In empirical work on multivariate financial time series, it is common to postulate a Multivariate GARCH model. We show that the popular Gaussian quasi-maximum likelihood estimator of MGARCH models is very sensitive to outliers in the data. We propose to use robust M-estimators and provide asymptotic theory for M-estimators of MGARCH models. The Monte Carlo study and empirical application docume...

Two common approaches for estimating a linear trend are 1) simple linear regression and 2) the epoch difference with possibly unequal epoch lengths. The epoch difference estimator for epochs of length M is defined as the difference between the average value over the last M time steps and the average value over the first M time steps divided by N 2 M, where N is the length of the time series. Bo...

The Liu estimator has consistently been demonstrated to be an attractive shrinkage method for reducing the effects of multicollinearity. The Poisson regression model is a well-known model in applications when the response variable consists of count data. However, it is known that multicollinearity negatively affects the variance of the maximum likelihood estimator (MLE) of the Poisson regressio...

Inverse sampling design is generally considered to be appropriate technique when the population is divided into two subpopulations, one of which contains only few units. In this paper, we derive the Horvitz-Thompson estimator for the population mean under inverse sampling designs, where subpopulation sizes are known. We then introduce an alternative unbiased estimator, corresponding to post-st...

Many different robust estimation approaches for the covariance matrix or, say, the shape matrix of multivariate data have been established until today. Tyler’s M-estimator has been recognized as the ‘most robust’ M-estimator for elliptically symmetric distributed data. Essentially, given the class of elliptically symmetric distributions it is a distribution-free MLestimator. We show that this p...

The traditional class of elliptical distributions is extended to allow for asymmetries. A completely robust dispersion matrix estimator (the ‘spectral estimator’) for the new class of ‘generalized elliptical distributions’ is presented. It is shown that the spectral estimator corresponds to an M-estimator proposed by Tyler (1983) in the context of elliptical distributions. Both the generalizati...

In this paper, we propose an NLOS source localization method that utilizes the robust statistics, namely, the α-trimmed mean and Hodges–Lehmann estimator. The root mean squared error average of the proposed methods is similar to that of the other estimators such as M-estimator and Taylor-series maximum likelihood estimator using the median, but the proposed robust estimators have advantages tha...

We introduce a new class of robust estimators for generalized linear models which is an extension of the class of projection estimators for linear regression. These projection estimators are defined using an initial robust estimator for a generalized linear model with only one unknown parameter. We found a bound for the maximum asymptotic bias of the projection estimator caused by a fraction ε ...

We consider robustness for estimation of point processes parameters. An influence functional measures the effect of contamination on estimators. We derive some of its properties, and use it to propose an M-estimator alternative to the MLE for the inhomogeneous Poisson process case. We also show the consistency and asymptotic normality of this estimator.

It is now evident that some robust methods such as MM-estimator do not address the concept of bounded influence function, which means their estimates still be affected by outliers in X directions or high leverage points (HLPs), even though they have efficiency and breakdown point (BDP). The Generalized M(GM) estimator, GM6 estimator put forward with main aim making a bound for HLPs weight funct...