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Abstract: This paper studies estimation in the proportional odds model, with time-dependent covariates, based on right-censored data. The estimation procedure is an extension of the Yang and Prentice (J. Amer. Statist. Assoc. 94 (1999) 125) approach to the time-dependent covariate case. The proposed estimators include a class of minimum distance estimators defined through weighted empirical odds function. These estimators are shown to be strongly consistent and asymptotically normal, with variances that can be consistently estimated. It also contains a simulation study making comparison of some of the estimators in the class. [Copyright &y& Elsevier]

For the task of “optimal” estimation of a (vector) parameter we consider two Pitman closeness type criterions. The first one uses the generalized Pitman closeness measure (see e.g., Saleh and Sen, 1991). The second one has been introduced by Ghosh and Sen (1991) and independently by Nayak (1991); we call it the average generalized closeness criterion. Pitman closeness type comparisons suffer from non transitivity in general. Nevertheless, within very general classes of pre-test estimators (PTE) we prove transitivity and other useful properties for the two criterions. Further, we restrict ourselves to linear regression models. We compare the ordinary least squares estimator with the restricted least squares estimator employing one restriction and discuss existence of best PTE corresponding to these models under the criterions mentioned above. [ABSTRACT FROM AUTHOR]

Based on one observation X from a N(θ, θ) distribution where θ(> 0) is an unknown parameter, this article provides an exact expression of the minimum variance unbiased estimator of θ based on the complete and sufficient statistic ∣X∣. Even though N(θ, θ) belongs to a one-parameter exponential family, I discuss some small surprises and intricacies that are worth noting. [ABSTRACT FROM AUTHOR]

If (X, Y) is an observation with distribution function F(x - θ, y), σ² = var(X), ρ = corr(X, Y) and I is the Fisher information on θ in (X, Y), then I ≧ {σ²(1 - ρ²)}-1. The equality sign holds under conditions closely related to the conditions for linearity of the Pitman estimator of θ from a sample from F(x - θ, y). The results are extensions of earlier results for the case when only the informative component X is observed. [ABSTRACT FROM AUTHOR]

The Pitman estimators for ordered scale parameters of two Pareto distributions are obtained here. In case of known ordering that have been modified using more informative priors, and found to be better in terms of risks. Some new estimators are also proposed and show that they improve upon Pitman estimators. The results were also verified by simulation study. [ABSTRACT FROM AUTHOR]

Independent random samples are drawn from k ( ≥ 2) normal populations having means Θ 1 ,..., Θ k ; Θ 1 ≤ Θ 2 ≤ · · · ≤ Θ k and known variances . Estimation of Θ = (Θ 1 ,..., Θ k ) with respect to the norm squared error loss is considered. Let δ p be the analog of the Pitman estimator of Θ, that is, the generalized Bayes estimator of Θ with respect to the uniform prior on the restricted space Ω = {Θ: Θ 1 ≤ Θ 2 ≤ · · · ≤ Θ k }. It has been proved earlier that when the ′s are equal, δ p is minimax. Here we exhibit for k = 3, that when ′s are unequal, the minimaxity of δ p may fail to hold. Furthermore, the risk performance of δ p is compared numerically with that of the restricted maximum likelihood estimator δ MLE and the usual estimator X = ( X 1 , X 2 , X 3 ). [ABSTRACT FROM AUTHOR]

This paper proposes a class of non-parametric test procedures for testing the null hypothesis that two distributions, F and G, are equal versus the alternative hypothesis that F is ‘more NBU (new better than used) at specified age t0’ than G. Using Hoeffding's two-sample U-statistic theorem, it establishes the asymptotic normality of the test statistics and produces a class of asymptotically distribution-free tests. Pitman asymptotic efficacies of the proposed tests are calculated with respect to the location and shape parameters. A numerical example is provided for illustrative purposes. [ABSTRACT FROM AUTHOR]

