In this paper we consider estimation and unit root testing in AR(1) models with infinite variance innovations. Specifically, we study the asymptotic properties of estimators obtained by dummying out ”large” innovations, i.e. exceeding a given threshold. These estimators reflect the common practice of dealing with large residuals by including impulse dummies in the estimated regression. Iterativ...

We consider benchmarked empirical Bayes (EB) estimators under the basic area-level model of Fay and Herriot while requiring the standard benchmarking constraint. In this paper we determine the excess mean squared error (MSE) from constraining the estimates through benchmarking. We show that the increase due to benchmarking is O(m−1), where m is the number of small areas. Furthermore, we find an...

Huber’s gross-errors contamination model considers the class Fε of all noise distributions F = (1 − ε)Φ + εH, with Φ standard normal, ε ∈ (0, 1) the contamination fraction, and H the contaminating distribution. A half century ago, Huber evaluated the minimax asymptotic variance in scalar location estimation, min ψ max F∈Fε V (ψ, F ) = 1 I(F ∗ ε ) (1) where V (ψ,F ) denotes the asymptotic varian...

In this correspondence, we present a new approach to two-dimensional (2-D) robust spline image smoothing based on the M-estimator algorithm. Unlike in other M-estimator based image processing algorithms, the new algorithm takes into consideration the spatial relations between picture elements. The contribution of the sample to the model depends not only on the current residual of that sample, b...

A class of robust location estimators called weighted randomly trimmed means are introduced and not only their consistency and asymptotic normality are proved, but their influence functions, asymptotic variances and breakdown points are also derived. They possess the same breakdown points as the median, and some of them own higher asymptotic relative efficiencies at the heavy-tailed distributio...

For a regression model Yt = gO(x t) + e t , the unknown function gO is estimated consistently using varying degree polynomial regression. Consistency is with respect to a class of norms similar to weighted Sobolev norms, and the method of proof involves metric entropy calculations that enable the development of rates of convergence in these norms. The estimator is viewed as the solution to some...

There is a vast literature on robust regression estimators, the bulk of which assumes that the dependent (outcome) variable is continuous. Evidently, there are no published results on the impact of tied values in terms of the Type I error probability. A minor goal in this paper to comment generally on problems created by tied values when testing the hypothesis of a zero slope. Simulations indic...

The purpose of this paper is to estimate the intensity of some random measure N on a set X by a piecewise constant function on a finite partition of X . Given a (possibly large) family M of candidate partitions, we build a piecewise constant estimator (histogram) on each of them and then use the data to select one estimator in the family. Choosing the square of a Hellinger-type distance as our ...

This paper presents a signal-to-noise ratio (SNR) estimation algorithm for advanced DVB-RCS systems using adaptive coding and modulation (ACM) in the reverse link of broadband satellite systems. Due to the absence of a repetitive pilot symbol structure, SNR estimation has to be performed using the fixed symbol preamble data. Moreover, sporadic nature of data traffic on the return link causes va...

This paper introduces a new robust technique that simultaneously estimates model parameters and the domain over which the model applies. It removes the implicit assumption of an innnite domain in standard estimation techniques, and is useful in several computer vision problems. Examples include curve tting, image segmentation, and estimating image-to-image transforms. This new technique , calle...