For generalized linear models （GLM）, in case the regressors are stochastic and have different distributions, the asymptotic properties of the maximum likelihood estimate （MLE） β^n of the parameters are studied. U...
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For generalized linear models （GLM）, in case the regressors are stochastic and have different distributions, the asymptotic properties of the maximum likelihood estimate （MLE） β^n of the parameters are studied. Under reasonable conditions, we prove the weak, strong consistency and asymptotic normality of β^n
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
The quasi-likelihood method has emerged as a useful approach to the parameter estimation of generalized linear models (GLM) in circumstances where there is insufficient distributional information to construct a likeli...
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The quasi-likelihood method has emerged as a useful approach to the parameter estimation of generalized linear models (GLM) in circumstances where there is insufficient distributional information to construct a likelihood function. Despite its flexibility, the quasi-likelihood approach to GLM is currently designed for an aggregate-sample analysis based on the assumption that the entire sample of observations is taken from a single homogenous population. Thus, this approach may not be suitable when heterogeneous subgroups exist in the population, which involve qualitatively distinct effects of covariates on the response variable. In this paper, the quasi-likelihood GLM approach is generalized to a fuzzy clustering framework which explicitly accounts for such cluster-level heterogeneity. A simple iterative estimation algorithm is presented to optimize the regularized fuzzy clustering criterion of the proposed method. The performance of the proposed method in recovering parameters is investigated based on a Monte Carlo analysis involving synthetic data. Finally, the empirical usefulness of the proposed method is illustrated through an application to actual data on the coupon usage behaviour of a sample of consumers.
We study the problem of recovering an unknownsignal x givenmeasurements obtained from a generalizedlinear model with a Gaussian sensing matrix. Two popular solutions are based on a linear estimator (x) over cap (L) a...
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We study the problem of recovering an unknownsignal x givenmeasurements obtained from a generalizedlinear model with a Gaussian sensing matrix. Two popular solutions are based on a linear estimator (x) over cap (L) and a spectral estimator (x) over cap (s). The former is a data-dependent linear combination of the columns of the measurement matrix, and its analysis is quite simple. The latter is the principal eigenvector of a data-dependent matrix, and a recent line of work has studied its performance. In this paper, we show howto optimally combine (x) over cap (L) and (x) over cap (s). At the heart of our analysis is the exact characterization of the empirical joint distribution of (x, (x) over cap (L), (x) over cap (s)) in the high-dimensional limit. This allows us to compute the Bayes-optimal combination of (x) over cap (L) and (x) over cap (s), given the limiting distribution of the signal x. When the distribution of the signal is Gaussian, then the Bayes-optimal combination has the form. (x) over cap (L) + (x) over cap (s) and we derive the optimal combination coefficient. In order to establish the limiting distribution of ( x, (x) over cap (L), (x) over cap (s)), we design and analyze an approximate message passing algorithm whose iterates give (x) over cap (L) and approach (x) over cap (s). Numerical simulations demonstrate the improvement of the proposed combination with respect to the two methods considered separately.
A two-phase bootstrap method is proposed for correcting covariate measurement error. Two data sets are needed: validation data for approximating the measurement model and data with a response variable. Bootstrap sampl...
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A two-phase bootstrap method is proposed for correcting covariate measurement error. Two data sets are needed: validation data for approximating the measurement model and data with a response variable. Bootstrap samples from both the data sets validation data are taken. Parameter estimates of the generalizedlinear model are calculated using expectations of the measurement model from the validation data as explanatory variables. The method is compared through simulation in logistic regression with the correction method proposed by Rosner, Willet, and Spiegelman (1991, Statistics in Medicine 8, 1051-1069). A real data example is also presented.
This paper extends the statistical method known as generalizedlinear Bayesian modeling developed by Adrian Raftery to the comparison of generalized linear models across multiple groups. The extension considers all re...
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This paper extends the statistical method known as generalizedlinear Bayesian modeling developed by Adrian Raftery to the comparison of generalized linear models across multiple groups. The extension considers all relevant hierarchical models in the model space and tests parameter equality across groups by using Bayesian posterior information from the models. The conclusion drawn by using the proposed approach tends to be more conservative than Raftery's method and the conventional likelihood ratio test, as the examples demonstrates. (C) 2002 Elsevier Science B.V. All rights reserved.
A direct extension of the approach described in Self, Mauritsen, and Ohara (1992, Biometrics 48, 31-39) for power and sample size calculations in generalized linear models is presented. The major feature of the propos...
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A direct extension of the approach described in Self, Mauritsen, and Ohara (1992, Biometrics 48, 31-39) for power and sample size calculations in generalized linear models is presented. The major feature of the proposed approach is that the modification accommodates both a finite and an infinite number of covariate configurations. Furthermore, for the approximation of the noncentrality of the noncentral chi-square distribution for the likelihood ratio statistic, a simplification is provided that not only reduces substantial computation but also maintains the accuracy. Simulation studies are conducted to assess the accuracy for various model configurations and covariate distributions.
In regression modeling, often a restriction that regression coefficients are non-negative is faced. The problem of model selection in non-negative generalized linear models (NNGLM) is considered using lasso, where reg...
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In regression modeling, often a restriction that regression coefficients are non-negative is faced. The problem of model selection in non-negative generalized linear models (NNGLM) is considered using lasso, where regression coefficients in the linear predictor are subject to non-negative constraints. Thus, non-negatively constrained regression coefficient estimation is sought by maximizing the penalized likelihood (such as the l(1)-norm penalty). An efficient regularization path algorithm is proposed for generalized linear models with non-negative regression coefficients. The algorithm uses multiplicative updates which are fast and simultaneous. Asymptotic results are also developed for the constrained penalized likelihood estimates. Performance of the proposed algorithm is shown in terms of computational time, accuracy of solutions and accuracy of asymptotic standard deviations. (C) 2016 Elsevier B.V. All rights reserved.
One of the popular method for fitting a regression function is regularization: minimizing an objective function which enforces a roughness penalty in addition to coherence with the data. This is the case when formulat...
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One of the popular method for fitting a regression function is regularization: minimizing an objective function which enforces a roughness penalty in addition to coherence with the data. This is the case when formulating penalized likelihood regression for exponential families. Most of the smoothing methods employ quadratic penalties, leading to linear estimates, and are in general incapable of recovering discontinuities or other important attributes in the regression function. In contrast, non-linear estimates are generally more accurate. In this paper, we focus on non-parametric penalized likelihood regression methods using splines and a variety of non-quadratic penalties, pointing out common basic principles. We present an asymptotic analysis of convergence rates that justifies the approach. We report on a simulation study including comparisons between our method and some existing ones. We illustrate our approach with an application to Poisson non-parametric regression modeling of frequency counts of reported acquired immune deficiency syndrome (AIDS) cases in the UK.
The paper presents the method of moments estimation for generalizedlinear measurement error models using the instrumental variable approach. The measurement error has a parametric distribution that is not necessarily...
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The paper presents the method of moments estimation for generalizedlinear measurement error models using the instrumental variable approach. The measurement error has a parametric distribution that is not necessarily normal, while the distributions of the unobserved covariates are nonparametric. We also propose simulation-based estimators for the situation where the closed forms of the moments are not available. The proposed estimators are strongly consistent and asymptotically normally distributed under some regularity conditions. Finite sample performances of the estimators are investigated through simulation studies.
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