity conditions and additional conditions given in the appendix. We also propose an algorithm which runs iteratively between fitting parametric components and fitting nonparametric components while holding the other fixed. EM algorithms are used in estimating the parametric components by a semiparametric estimating equation and in estimating the nonparametric components by smoothing methods. It is proved that the estimators from this iterative algorithm equal to the conditional expectations (conditioned on observed data) of the semiparametric efficient estimators from complete data. The methodology is illustrated and evaluated by numerical examples.
Beginning with familiar models and moving onto advanced semiparametric modelling tools Semiparametric Odds Ratio Model and its Applications introduces readers to a new range of flexible statistical models and provides guidance on their application using real data examples. This books range of real-world examples and exploration of common statistical problems makes it an invaluable reference for research professionals and graduate students of biostatistics, statistics, and other quantitative fields. Key Features: Introduces flexible statistical models that have yet to systematically introduced in course materials. Discusses applications of the proposed modelling framework in several important statistical problems, ranging from biased sampling designs and missing data, graphical models, survival analysis, Gibbs sampler and model compatibility, and density estimation. Includes real data examples to demonstrate the use of the proposed models, and estimation and inference tools.
Kosorok’s brilliant text provides a self-contained introduction to empirical processes and semiparametric inference. These powerful research techniques are surprisingly useful for developing methods of statistical inference for complex models and in understanding the properties of such methods. This is an authoritative text that covers all the bases, and also a friendly and gradual introduction to the area. The book can be used as research reference and textbook.
Separation of signal from noise is the most fundamental problem in data analysis, arising in such fields as: signal processing, econometrics, actuarial science, and geostatistics. This book introduces the local regression method in univariate and multivariate settings, with extensions to local likelihood and density estimation. Practical information is also included on how to implement these methods in the programs S-PLUS and LOCFIT.