Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userSemiparametric Mixture Regression with Unspecified Error Distributions
66
0
0.0
(
0
)
Added by
Weixin Yao
Publication date
2018
fields
Mathematical Statistics
and research's language is
English
Ask ChatGPT about the research
No Arabic abstract
In fitting a mixture of linear regression models, normal assumption is traditionally used to model the error and then regression parameters are estimated by the maximum likelihood estimators (MLE). This procedure is not valid if the normal assumption is violated. To relax the normal assumption on the error distribution hence reduce the modeling bias, we propose semiparametric mixture of linear regression models with unspecified error distributions. We establish a more general identifiability result under weaker conditions than existing results, construct a class of new estimators, and establish their asymptotic properties. These asymptotic results also apply to many existing semiparametric mixture regression estimators whose asymptotic properties have remained unknown due to the inherent difficulties in obtaining them. Using simulation studies, we demonstrate the superiority of the proposed estimators over the MLE when the normal error assumption is violated and the comparability when the error is normal. Analysis of a newly collected Equine Infectious Anemia Virus data in 2017 is employed to illustrate the usefulness of the new estimator.
rate research
Read More
It is possible to approach regression analysis with random covariates from a semiparametric perspective where information is combined from multiple multivariate sources. The approach assumes a semiparametric density ratio model where multivariate distributions are regressed on a reference distribution. A kernel density estimator can be constructed from many data sources in conjunction with the semiparametric model. The estimator is shown to be more efficient than the traditional single-sample kernel density estimator, and its optimal bandwidth is discussed in some detail. Each multivariate distribution and the corresponding conditional expectation (regression) of interest are estimated from the combined data using all sources. Graphical and quantitative diagnostic tools are suggested to assess model validity. The method is applied in quantifying the effect of height and age on weight of germ cell testicular cancer patients. Comparisons are made with multiple regression, generalized additive models (GAM) and nonparametric kernel regression.
This paper introduces and analyzes a stochastic search method for parameter estimation in linear regression models in the spirit of Beran and Millar (1987). The idea is to generate a random finite subset of a parameter space which will automatically contain points which are very close to an unknown true parameter. The motivation for this procedure comes from recent work of Duembgen, Samworth and Schuhmacher (2011) on regression models with log-concave error distributions.
As a competitive alternative to least squares regression, quantile regression is popular in analyzing heterogenous data. For quantile regression model specified for one single quantile level $tau$, major difficulties of semiparametric efficient estimation are the unavailability of a parametric efficient score and the conditional density estimation. In this paper, with the help of the least favorable submodel technique, we first derive the semiparametric efficient scores for linear quantile regression models that are assumed for a single quantile level, multiple quantile levels and all the quantile levels in $(0,1)$ respectively. Our main discovery is a one-step (nearly) semiparametric efficient estimation for the regression coefficients of the quantile regression models assumed for multiple quantile levels, which has several advantages: it could be regarded as an optimal way to pool information across multiple/other quantiles for efficiency gain; it is computationally feasible and easy to implement, as the initial estimator is easily available; due to the nature of quantile regression models under investigation, the conditional density estimation is straightforward by plugging in an initial estimator. The resulting estimator is proved to achieve the corresponding semiparametric efficiency lower bound under regularity conditions. Numerical studies including simulations and an example of birth weight of children confirms that the proposed estimator leads to higher efficiency compared with the Koenker-Bassett quantile regression estimator for all quantiles of interest.
In this paper, we focus on the variable selection techniques for a class of semiparametric spatial regression models which allow one to study the effects of explanatory variables in the presence of the spatial information. The spatial smoothing problem in the nonparametric part is tackled by means of bivariate splines over triangulation, which is able to deal efficiently with data distributed over irregularly shaped regions. In addition, we develop a unified procedure for variable selection to identify significant covariates under a double penalization framework, and we show that the penalized estimators enjoy the oracle property. The proposed method can simultaneously identify non-zero spatially distributed covariates and solve the problem of leakage across complex domains of the functional spatial component. To estimate the standard deviations of the proposed estimators for the coefficients, a sandwich formula is developed as well. In the end, Monte Carlo simulation examples and a real data example are provided to illustrate the proposed methodology. All technical proofs are given in the supplementary materials.
The aim of this paper is to present a mixture composite regression model for claim severity modelling. Claim severity modelling poses several challenges such as multimodality, heavy-tailedness and systematic effects in data. We tackle this modelling problem by studying a mixture composite regression model for simultaneous modeling of attritional and large claims, and for considering systematic effects in both the mixture components as well as the mixing probabilities. For model fitting, we present a group-fused regularization approach that allows us for selecting the explanatory variables which significantly impact the mixing probabilities and the different mixture components, respectively. We develop an asymptotic theory for this regularized estimation approach, and fitting is performed using a novel Generalized Expectation-Maximization algorithm. We exemplify our approach on real motor insurance data set.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
