We address the problem of estimating generalized linear models when some covariate values are missing but imputations are available to fill-in the missing values. This situation generates a bias-precision trade-off in...
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We address the problem of estimating generalized linear models when some covariate values are missing but imputations are available to fill-in the missing values. This situation generates a bias-precision trade-off in the estimation of the model parameters. Extending the generalized missing-indicator method proposed by Dardanoni et al. (2011) for linear regression, we handle this trade-off as a problem of model uncertainty using Bayesian averaging of classical maximum likelihood estimators (BAML). We also propose a block model averaging strategy that incorporates information on the missing-data patterns and is computationally simple. An empirical application illustrates our approach. (C) 2014 Elsevier B.V. All rights reserved.
We derive conditions for L-2 differentiability of generalized linear models with error distributions not necessarily belonging to exponential families, covering both cases of stochastic and deterministic regressors. T...
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We derive conditions for L-2 differentiability of generalized linear models with error distributions not necessarily belonging to exponential families, covering both cases of stochastic and deterministic regressors. These conditions induce smoothness and integrability conditions for corresponding GLM-based time series models. (C) 2014 The Authors. Published by Elsevier B.V.
Empirical likelihood inference for generalized linear models with fixed and adaptive designs is considered. It is shown that the empirical log-likelihood ratio at the true parameters converges to the standard chi-squa...
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Empirical likelihood inference for generalized linear models with fixed and adaptive designs is considered. It is shown that the empirical log-likelihood ratio at the true parameters converges to the standard chi-square distribution. Furthermore, we obtain the maximum empirical likelihood estimate of the unknown parameter and the resulting estimator is shown to be asymptotically normal. Some simulations are conducted to illustrate the proposed method.
In the presented thesis we deal with the generalized linear models framework in a claims reserving problem. Claims reserving in non-life insurance is firstly described and the considered class of models is introduced....
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In the presented thesis we deal with the generalized linear models framework in a claims reserving problem. Claims reserving in non-life insurance is firstly described and the considered class of models is introduced. Consequently, this branch of stochastic modelling is implemented in the reserving setup. For computation of the risk associated with claims reserving, we need a predictive distribution of future liabilities in order to evaluate risk measures such as Va- lue at Risk and Conditional Value at Risk. Since datasets in non-life insurance commonly consist of a small number of observations and estimation of predictive distributions can be complicated, we adopt a bootstrap method for this purpose. Model fitting, simulations and consequent measuring of the reserving risk are performed within the use of real-life data. Based on this, an analysis of fitted models and their comparison together with graphical outputs is included. 1
We consider estimation in generalized linear models when there are many potential predictors and some of them may not have influence on the response of interest. In the context of two competing models where one model ...
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We consider estimation in generalized linear models when there are many potential predictors and some of them may not have influence on the response of interest. In the context of two competing models where one model includes all predictors and the other restricts variable coefficients to a candidate linear subspace based on subject matter or prior knowledge, we investigate the relative performances of Stein type shrinkage, pretest, and penalty estimators (L(1)GLM, adaptive L(1)GLM, and SCAD) with respect to the unrestricted maximum likelihood estimator (MLE). The asymptotic properties of the pretest and shrinkage estimators including the derivation of asymptotic distributional biases and risks are established. In particular, we give conditions under which the shrinkage estimators are asymptotically more efficient than the unrestricted MLE. A Monte Carlo simulation study shows that the mean squared error (MSE) of an adaptive shrinkage estimator is comparable to the MSE of the penalty estimators in many situations and in particular performs better than the penalty estimators when the dimension of the restricted parameter space is large. The Steinian shrinkage and penalty estimators all improve substantially on the unrestricted MLE. A real data set analysis is also presented to compare the suggested methods. (C) 2014 Elsevier B.V. All rights reserved.
When employing generalized linear models, interest often focuses on estimation of odds ratios or relative risks. Additionally, researchers often make overall conclusions, requiring accurate estimation of a set of thes...
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When employing generalized linear models, interest often focuses on estimation of odds ratios or relative risks. Additionally, researchers often make overall conclusions, requiring accurate estimation of a set of these quantities. Consequently, simultaneous estimation is warranted. Current simultaneous estimation methods only perform well in this setting when there are a very small number of comparisons and/or the sample size is relatively large. Additionally, the estimated quantities can have significant bias especially at small sample sizes. The proposed bounds: (1) perform well for a small or large number of comparisons, (2) exhibit improved performance over current methods for small to moderate sample sizes, (3) provide bias adjustment not reliant on asymptotics, and (4) avoid the infinite parameter estimates that can occur with maximum-likelihood estimators. Simulations demonstrate that the proposed bounds achieve the desired level of confidence at smaller sample sizes than previous methods.