The importance of chord span for estimations of closeness (similarity or resemblance) was examined. The subjects (musically trained and less-trained) were asked to rate closeness between pentachords with spans varying from 6 to 22 semitones. Closeness estimations were found to be only weakly correlated with theoretical similarities calculated by eleven similarity measures. The factors that did guide closeness estimations were analysed using regression analysis and multidimensional scaling. Chord span, common pitches and set-class identity were found to be factors guiding estimations in both subject subgroups. Additional factors guiding the estimations of the trained group were the degree of dissonance, chord voicing and common pitch classes. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the effects of cross-sectional disturbance correlation in a homogeneous panel data unit root test. As reported by other authors, the unit root test has incorrect size in the presence of cross-sectional correlation. We suggest that a previously known estimator can be used to reduce the size distortions. We supply response surface estimates for critical values and study the size characteristics of the proposed test. We find that the suggested estimator performs well in small-sample homogeneous panel data unit root tests. The reduction in size distortion comes at a small cost of lower power against a stationary alternative. [ABSTRACT FROM AUTHOR]

Control charts are used widely to distinguish between random and assignable causes of variation in the process, i.e., they are used to monitor for permanent shifts in the process. However, a control chart does not indicate the exact time when such a shift occurs. Since a shift in the process usually occurs much earlier before it is detected, the search for the assignable cause could be quite difficult. The search depends on the process engineers’ experience and knowledge of the process. This article discusses an approach based on the work of Samuel et al. (see Samuel, T. R., Pignatiello, J. J. Jr., Calvin, J. A. (1998). Identifying the Time of a Step Change with [Xbar] Control Charts. Quality Engineering, 10(3):521–527.) to identify the time of a permanent shift in the mean of a process with CUSUM control charts. [ABSTRACT FROM AUTHOR]

In this article we present for formulae for the determination of Pitman Nearness in comparing the coefficient of determination with its adjusted version in regression models for a given sample size. We generalize this finding to compare R² with a nonnegative parts version of the adjusted R². We compare our small, medium, and large sample results with the asymptotic results of Kumar and Srivastava (2004). [ABSTRACT FROM AUTHOR]

A robust estimator is developed for the location and scale parameters of a location-scale family. The estimator is defined as the minimizer of a minimum distance function that measures the distance between the ranked set sample empirical cumulative distribution function and a possibly misspecified target model. We show that the estimator is asymptotically normal, robust, and has high efficiency with respect to its competitors in literature. It is also shown that the location estimator is consistent within the class of all symmetric distributions whereas the scale estimator is Fisher consistent at the true target model. The paper also considers an optimal allocation procedure that does not introduce any bias due to judgment error classification. It is shown that this allocation procedure is equivalent to Neyman allocation. A numerical efficiency comparison is provided. [Copyright &y& Elsevier]

The asymmetry of a univariate continuous distribution is commonly measured by the classical skewness coefficient. Because this estimator is based on the first three moments of the dataset, it is strongly affected by the presence of one or more outliers. This article investigates the medcouple, a robust alternative to the classical skewness coefficient. We show that it has a 25% breakdown value and a bounded influence function. We present a fast algorithm for its computation, and investigate its finite-sample behavior through simulated and real datasets. [ABSTRACT FROM AUTHOR]

A fundamental problem encountered in statistics is that of testing the equality of two population parameters those measure variability. There are several tests available in the literature for the two-sample scale problem. However, much attention has not been given to the tests that take care of suspected outliers at the extremes. In this paper, we propose a class of distribution-free tests for the two-sample scale problem which is resistant to extreme outliers in the data. The performance of the class in terms of Pitman relative efficiency has been evaluated with respect to many available tests for some standard distributions. [ABSTRACT FROM AUTHOR]

Sample coefficient of determination and its adjusted version are two popular measures for the goodness of fit in linear regression models. Their performance properties under the criteria of Pitman nearness and concentration probability are analyzed using large sample approximations and are compared with those under the criteria of bias and mean squared error. [ABSTRACT FROM AUTHOR]

Carpenter and Hebert [Carpenter, M., Hebert, J. L. (1997). Estimating guaranteed lifetimes of systems in a random environment. Comm. Statistics Theory Methods 26:309–316] consider competing estimators for the minimum and maximum location parameters from joint samples of an exponential mixture. They develop bias-corrected estimators for these extrema and show that the new estimators dominate the maximum likelihood estimators in terms of absolute bias and mean squared error. In this article, we compare these estimators in terms of Pitman's measure of closeness. We present a general result that facilitates the calculation of the Pitman probabilities when the moment-generating function for the mixing distribution is known. We also provide sufficient conditions under which the estimators proposed by Carpenter and Hebert dominate the maximum likelihood estimators in terms of Pitman's measure of closeness, and we provide sufficient conditions under which the bias-corrected estimators are inadmissible in this measure. [ABSTRACT FROM AUTHOR]

