Related papers: A robust approach for generalized linear models ba…

Beta regression models are widely used for modeling continuous data limited to the unit interval, such as proportions, fractions, and rates. The inference for the parameters of beta regression models is commonly based on maximum likelihood…

The generalised linear model (GLM) is a very important tool for analysing real data in biology, sociology, agriculture, engineering and many other application domain where the relationship between the response and explanatory variables may…

We propose regularization methods for linear models based on the $L_q$-likelihood, which is a generalization of the log-likelihood using a power function. Some heavy-tailed distributions are known as $q$-normal distributions. We find that…

We propose a robust variable selection procedure using a divergence based M-estimator combined with a penalty function. It produces robust estimates of the regression parameters and simultaneously selects the important explanatory…

Highly robust and efficient estimators for the generalized linear model with a dispersion parameter are proposed. The estimators are based on three steps. In the first step the maximum rank correlation estimator is used to consistently…

Generalized Linear Models are routinely used in data analysis. The classical procedures for estimation are based on Maximum Likelihood and it is well known that the presence of outliers can have a large impact on this estimator. Robust…

A weighted likelihood technique for robust estimation of a multivariate Wrapped Normal distribution for data points scattered on a p-dimensional torus is proposed. The occurrence of outliers in the sample at hand can badly compromise…

In this article, we propose a novel logistic quasi-maximum likelihood estimation (LQMLE) for general parametric time series models. Compared to the classical Gaussian QMLE and existing robust estimations, it enjoys many distinctive…

Bai (2010) and Bai et al. (2012) proposed robust mixture regression method based on the M regression estimation. However, the M-estimators are robust against the outliers in response variables, but they are not robust against the outliers…

Model averaging is an alternative to model selection for dealing with model uncertainty, which is widely used and very valuable. However, most of the existing model averaging methods are proposed based on the least squares loss function,…

This article introduces a robust hypothesis testing procedure: the Lq-likelihood-ratio-type test (LqRT). By deriving the asymptotic distribution of this test statistic, the authors demonstrate its robustness both analytically and…

Parameter estimation with the maximum $L_q$-likelihood estimator (ML$q$E) is an alternative to the maximum likelihood estimator (MLE) that considers the $q$-th power of the likelihood values for some $q<1$. In this method, extreme values…

Generalized linear models (GLMs) form one of the most popular classes of models in statistics. The gamma variant is used, for instance, in actuarial science for the modelling of claim amounts in insurance. A flaw of GLMs is that they are…

In this article, we consider the parameter estimation of regression model with pth order autoregressive (AR(p)) error term. We use the Maximum Lq-likelihood (MLq) estimation method that is proposed by Ferrari and Yang (2010a), as a robust…

Ordinary least square (OLS), maximum likelihood (ML) and robust methods are the widely used methods to estimate the parameters of a linear regression model. It is well known that these methods perform well under some distributional…

The maximum likelihood principle is widely used in statistics, and the associated estimators often display good properties. indeed maximum likelihood estimators are guaranteed to be asymptotically efficient under mild conditions. However in…

Generalized linear models (GLMs) are fundamental tools for statistical modeling, with maximum likelihood estimation (MLE) serving as the classical approach for parameter inference. While MLE performs well for canonical GLMs, it can become…

We consider model selection in generalized linear models (GLM) for high-dimensional data and propose a wide class of model selection criteria based on penalized maximum likelihood with a complexity penalty on the model size. We derive a…

We consider the parameter estimation problem of a probabilistic generative model prescribed using a natural exponential family of distributions. For this problem, the typical maximum likelihood estimator usually overfits under limited…

Linear mixed models (LMMs) are a popular class of methods for analyzing longitudinal and clustered data. However, such models can be sensitive to outliers, and this can lead to biased inference on model parameters and inaccurate prediction…