George W. Snedecor,Pioneer Statistician, 1881–1974

Users of statistical packages need to be aware of the influence that outlying data points can have on their statistical analyses. Robust procedures provide formal methods to spot these outliers and reduce their influence. Although a few robust procedures are mentioned in this article, one is emphasized; it is motivated by maximum likelihood estimation to make it seem more natural. Use of this procedure in regression problems is considered in some detail, and an approximate error structure is stated for the robust estimates of the regression coefficients. A few examples are given. A suggestion of how these techniques should be implemented in practice is included.     

Effects of non-normality and mild heteroscedasticity on estimators in regression

Several estimators are examined for the simple linear regression model under a controlled, experimental situation with multiple observations at each design point. The model is examined under normal and non-normal error distributions and mild heterogeneity of variances across the chosen design points. We consider the ordinary, generalized, and estimated generalized least squares estimators and several examples of M estimators. The asymptotic properties of the M estimator using the Huber ψ are presented under these conditions for the multiple regression model. A simulation study is also presented which indicates that the M estimator possesses strong robustness properties under the presence of both non-normality and mild heteroscedasticity o£ errors. Finally, the M estimates are compared to the least squares estimates in two examples.     

Constructing estimators of a mean vector through orthogonal reparametrization and differential equations

The simultaneous estimation of a mean vector is explored by reparametrizing it into its direction and norm components. A type of Pythagorean relation is employed to construct an estimate of the norm component, which results in solving an ordinary amerenuai equation, me james-Diem estimator is snown to be optimum in a class of estimators derived from general solutions of the ordinary differential equation. A new Stein-type estimator in the case of the inverse Gaussian distribution is constructed.     

On location and scale parameters of exponential distributions with censored observations

In this paper we first address the problem of estimating the common scale of several exponential distributions with unknown location parameters when censored samples are observed. The improved estimators are basically Stein type testimators. These testimators are then used to construct improved estimators of location parameters.     

AN ESTIMATION PROCEDURE FOR ERROR VARIANCE INCORPORATING PTS FOR RANDOM EFFECTS MODEL UNDER LINEX LOSS FUNCTION

In the present paper an estimator of the error variance for a three-way layout in random effects model incorporating two preliminary tests of significance has been proposed. It has been well recognized that estimation of parameters, of interest under asymmetric loss function (ASL) is generally better than that under squared error loss function (SELF), particularly where overestimation and underestimation are not equally penalised. As neither overestimation nor underestimation of error variance is desirable, with this motivation, the proposed estimator for the error variance has been studied under LINEX loss function. It is claimed that, with proper choice of degree of asymmetry and level of significance, proposed the sometimes pool estimator performs fairly better than unbiased estimator. Recommendations regarding its application have been attempted.     

Unbiasedness of fourier integral estimator under weaker assumptions

The Fourier integral estimator (FIE) of the hazard rate function have been introduced by Singpurwalla and Wong (1983) in order to improve the rate of convergence of mean square error. However, the asymptotic properties are derived under several assumptions. These assumptions are too strong to be satisfied in most applications. The situation becomes worse when some of these assumptions appear contradictory to each other. This greatly limits the usage of FIE. This paper endeavors to release or weaken some of these assumptions and therefore expand the applicable coverage of FIE.     

Maximum-likelihood-schätzungen für parameter in homogenen markovschen ketten

A class of homogeneous MARKOV chains with arbitrary intial distributions is considered, which in general contains also the class treated by BILLINGSLEY [2]. The existence of strongly consistent and asymptotically normal maximum-likelihood estimates for unknown parameters is shown. Also the case of a random sample size is treated.     

A note on estimation of the shape of density level sets of star-shaped distributions

Elliptically contoured distributions generalize the multivariate normal distributions in such a way that the density generators need not be exponential. However, as the name suggests, elliptically contoured distributions remain to be restricted in that the proportional density level sets ought to be ellipsoids. In star-shaped distributions, this restriction is relaxed and the density level sets are allowed to be boundaries of arbitrary proportional star-shaped sets. In this note, we propose a non parametric estimator of the shape of density level sets of star-shaped distributions, and prove its strong consistency with respect to the Hausdorff distance. We illustrate our estimator with simulated and real data.