This paper compares two point estimators of fraction defective of a normal distribution when both population parameters are unknown; the rflinimum variance unbiased estimator, P(z), and the maximum likelihood estimator, F(x). Using minimum mean squared error as a criterion, i t is shown that the choice of estimator depends upon the true value of F(x), and the sample size. In the domain ,0005 5 ...

This paper studies the limiting behavior of Tyler’s and Maronna’s Mestimators, in the regime that the number of samples n and the dimension p both go to infinity, and p/n converges to a constant y with 0 < y < 1. We prove that when the data samples are identically and independently generated from the Gaussian distribution N(0, I), the difference between 1 n ∑n i=1 xix T i and a scaled version o...

In finite sample studies redescending M -estimators outperform bounded M -estimators (see for example, Andrews et al., 1972). Even though redescenders arise naturally out of the maximum likelihood approach if one uses very heavy-tailed models, the commonly used redescenders have been derived from purely heuristic considerations. Using a recent approach proposed by Shurygin, we studied the optim...

The breakdown point behavior of M-estimators in linear models with xed designs, arising from planned experiments or qualitative factors, is characterized. Particularly, this behavior at xed designs is quite diierent from that at designs which can be corrupted by outliers|the situation prevailing in the literature. For xed designs, the breakdown points of robust M-estimators (those with bounded ...

In this paper we propose an estimator of the entropy of a continuous random variable. The estimator is obtained by modifying the estimator proposed by Vasicek (1976). Consistency of estimator is proved, and comparisons are made with Vasicek’s estimator (1976), van Es’s estimator (1992), Ebrahimi et al.’s estimator (1994) and Correa’s estimator (1995). The results indicate that the proposed esti...

Rényi entropy is an information-theoretic measure of randomness which is fundamental to several applications. Several estimators of Rényi entropy based on k-nearest neighbor (kNN) based distances have been proposed in literature. For d-dimensional densities f , the variance of these Rényi entropy estimators of f decay as O(M), whereM is the sample size drawn from f . On the other hand, the bias...

Global motion estimation is an important task in a variety of video processing applications, such as coding, segmentation, classification/indexing or mosaicing. Due to the possible presence of differently moving foreground objects and other sources of distortions, robust methods such as M-estimators have to be applied. We present a simplified implementation of a robust M-estimator for global mo...

We propose an estimator for the CDF G of the sojourn time in a steady-state M/G/∞ queueing system, when the available data consists of the arrival and departure epochs alone, without knowing which arrival corresponds to which departure. The estimator is a generalization of an estimator proposed by Brown (1970), and is based on a functional relationship between G and the distribution of the time...

We propose a simple and semi-parametric estimator for the tail index of a regular varying elliptical random vector. Since, for univariate random variables, our estimator boils down to the Hill estimator and it inherits the simplicity and asymptotic properties, we name it after Bruce M. Hill. The estimator is based on the distance between an elliptical probability contour and the outer – or exce...

High-dimensional time-series data from a wide variety of domains, such as neuroscience, are being generated every day. Fitting statistical models to such data, to enable parameter estimation and time-series prediction, is an important computational primitive. Existing methods, however, are unable to cope with the high-dimensional nature of these data, due to both computational and statistical r...