Recent literature on panel data emphasizes the importance of accounting for time-varying unobservable individual effects, which may stem from either omitted individual characteristics or macro-level shocks that affect...
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Recent literature on panel data emphasizes the importance of accounting for time-varying unobservable individual effects, which may stem from either omitted individual characteristics or macro-level shocks that affect each individual unit differently. In this paper, we propose a simple specification test of the null hypothesis that the individual effects are time-invariant against the alternative that they are time-varying. Our test is an application of Hausman (1978) testing procedure and can be used for any generalizedlinear model for panel data that admits a sufficient statistic for the individual effect. This is a wide class of models which includes the Gaussian linear model and a variety of nonlinearmodels typically employed for discrete or categorical outcomes. The basic idea of the test is to compare two alternative estimators of the model parameters based on two different formulations of the conditional maximum likelihood method. Our approach does not require assumptions on the distribution of unobserved heterogeneity, nor it requires the latter to be independent of the regressors in the model. We investigate the finite sample properties of the test through a set of Monte Carlo experiments. Our results show that the test performs well, with small size distortions and good power properties. We use a health economics example based on data from the Health and Retirement Study to illustrate the proposed test. (C) 2014 Elsevier B.V. All rights reserved.
The power-conditional-expected-posterior (PCEP) prior developed for variable selection in normal regression models combines ideas from the powerprior and expected-posterior prior, relying on the concept of random imag...
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ISBN:
(纸本)9783319162386;9783319162379
The power-conditional-expected-posterior (PCEP) prior developed for variable selection in normal regression models combines ideas from the powerprior and expected-posterior prior, relying on the concept of random imaginary data, and provides a consistent variable selection method which leads to parsimonious selection. In this paper, the PCEP methodology is extended to generalized linear models (GLMs). We define the PCEP prior in the GLM setting, explain the connections to other default model-selection priors, and present various posterior representations which can be used for model-specific posterior inference or for variable selection. The method is implemented for a logistic regression example with Bernoulli data. Results indicate that the PCEP prior leads to parsimonious selection for logistic regression models, similarly to the case of normal regression. Current limitations in generalizing the applicability of PCEP and possible solutions are discussed.
With a globally aging population, the burden of care of cognitively impaired older adults is becoming increasingly concerning. Instances of Alzheimer's disease and other forms of dementia are becoming ever more fr...
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ISBN:
(纸本)9781424479290
With a globally aging population, the burden of care of cognitively impaired older adults is becoming increasingly concerning. Instances of Alzheimer's disease and other forms of dementia are becoming ever more frequent. Earlier detection of cognitive impairment offers significant benefits, but remains difficult to do in practice. In this paper, we develop statistical models of the behavior of older adults within their homes using sensor data in order to detect the early onset of cognitive decline. Specifically, we use inhomogenous Poisson processes to model the presence of subjects within different rooms throughout the day in the home using unobtrusive sensing technologies. We compare the distributions learned from cognitively intact and impaired subjects using information theoretic tools and observe statistical differences between the two populations which we believe can be used to help detect the onset of cognitive decline.
Objective. This study explores the statistical relations between the accumulation of heavy metals in moss and natural surface soil and potential influencing factors such as atmospheric deposition by use of multivariat...
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Objective. This study explores the statistical relations between the accumulation of heavy metals in moss and natural surface soil and potential influencing factors such as atmospheric deposition by use of multivariate regression-kriging and generalized linear models. Based on data collected in 1995, 2000, 2005 and 2010 throughout Norway the statistical correlation of a set of potential predictors (elevation, precipitation, density of different land uses, population density, physical properties of soil) with concentrations of cadmium (Cd), mercury and lead in moss and natural surface soil (response variables), respectively, were evaluated. Spatio-temporal trends were estimated by applying generalized linear models and geostatistics on spatial data covering Norway. The resulting maps were used to investigate to what extent the HM concentrations in moss and natural surface soil are correlated. Results. From a set of ten potential predictor variables the modelled atmospheric deposition showed the highest correlation with heavy metals concentrations in moss and natural surface soil. Density of various land uses in a 5 km radius reveal significant correlations with lead and cadmium concentration in moss and mercury concentration in natural surface soil. Elevation also appeared as a relevant factor for accumulation of lead and mercury in moss and cadmium in natural surface soil respectively. Precipitation was found to be a significant factor for cadmium in moss and mercury in natural surface soil. The integrated use of multivariate generalized linear models and kriging interpolation enabled creating heavy metals maps at a high level of spatial resolution. The spatial patterns of cadmium and lead concentrations in moss and natural surface soil in 1995 and 2005 are similar. The heavy metals concentrations in moss and natural surface soil are correlated significantly with high coefficients for lead, medium for cadmium and moderate for mercury. From 1995 up to 2010 the modell
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