We consider robust permutation tests based on an estimating equation comparing the test statistics based on the score function with those based on the M-estimate. First we obtain a form for the tests so that the exact tests may be carried out using the same algorithms as used for permutation tests based on the mean. Then we compare the efficiencies of the tests in two cases, equivalent to the sign test and a test based on Huber scores, showing that they are equivalent in the Pitman sense but that they have different Bahadur slopes with neither exceeding the other over the whole range. [Copyright &y& Elsevier]

A novel approach aimed at evaluating the diagnosability of regular systems under the PMC model is introduced. The diagnosability is defined as the ability to provide a correct diagnosis, although possibly incomplete. This concept is somehow intermediate between one-step diagnosability and sequential diagnosability. A lower bound to diagnosability is determined by lower bounding the minimum of a “syndrome-dependent” bound tσ over the set of all the admissible syndromes. In turn, tσ is determined by evaluating the cardinality of the smallest consistent fault set containing an aggregate of maximum cardinality. The new approach, which applies to any regular system, relies on the “edge-isoperimetric inequalities” of connected components of units declaring each other non-faulty. This approach has been used to derive tight lower bounds to the diagnosability of toroidal grids and hypercubes, which improve the existing bounds for the same structures. [Copyright &y& Elsevier]

We generalize the notion of Brownian bridge. More precisely, we study a standard Brownian motion for which a certain functional is conditioned to follow a given law. Such processes appear as weak solutions of stochastic differential equations that we call conditioned stochastic differential equations. The link with the theory of initial enlargement of filtration is made and after a general presentation several examples are studied: the conditioning of a standard Brownian motion (and more generally of a Markov diffusion) by its value at a given date, the conditioning of a geometric Brownian motion with negative drift by its quadratic variation and finally the conditioning of a standard Brownian motion by its first hitting time of a given level. As an application, we introduce the notion of weak information on a complete market, and we give a “quantitative” value to this weak information. [Copyright &y& Elsevier]

We consider Pitman-closeness to evaluate the performance of univariate and multivariate forecasting methods. Optimal weights for the combination of forecasts are calculated with respect to this criterion. These weights depend on the assumption of the distribution of the individual forecasts errors. In the normal case they are identical with the optimal weights with respect to the MSE-criterion (univariate case) and with the optimal weights with respect to the MMSE-criterion (multivariate case). Further, we present a simple example to show how the different combination techniques perform. There we can see how much the optimal multivariate combination can outperform different other combinations. In practice, we can find multivariate forecasts e.g., in econometrics. There is often the situation that forecast institutes estimate several economic variables. [ABSTRACT FROM AUTHOR]

This paper presents a ranked set sample allocation procedure that is optimal for a number of nonparametric test procedures. We define a function that measures the amount of information provided by each observation given the actual joint ranking of all the units in a set. The optimal ranked set sample allocates order statistics by maximizing this information function. This paper shows that the optimal allocation of order statistics in a ranked set sample is determined by the location of the mode(s) of the underlying distribution. For unimodal, symmetric distributions, optimal allocation always quantifies the middle observation(s). If the underlying distribution with cdf F is a multi-modal distribution with modes $R\_\{1\},\; \backslash ldots,\; R\_\{k\}$, then the optimal allocation procedure quantifies observations at $mF(R\_\{1\}),\; \backslash ldots,\; mF(R\_\{k\})$ in a set of size m. We provide similar results for unimodal, asymmetric distributions. We also propose a new sign test which considers the relative positions of the quantified observations from the same cycle in a ranked set sample. The proposed sign test provides improvement in the Pitman efficiency over the ranked set sample sign test of Hettmansperger (1995). It is shown that the information optimal allocation procedure induced by Pitman efficiency is equivalent to the optimal allocation procedure induced by the information criteria. We show that the finite sample distribution of the proposed test based on this optimal design is binomial. [ABSTRACT FROM AUTHOR]

Les auteurs s'intéressent à la classe de tests de rang conditionnellement libres introduite par Monga et Tardif (1994) pour des plans de carrés latins en réplique. lls montrent qu'il est possible d'élargir cette classe grâce à l'emploi de la méthode du rangement après substitution. Us obtiennent le comportement asymptotique inconditionnel de tout membre de la classe élargie à la fois sous l'hypothèse nulle d'absence d'effets dus aux traitements et sous une suite de contre-hypothèses contiguës. Ceci leur permet d'établir l'efficacité asymptotique au sens de Pitman de tout membre relativement au test asymptotiquement minimax et de conclure qu'au moins un membre de la classe est asymptotiquement aussi efficace que ce dernier. [ABSTRACT FROM AUTHOR]

