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In this paper we offer a complete methodology of cumulative slicing estimation to sufficient dimension reduction. In parallel to the classical slicing estimation, we develop three methods that are termed, respectively, as cumulative mean estimation, cumulative variance estimation, and cumulative directional regression. The strong consistency for p= O( n1 / 2 / log n) and the asymptotic normality for p= o( n1 / 2) are established, where p is the dimension of the predictors and n is sample size. Such asymptotic results improve the rate p= o( n1 / 3) in many existing contexts of semiparametric modeling. In addition, we propose a modified BIC-type criterion to estimate the structural dimension of the central subspace. Its consistency is established when p= o( n1 / 2). Extensive simulations are carried out for comparison with existing methods and a real data example is presented for illustration. [ABSTRACT FROM AUTHOR]

The two-dimensional controlled selection problem and the problem of maximizing the overlap of old and new primary sampling units after restratification and change of selection probabilities have been studied for several decades but have never been completely solved until now. Using transportation theory, complete solutions are obtained here for these and other problems. The solution to the controlled selection problem is based on a specific transportation model that was originally developed, in a previous paper by Cox and Ernst (1982), to solve completely the controlled rounding problem, namely the problem of optimally rounding real-valued entries in a two-way tabular array to adjacent integer values in a manner that preserves the tabular (additive) structure of the array. This model is also applied to other statistical problems, such as raking and statistical disclosure for frequency count tabulations and microdata. [ABSTRACT FROM AUTHOR]

The problem considered is the estimation of the population total of some characteristic from a simple random sample containing a few large or extreme observations. The effect of these large units in the sample is to distort the estimate of the population total. It is therefore important to correct the weights for such units or deflate their values at the estimation stage once they have been sampled and identified as unusually large units. In this paper, three estimators that alter the usual sampling weights have been considered. The efficiencies of these estimators have been worked out in terms of the ratio of the mean squared error of the usual estimator of the population total to the mean squared error of these estimators. A numerical study of these estimators is also discussed. [ABSTRACT FROM AUTHOR]

In this paper we consider four alternative forms of two-parameter normal and nonnormal error distributions and report on a Monte Carlo study of the small-sample properties of least squares, two-stage least squares, three-stage least squares and full information maximum likelihood estimators. On the basis of 1,000 replications of sample size 20 in two experiments on an overidentified model, we found that the small-sample rankings of econometric estimators of both structural coefficients and forecasts of endogenous variables, according to parametric and nonparametric measures of bias, dispersion, and dispersion including bias, do not change for any of the four error distributions. Further, least squares is the most biased and maintains the Gauss-Markov property of minimum variance. The large bias of least squares, however, more than offsets the small variance, so that least squares exhibits the largest mean squares of the four estimators. Maximum likelihood is least biased and most efficient, except as an estimator of structural coefficients on the parametric measure of mean squared error. [ABSTRACT FROM AUTHOR]

Loglinear models are classified as direct or indirect depending on whether the maximum likelihood estimates of cell values are explicit functions of the sufficient statistics or not. For saturated (hence, direct) models, Goodman (1970) and Bishop, Fienberg, and Holland (1975) used the delta method to calculate the asymptotic variances of various u terms in the loglinear models. In the present paper, this approach has been generalized to direct unsaturated hierarchical loglinear models. General rules for determining closed form expressions for asymptotic variances in such situations are obtained; bounds for the asymptotic variances of a terms in indirect models are considered; and these rules are compared with other methods of producing asymptotic variances. [ABSTRACT FROM AUTHOR]

Most of the literature on survey sampling deals with a single stratifying variable. In this paper an attempt is made to study the effect of using two stratifying variables. We present an approximation to the variance of the study variable under the assumption of a linear regression on the two stratifying variables. This approximation depends only on the number of strata, the simultaneous density of the stratifying variables, and the correlations between the study variable and each of the stratifying variables. The results indicate that in many practical situations the gain from using two stratifying variables over one is nontrivial. [ABSTRACT FROM AUTHOR]

Among the unequal probability sampling without replacement procedures applicable for arbitrary sample size, those of Goodman and Kish and of Sampford are relatively simple to operate besides satisfying the criterion that the inclusion probability of each population unit is proportional to its size. Considering the Horvitz-Thompson estimator for estimating the population total, we show in this paper that Sampford's procedure is more efficient than the Goodman and Kish procedure. Our result is a generalization of Rao's result wherein he compared Durbin's procedure with that of Goodman and Kish. [ABSTRACT FROM AUTHOR]

There are growing demands to use prior and sample information for parameter estimation of a regression model in order to maintain consistency with underlying theory. To meet such demands, this paper provides an inequality constrained least-squares (ICLS) estimation, specifies an untrancated variance-covariance matrix of the ICLS estimates, and discusses their statistical properties in large-and small-sample cases. Finally, the ICLS and the ordinary least-squares OLS estimates are compared in terms of sample bias, sample mean-square error MSE and sample variance of the estimates by a Monte Carlo study. [ABSTRACT FROM AUTHOR]

This paper considers a system of two seemingly unrelated equations. Without imposing any additional restrictions on the matrices of observations on the independent variables in the two equations, we derive the exact second moments of Zellner's estimator [9]. Though not uniformly more efficient than the corresponding single-equation least-squares estimator, a definite efficiency gain results using Zellner's estimator in the presence of high contemporaneous correlation coefficient (p) between the disturbances in the two equations, and little loss results when the true p is small and the excess of the sample size over the number of distinct regressors in this system is greater than 12. [ABSTRACT FROM AUTHOR]

In this paper we present the asymptotically best linear unbiased estimators for the location and scale parameters of the logistic distribution based on samples where there may be Type 2 censoring in the tails, Given the amount of censoring, the weights of the estimators can be expressed in simple closed forms, Comparisons of these with the best linear unbiased estimators and the Cramer-Rao lower bounds demonstrate that they have good efficiency even for small samples. [ABSTRACT FROM AUTHOR]