ARFIMA processes and outliers: a weighted likelihood approach

In this paper, we consider the problem of robust estimation of the fractional parameter, d, in long memory autoregressive fractionally integrated moving average processes, when two types of outliers, i.e. additive and innovation, are taken into account without knowing their number, position or intensity. The proposed method is a weighted likelihood estimation (WLE) approach for which needed definitions and algorithm are given. By an extensive Monte Carlo simulation study, we compare the performance of the WLE method with the performance of both the approximated maximum likelihood estimation (MLE) and the robust M-estimator proposed by Beran (Statistics for Long-Memory Processes, Chapman & Hall, London, 1994). We find that robustness against the two types of considered outliers can be achieved without loss of efficiency. Moreover, as a byproduct of the procedure, we can classify the suspicious observations in different kinds of outliers. Finally, we apply the proposed methodology to the Nile River annual minima time series.     

Robust stepwise regression

The selection of an appropriate subset of explanatory variables to use in a linear regression model is an important aspect of a statistical analysis. Classical stepwise regression is often used with this aim but it could be invalidated by a few outlying observations. In this paper, we introduce a robust F-test and a robust stepwise regression procedure based on weighted likelihood in order to achieve robustness against the presence of outliers. The introduced methodology is asymptotically equivalent to the classical one when no contamination is present. Some examples and simulation are presented.     

Weighted likelihood latent class linear regression

Statistical Methods & Applications - A weighted likelihood approach for robust fitting of a finite mixture of linear regression models is proposed. An EM type algorithm and its variant based on...     

Robust multivariate diagnostics for PLSR and application on high dimensional spectrally overlapped drug systems

ABSTRACT

Statistical methods are effectively used in the evaluation of pharmaceutical formulations instead of laborious liquid chromatography. However, signal overlapping, nonlinearity, multicollinearity and presence of outliers deteriorate the performance of statistical methods. The Partial Least Squares Regression (PLSR) is a very popular method in the quantification of high dimensional spectrally overlapped drug formulations. The SIMPLS is the mostly used PLSR algorithm, but it is highly sensitive to outliers that also effect the diagnostics. In this paper, we propose new robust multivariate diagnostics to identify outliers, influential observations and points causing non-normality for a PLSR model. We study performances of the proposed diagnostics on two everyday use highly overlapping drug systems: Paracetamol–Caffeine and Doxylamine Succinate–Pyridoxine Hydrochloride.     

Robust Inference in Generalized Linear Models

Robust inference on the parameters in generalized linear models is performed using the weighted likelihood method. Two cases are considered: a case with replicated observations and a case with a single observation of the dependent variable for each combination of the explanatory variables. The first case is common in the design of experiments, while the second case arises in observational studies. Theoretical and computational results on real datasets are presented and compared with other existing techniques.     

Weighted likelihood mixture modeling and model-based clustering

Statistics and Computing - A weighted likelihood approach for robust fitting of a mixture of multivariate Gaussian components is developed in this work. Two approaches have been proposed that are...     

Bias bound for the minimax estimator

The bias bound function of an estimator is an important quantity in order to perform globally robust inference. We show how to evaluate the exact bias bound for the minimax estimator of the location parameter for a wide class of unimodal symmetric location and scale family. We show, by an example, how to obtain an upper bound of the bias bound for a unimodal asymmetric location and scale family. We provide the exact bias bound of the minimum distance/disparity estimators under a contamination neighborhood generated from the same distance.