Changes in calibration curves from one time to the next. caused by drift, often require measuring devices to be rccalibrated at frequent intervals. In such situations the usual practice is to estimate the unknown values of test samples using only data from the corresponding calibration period. Under a random coefficient regression model for the different calibration curves, however, it can be shown that it is more efficient to combine the data from all calibration periods to estimate the unknowns. We consider a particular class of point estimators obtained by inverting suitable prediction functions and show that the estimator obtained from a best prediction function is optimal in a sense defined by Godambe (1960) and Durbin (1960) in the context of unbiased estimating equations. We also compare the smallsample performance of this estimator with the usual estimator using the Pitman closeness criterion. [ABSTRACT FROM AUTHOR]

In the adaptive cluster design introduced by Thompson (1990), a finite population of units under investigation is partitioned into networks on the basis of a specdied condition for adding neighbourhoods to a sampled unit. An initial sample of units is taken and a network may be sampled more than once. In this paper, we introduce a modification of the design in which networks are sampled only once. Two unbiased estimators are considered and the Rao-Blackwell theorem is used to improve them in terms of efficiency. The various estimators are compared using two examples. [ABSTRACT FROM AUTHOR]

On considère le problème d'estimer le quantile d'un distribution exponentielle, avec paramètres de position et d'échelle inconnus, à l'aide de la mesure de précision de Pitman (PMC). La fonction de perte est nécessaire à la satisfaction de quelques conditions faibles, mais est autrement arbitraire. Un estimateur optimal est obtenu de la catégorie des estimateurs équivariants de position-échelle et son admissibilité selon la PMC est examinée. [ABSTRACT FROM AUTHOR]

On considère l'estimation des puissances de la variance généralisée d'une loi normale multivariée de moyenne inconnue. On démontre l'inadmissibilité de l'estimateur équivariant sous les transformations affines et qui est le plus proche dans le sens de Pitman. [ABSTRACT FROM AUTHOR]

On étudie la relation entre les efficacités de Hodges-Lehmann et de Pitman cela dans le contexte de tests unilatéraux à propos ďun paramètre réel. On montre que pour des tests basés sur des sommes ďobservations indépendantes et identiquement distribuées, ľefficacité locale de Hodges-Lehmann est équivalente à ľefficacité de Pitman. Il est prouvé que cette équivalence demeure valable pour des tests basés sur deux classes de M-estimateurs pour un paramètre de position. Dans tous les cas considérés on obtient des formules explicites pour ľefficacité de Hodges-Lehmann. [ABSTRACT FROM AUTHOR]

The article presents research which examined the asymptotic efficiencies of two nonparametric classification rules. The researchers analyzed the effectiveness of the rules when applied in univariate populations having different changes of scale and location shifts. They also assessed the consistency of the classification procedure when the distributions of numbers are fixed in the Pitman sense.

Comments on a paper by Christian P. Robert, J.T. Gene Hwang, and William E. Strawderman published in the "Journal of the American Statistical Association" on the Pitman closeness criterion (PCC). Incompatibility of the criterion with the usual theoretic analysis; Dependency of the criterion's value on the joint distribution of two competing estimators; Role of PCC in decision theory.

A Unified approach to asymptotic rank tests is presented for a wide class of univariate and multivariate models, including repeated measures designs without compound symmetry. The models are assumed to be balanced and complete with more than one replication per cell. The proposed rank tests are constructed by ranking all of the observations together regardless of row, column, or component membership. This method of ranking offers increased power over the method of n-rankings. The resulting test statistic is a quadratic form in linear rank statistics. Asymptotic distributions are determined under Pitman alternatives that allow for both scale and location alternatives. The resulting statistics include tests for factor effects (both scale and location differences) in one-, two-, and higher-way layouts with repeated measures on one or several factors without assuming equicorrelation. Also included are tests for the multivariate two- and k-sample problem, as well as multivariate versions of the tests for multiway layouts and repeated measures designs. For many of the repeated measures designs without equicorrelation, no other rank based statistics have been previously studied. The results also include the asymptotic distributions for many possible rank transform tests for univariate and multivariate models, as well as a rich class of aligned rank tests. [ABSTRACT FROM AUTHOR]

