1,721,124 research outputs found
DENSITY-ESTIMATION UNDER THE KOZIOL-GREEN MODEL OF CENSORING BY PENALIZED LIKELIHOOD METHODS
No full textWe propose two density estimators of the survival distribution in the setting of the Koziol-Green random-censoring model. The estimators are obtained by maximum-penalized-likelihood methods, and we provide an algorithm for their numerical evaluation. We establish the strong consistency of the estimators in the Hellinger metric, the L(p)-norms, p = 1,2,-infinity, and a Sobolev norm, under mild conditions on the underlying survival density and the censoring distribution
Minimax estimation of a bounded squared mean
No full textConsider a normal model with unknown mean bounded by a known constant. This paper deals with minimax estimation of the squared mean. We establish an expression for the asymptotic minimax risk. This result is applied in nonparametric estimation of quadratic functionals
Variable bandwidth and local linear-regression smoothers
No full textIn this paper we introduce an appealing nonparametric method for estimating the mean regression function. The proposed method combines the ideas of local linear smoothers and variable bandwidth. Hence, it also inherits the advantages of both approaches. We give expressions for the conditional MSE and MISE of the estimator. Minimization of the MISE leads to an explicit formula for an optimal choice of the variable bandwidth. Moreover, the merits of considering a variable bandwidth are discussed. In addition, we show that the estimator does not have boundary effects, and hence does not require modifications at the boundary. The performance of a corresponding plug-in estimator is investigated. Simulations illustrate the proposed estimation method
Flexible Mean and Dispersion Function Estimation in Extended Generalized Additive Models
Full text linkReal data may expose a larger (or smaller) variability than assumed in an exponential family modeling, the basis of Generalized linear models and additive models. To analyze such data, smooth estimation of the mean and the dispersion function has been introduced in extended generalized additive models using P-splines techniques. This methodology is further explored here by allowing for the modeling of some of the covariates parametrically and some nonparametrically. The main contribution in this article is a simulation study investigating the finite-sample performance of the P-spline estimation technique in these extended models, including comparisons with a standard generalized additive modeling approach, as well as with a hierarchical modeling approach
Loess
No full textLinear least squares regression is among the most well known classical methods. This and other parametric least squares regression models do not perform well when the modeling is too restrictive to capture the nonlinear effect the covariates have on the response. Locally weighted least squares regression (loess) is a modern technique that combines much of the simplicity of the classical least squares method with the flexibility of nonlinear regression. The basic idea behind the method is to model a regression function only locally as having a specific form. This paper discusses the method in the univariate and multivariate case and robustifications of the technique, and provides illustrative examples. © 2010 John Wiley & Sons, Inc
Variable bandwidth and local linear-regression smoothers
No full textIn this paper we introduce an appealing nonparametric method for estimating the mean regression function. The proposed method combines the ideas of local linear smoothers and variable bandwidth. Hence, it also inherits the advantages of both approaches. We give expressions for the conditional MSE and MISE of the estimator. Minimization of the MISE leads to an explicit formula for an optimal choice of the variable bandwidth. Moreover, the merits of considering a variable bandwidth are discussed. In addition, we show that the estimator does not have boundary effects, and hence does not require modifications at the boundary. The performance of a corresponding plug-in estimator is investigated. Simulations illustrate the proposed estimation method
Smooth estimation of mean and dispersion function in extended generalized additive models with application to Italian induced abortion data
Full text linkWe analyse data on abortion rate (AR) in Italy with a particular focus on different behaviours in different regions in Italy. The aim is to try to reveal the relationship between the AR and several covariates that describe in some way the modernity of the region and the condition of the women there. The data are mostly underdispersed and the degree of underdispersion also varies with the covariates. To analyse these data, recent techniques for flexible modelling of a mean and dispersion function in a double exponential family framework are further developed now in a generalized additive model context for dealing with the multivariate set-up. The appealing unified framework and approach even allow to semi-parametric modelling of the covariates without any additional efforts. The methodology is illustrated on ozone-level data and leads to interesting findings in the Italian abortion data
Nonparametric estimation of mean and dispersion functions in extended generalized linear models
Full text linkWe study joint nonparametric estimators of the mean and the dispersion functions in extended double exponential family models. The starting point is the exponential family and the generalized linear models setting. The extended models allow for both overdispersion and underdispersion, or even a combination of both. We simultaneously estimate the dispersion function and the mean function by using P-splines with a difference type of penalty to avoid overfitting. Special attention is given to the smoothing parameter selection as well as to implementation issues. The performance of the method is investigated via simulations. A comparison with other available methods is made. We provide applications to several sets of data, including continuous data, counts and proportions
Robust Estimation of Mean and Dispersion Functions in Extended Generalized Additive Models
Full text linkGeneralized linear models are a widely used method to obtain parametric estimates for the mean function. They have been further extended to allow the relationship between the mean function and the covariates to be more flexible via generalized additive models. However, the fixed variance structure can in many cases be too restrictive. The extended quasilikelihood (EQL) framework allows for estimation of both the mean and the dispersion/variance as functions of covariates. As for other maximum likelihood methods though, EQL estimates are not resistant to outliers: we need methods to obtain robust estimates for both the mean and the dispersion function. In this article, we obtain functional estimates for the mean and the dispersion that are both robust and smooth. The performance of the proposed method is illustrated via a simulation study and some real data examples
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