The performance of the adaptive optimal estimator under the extended balanced loss function

The adaptive optimal estimator of Farebrother (1975) is discussed by many authors, but the goodness of fitted model criterion that is used to investigate the performance of estimators is quite often ignored. Shalabh, Toutenburg, and Heumann (2009) proposed the extended balanced loss function in which the mean squared error and the Zellner's balanced loss function are just special cases of it. In this paper, we discuss the performance of the adaptive optimal estimator of Farebrother (1975) under the extended balanced loss function. Moreover, a Monte Carlo simulation experiment is conducted to examine the performance of the estimator in finite samples.     

Statistical theory of the analysis of experimental designs

(Abstracts of papers presented at the Annual Meeting of the Statistical Science Association of Canada; May 29, 30, 31, 1975. / R$eAsum$eAs des articles pr$eAsent$eAs au congres annuel; 29, 30, 31 mai 1975; University of Alberta, Edmonton, Alberta.)     

On the minimum mean squared error estimators in a regression model

In this paper we analyze the properties of two estimators oroposed by Farebrother (1975) for linear regression models.     

A note on the solution of sample size problems using the Odeh and Fox charts

The usefulness of the Odeh and Fox (1975) charts is much enhanced by having φ for v₂ = ∞, a value quickly found from a table of Haynam, Govindarajulu and Leone (1970).     

A note on the geometry of kullback-leibler information numbers

Csiszar (1975) has shown thdt kullhack-Leibler information numbers possess some geometrical properties much like those in Euclidean geometry. Thls paper extends these results by characterizing the shortest line between two ditributions as well as the midpoit of the line.     

Multicollinearity and the value of a priori information

A measure of multicollinearity is defined which is useful in evaluating maintained hypotheses and aiding estimator selection as it suggests when a non-traditional estimator proposed by Bock (1975) is minimax and dominates ordinary least squares. An example is used to illustrate the presented methodology.     

A note on the admissibility of relative to the linex loss function

The purpose of this note is to give a correct proof of a result in Rojo (1987). Let 2 be the mean of a random sample of size n from a normal 2 distribution with unknown mean 0 and known variance o . Following earlier work by Zellner (1986), Rojo (1987) considered the admissibility of the linear estimator c; + d relative to Variants (1975) asymmetric LINEX loss function     

On the robustness of the optimum balanced 2m factorial designs of resolution v (given by Srivastava and Chopra) in the presence of outliers

In this paper we study the sensitivity of the optimum balanced resolution V plans for 2^m factorials, to outliers, using the measure suggested by Box and Drapper (1975). We observe that the designs are robust, i.e., have low sensitivity.     

Comparing the relative efficiency of three sequential procedures

We consider the sequential procedures developed by Robbins and Siegmund (1974), Louis (1975) and Zoubeidi (1992) for comparing the means of two treatments. We let the procedures have equal power functions and compare their Bayes and minimax risks using the invariance property of their power functions. For each of several formulations of the problem we determine the most relatively efficient procedure and compute its expected total sample size.     

A Survey regarding the Reporting of Simulation Studies

Hoaglin and Andrews (1975) proposed standards for computational practice and the reporting of computation-based studies. They observed that “statisticians … often pay too little attention to their own principles of design.” To see if the design and reporting had improved, we surveyed five major statistical journals for 1975, 1978, and 1981 to ascertain whether reported simulation studies involved a specified design, justified the choice of the number of iterations, and specified the random number generator(s) used. Eighteen percent of the 1,198 papers surveyed included results based on simulation. We found that 9% of the papers including a simulation study justified the choice of the number of iterations and 44% at least partially specified the random number generator. Hoaglin and Andrews's observation appears still to be true.     

Estimation of the mean of an exponential distribution in the presence of an outlier

Kale and Sinha (1971) have found an estimator of the mean of an exponential distribution in the présence of an outlying observation with higher expected value. Here an alternative estimator of the mean is proposed and it is compared with the estimator of Kale and Sinha (1971) and the maximum likelihood estimator given by Kale (1975). The proposed estimator is found to be more efficient than the latter two estimators in some cases.     

On the Cusum test for parameter changes in garch(1,1) Models

This paper considers the problem of testing parameter constancy in GARCH(1,1) models. A cusum of squares test is propesed in analogy Of Incl´n and Tiao (1394)'s statistic. its limiting distribution is derived via using the invariance principle for mixingaie sequences obtained by McLeish(1975). Simulation results are illustrated to demonstrate the validity of the cusum test.     

Percentage points and power calculations for outlier tests in a regression situation

The usefulness of an extra sum of squares statistics Q_K for detecting K outliers has been discussed previously in the context of two-way tables. (See Gentleman and Wilk, 1975a, 1975b; John and Draper 1978; and Draper and John, 1980,) That work is extended here to straight line regression situations arising from, and motivated by, a specific set of research data. Percentage points for the appropriate test statistics are obtained by simulation, and approximations for these percentage points are suggested. Power calculations made for various designs and outlier situations are briefly summarized.     

On the factorial approach providing the true index of cost of living: an interpretation of a special pair of equations

This note presents an interpretation of a special pair of the six equations which were derived in the context of providing the true index of cost of living through what has been called “the factorial approache”[See Banerjee (1961a,b) and Banerjee (1975).]     

Further remarks on estimating the parameter of a noncentral chi-square distribution

Perlman and Rasmussen (1975) have found estimators of the non-centrality parameter of a noncentral chi-square distribution which have lower mean square error than the maximum likelihood estimator. This paper studies some extensions of their estimators and some related problems.     

A unification of tail estimators

This work considers estimators of the tails of the cdf, quantile function and edf, which are generally applicable because they use only those observations in the sample which exceed a high threshold value. Three seemingly different approaches have been proposed by Hill (1975), Hall (1982), and Pickands (1975). Herein the tail behavior of the underlying probability model is expressed using the density-quantile function. This general tail behavior model is shown to be a common origin for the parametric models proposed by Hill, Hall, and Pickands' GPD model. Further, this tail behavior model motivates a representation for the quantile function of the exceedences which is used to obtain a parametric model for tail estimates using the exceedences which unifies the seemingly different tail estimators mentioned above.     

A note on the universal optimality criterion for full rank models

The aim of this note is to suggest a revised formulation of the universal optimality criterion for full rank models as stated in Kiefer (1975). We have presented the relevant results with indications of some possible applications.     

Regional types of mortality order in the light of statistical analysis of main components

This is an analysis of abbreviated life tables for Polish regions for 1973 to 1975. Life tables are given for 49 voivodships by age groups, and data on average life expectancies are provided.     

Statistical inference about the shape parameter of the exponential power distribution

After being proposed by Smith & Bain (1975), the exponential power distribution has been discussed by many authors. This paper proposes a simple exact statistical test for the shape parameter of an exponential power distribution, as well as an exact confidence interval for the same parameter. Necessary critical values of the test are given. The method provided in this paper can be used for type II censored data. Comparing this method to the existing approaches, this method requires less calculation or less tables, and is easier to use in practice.     

Equivariance of ridge estimators through standardization,a note

We show that standardization of data recommended for Ridge Regression (RR) by Hoerl and Kennard (1970 a8b), Marquardt and Snee (1975), and others is worthwhile despite the criticisms by Swamy, Mehta and Rappoport (SMR) (1978).