Confidence intervals for median survival times are derived for censored survival data. The intervals are obtained by using the quantiles of the Kaplan-Meier product-limit estimator and have the same Pitman efficiency as the intervals found by inverting the sign test. Two-sample tests and confidence intervals for the difference in median survival times are then developed based on the comparison of the one-sample confidence intervals. Several methods for choosing the confidence coefficients of the corresponding one-sample confidence intervals are developed. The Pitman efficiencies of these two-sample tests are the same as that of the median test proposed by Brookmeyer and Crowley (1982a). The procedures can also be used for the accelerated failure time model, proportional hazard model, and the Behrens-Fisher problem. Nonparametric two-sample inference procedures are useful In comparing the responses of treatment and control groups. In medical follow-up studies the data are usually subjected to censoring. Although many of the two-sample procedures have been extended to accommodate censored data, we show in this article how to construct two-sample tests and confidence intervals based on one-sample confidence intervals. This method was first discussed in Hettmansperger (1984a) for uncensored data where a confidence interval for the difference in population medians is constructed by subtracting the endpoints of one (one-sample) interval from the opposite endpoints of the other. The test then rejects the null hypothesis of equal medians if the one-sample intervals are disjoint. Hettmansperger used the sign interval as the one-sample interval, which is obtained by inverting the sign test. In the presence of censoring we modify the sign interval to the so-called quantile interval, whose endpoints are the quantiles of the product-bruit estimator of Kaplan and Meier (1958). After deriving the asymptotic properties of the quantile interval, we show, for specified overall level α, three ways to select the confidence coefficients for the one-sample quantile intervals. For α = 05 and equal confidence coefficients for both samples, the one sample confidence coefficients are in the neighborhood of 85 under the Koziol-Green model, compared with .975 had Bonferroni inequality or independence of the two samples been used. The procedures are then applied to data from a colorectal cancer clinical trial to compare four treatments, and they appear to be quite robust. [ABSTRACT FROM AUTHOR]

Sufficient conditions are given that guarantee the limiting distribution of a test proposed by Agresti and Pendergast (1986) to detect treatment effects in repeated-measures designs. The test, which is appropriate for either the original or aligned data, is related to one proposed by Koch (1969) and to the rank-transformation statistic. Using Pitman asymptotic-relative-efficiency comparisons, situations are presented where these tests are more efficient than their standard parametric and nonparametric competitors. The problem of detecting ordered alternatives in repeated-measures designs is also considered. A rank transformation analog of Page's (1963) L is shown to be generally more efficient in the Pitman sense than the standard competitors when the number of treatments is not too large. [ABSTRACT FROM AUTHOR]

Monte Carlo "swindles" or variance reduction techniques exploit the experimenter's knowledge of the stochastic structure governing the simulated data to construct more precise estimates of unknown parameters. Alternatively, one can reduce the number of replications (and thus the cost) needed to gain a desired level of precision. This article reviews the common case of swindles based on variance decompositions for estimating efficiencies and variances of location and regression estimators. We then propose a new swindle based on Fisher's efficient score function that can be applied profitably to a much wider range of situations than can the Gaussian-over-independent swindles used in many studies of robust estimators. We compare these methods by performing simulations for the efficiencies of location estimates and by placing them in a simple geometric framework. As an illustration, the score function swindle is used to estimate the variances of Pitman estimates of location for samples from selected t-distributions. Finally, we sketch applications to scale estimation, exponential regression, statistical decision theory, and bootstrap computations. [ABSTRACT FROM AUTHOR]

The influence curve introduced by Hampel (1968) is applied to goodness-of-fit statistics. The efficacy curve is then defined to be the square of the influence curve weighted by a constant that arises in the context of approximate Bahadur efficiency. For a number of goodness-of-fit statistics, the ratios of these curves are shown to be equal to asymptotic relative efficiencies in the Pitman sense when testing for point contamination. These efficacy curves graphically portray the sensitivities of certain goodness-of-fit statistics to minor perturbations in the assumed distribution. [ABSTRACT FROM AUTHOR]

The limit distribution of Cochran's Q statistic for testing the equality of k proportions in matched samples is obtained for sequences of Pitman alternatives. Comparison of the asymptotic power of the test based on the Q statistic with that of the test based on Wald's statistic for the same asymptotic level shows that neither test is uniformly better than the other. We study by simulation a modified Q test using an estimated critical value obtained from a Satterthwaite-type approximation for cases when the proportions to be compared are near one-half and k = 4. The operating characteristics agree closely with estimated values in samples of 50 and 100, while the agreement with the Wald statistics was occasionally poor. [ABSTRACT FROM AUTHOR]

