Jatinder S. Mehta

The existence of moments of some simple Bayes estimators of coefficients in a simultaneous equation model

Abstract In this paper a simple modification of the usual k-class estimators has been suggested so that for 0 ≦ k ≦ 1 the problem of the non-existence of moments disappears. These modified estimators can be interpreted either as Bayes estimators or as constrained estimators subject to the restriction that the squared length of the coefficient vector is less than or equal to a given number.

On Bayesian estimation of seemingly unrelated regressions when some observations are missing

Abstract In this paper we have considered the problem of estimating the parameters of two seemingly unrelated regression equations when the number of available observations on all the variables in the first equation exceeds the number of available observations on all the variables in the second equation. We have shown how, within the Bayesian framework, extra observations on all the variables in the first equation can be readily and formally utilized in obtaining the exact or an approximate posterior distributions of all the coefficients including those in the second equation.

Estimation of common coefficients in two regression equations

Abstract In this paper we consider a problem of estimating K common coefficients in two regression models. Assuming that the disturbances of the two equations have different variances, it is shown that, under some general conditions, it is possible to combine information on both the equations to obtain estimators which are more efficient than the one based on just one of the two equations.

On the existence of moments of partially restricted reduced form coefficients

Abstract In this paper ridgelike Bayesian estimators of structural coefficients have been used to form the partially restricted reduced form estimators. These partially restricted reduced form estimators are simple in form and possess finite sampling moments and risk in contrast to other restricted reduced form estimators that possess no finite moments and have infinite risk relative to quadratic loss functions. The usual k -class implied partially restricted reduced form estimators with 0≦ k ≦1 do not posses finite moments unless the degree of overidentification (or the excess of sample size over the number of coefficients) of the structural equation being estimated is suitably restricted.

Empirical best linear unbiased prediction in misspecified and improved panel data models with an application to gasoline demand

We emphasize using our solutions to the problems of omitted variables, measurement errors, and unknown functional forms to improve model specification, and to estimate the mean square error of an empirical best linear unbiased predictor of an individual drawing of the dependent variable of an improved model. We illustrate using data to compare the forecasting performances of misspecified and improved models of the U.S. gasoline market. The performance criterion used is the tightness of the distribution of the absolute relative errors in out-of-sample multi-step-ahead forecasts around zero. The results show that significant improvements in forecasting accuracy can be obtained by improving the specifications of misspecified models. Numerical algorithms for generating forecasts from a rolling forecast method are presented

Ridge regression estimation of the Rotterdam model

Abstract The best guesses of unknown coefficients specified in Theils model of introspection are like predictions and not like de Finettis prevision and therefore not the values taken by random variables. Constrained least squares procedures can be formulated which are free of these difficulties. The ridge estimator is a simple version of a constrained least squares estimator which can be made operational even when little prior information is available. Our operational ridge estimators are nearly minimax and are not less stable than least squares in the presence of high multicollinearity. Finally, we have presented the ridge estimates for the Rotterdam demand model.

An efficient method of estimating the true value of a population characteristic from its discrepant estimates

A fruitful method of pooling data from disparate sources, such as a set of sample surveys, is developed. This method proceeds by finding the first two moments of two conditional distributions derived from a joint distribution of two sample estimators of employment for each of several geographical areas. The nature of the two estimators is such that one of them can yield a better estimate of national employment than the other. The regression of the former estimator on the latter estimator with stochastic intercept and slope is used to generate an improved estimator that is equal to bias- and error-corrected estimator for each area with probability 1. This analysis is extended to cases where more than two estimates of employment are available for each area.

Small Area Estimation with Correctly Specified Linking Models

It is possible to improve the precision of a sample estimator for a small area based on sparse area-specific data by combining it with a model of its estimand, provided that this model is correctly specified. A proof of this result and the method of correctly specifying the models of the estimands of sample estimators are given in this paper. Widely used two-step estimation is shown to yield inconsistent estimators. The accuracies of different sample estimates of a population value can be improved by simultaneously estimating the population value and sums of the sampling and non-sampling errors of these sample estimates.

Microfluorometry analysis II. A bayesian approach

Abstract In flow microfluorometry (FMF) analysis cells stained with a fluorescent dye that binds specifically to DNA are passed through the instrument. The number of cells in the population having a fluorescence intensity is recorded in a single channel of a multichannel pulse height analyzer. The result is a DNA fluorescence histogram for the population. A method for decomposing an FMF histogram into its G 1 , S and G 2 + M components, corresponding to similarly designated phases of the cell cycle is given. This technique can also be applied to find the parameters in all of the previous approaches. The parameters are calculated by iteration which eliminates the need for non-linear optimization procedures.