An adaptive distribution-free test procedure for location based on a one-parameter family of score functions is proposed. The family of score functions is derived from the symmetric lambda distributions introduced by Tukey. The resulting test attains Pittman efficiency one for a large set of underlying lambda distributions. In addition, the test has Pitman efficiency 3/pi at the normal alternative. The procedure can easily be extended to the multisample problem. [ABSTRACT FROM AUTHOR]

For three symmetric distributions and six sample sizes, this article presents estimates of the small-sample variance of Pitman's location-invariant and location-scale-invariant estimators of location. It then compares these two estimators and investigates the closeness of the Cramer-Rao bound when estimators are required to be invariant. Expressions of the form c/(n -- d) prove quite effective in fitting variances of Pitman estimators, and d can be interpreted as the amount of Fisher information "lost." In terms of relative efficiency, maximum-likelihood estimators and linear combinations of order statistics offer computationally attractive alternatives to the Pitman estimators. [ABSTRACT FROM AUTHOR]

The article develops new approximations to the distribution function of a general econometric estimator or test statistic from a linear model. The method relies heavily on the general arguments for the validity of Edgeworth approximations, and produces formulae of a similar type, except that, instead of using the cumulative normal distribution, an Imhof distribution is used derived from the exact distribution of a linear combination of the sample data second moments. On theoretical grounds this might be expected to give better approximations for some estimators. In practice comparisons were made between computed approximations of both types for several simple cases. [ABSTRACT FROM AUTHOR]

This article examines the performance of ordinary least squares, generalized least squares, and Pagan's (1986) double-length estimator (DLE) in several rational-expectations models. The three approaches are equivalent in the simplest of models but may differ appreciably in models typically encountered in applied work. Small-sample properties of the estimators are examined in several contemporary macroeconomic models. The following conclusions are reached: (a) All estimators exhibit similar sampling distributions in a monetary-neutrality framework, (b) the least squares procedures maintain smaller sampling variance and deliver more reliable tests in a permanent-income model in very small samples, (c) DLE generally delivers superior performance in a nonlinear aggregate-supply model with unanticipated "shock" regressors, and (d) overall, DLE outperforms the LS alternatives except in the smallest of samples. [ABSTRACT FROM AUTHOR]

Discusses how to compare estimators for population variance using Pitman nearness. Mean squared error; Computation of Pitman nearness probabilities; Comparisons and admissibility results.

The local power of test statistics is analyzed by extending the notion of Pitman sequences to sequences of data-generating processes (DGP's) that approach the null hypothesis without necessarily satisfying the alternative. A space of probability densities is defined and endowed with the structure of an infinite-dimensional Hilbert manifold, which permits a geometrical interpretation of hypothesis testing. The three classical test statistics—LR, Wald, and LM—are shown to tend asymptotically to the same random variable under all sequences of local DGP's. The power of these statistics is seen to depend on the null, the alternative, and the sequence of DGP's in a simple and geometrically intuitive way. Moreover, for any test statistic that is asymptotically chi-squared under the null, there exists an "implicit alternative hypothesis" against which that statistic will have highest power, and which coincides with the explicit alternative for the classical test statistics. [ABSTRACT FROM AUTHOR]

The idea of transferability is to employ in model estimation, fitted model parameters computed from a different data set. The combined estimator approach to the transferability problem is expressed as a linear combination of the unbiased direct estimators on the two data sets. The major gain is in variance reduction. The combined estimator is shown to have superior accuracy, in a Mean Square Error sense, to a unbiased direct estimator whenever the transfer bias is relatively small. A test that indicates if the combined estimator is superior to the direct estimator is provided. Variances of the direct estimators are assumed to be known. Monte Carlo experiments are performed to assess the quality of the approximations. The results show that the approximations used are highly conservative. An empirical example of the combined estimator applied to a discrete choice problem is presented. [ABSTRACT FROM AUTHOR]

Reexamines scaling from the perspective of Pitman closeness in statistics, often used for comparing competing estimators. Pitman closeness of Searle's estimator; Scaled estimators of Arnhold and Hebert; Scaling for improved estimation.