A generalized estimator representing a class of estimators is proposed for the estimation of regression coefficients in the linear regression model when the error components have the joint multivariate Student-t distr...
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A generalized estimator representing a class of estimators is proposed for the estimation of regression coefficients in the linear regression model when the error components have the joint multivariate Student-t distribution. Approximate expressions for the bias and the risk of the proposed generalized estimator under a general quadratic loss function are found and a comparative study among some of the estimators of the class is made. A generalized efficiency (dominance) condition of the class over the usual minimum variance unbiased estimator (MVUE) is also given.
The coverage errors of the empirical likelihood confidence regions for beta in a linear regression model, Y(i) = x(i)beta + epsilon(i), 1 less-than-or-equal-to i less-than-or-equal-to n. are of order n-1. Bartlett cor...
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The coverage errors of the empirical likelihood confidence regions for beta in a linear regression model, Y(i) = x(i)beta + epsilon(i), 1 less-than-or-equal-to i less-than-or-equal-to n. are of order n-1. Bartlett corrections may be employed to reduce the order of magnitude of the coverage errors to n-2. For practical implementation of Bartlett correction, an empirical Bartlett correction is given.
models are proposed to extend the monthly streamflow data at a site where the available historic rainfall and streamflow data are too short for adequate systems study, subject to the condition that there are no gaugin...
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models are proposed to extend the monthly streamflow data at a site where the available historic rainfall and streamflow data are too short for adequate systems study, subject to the condition that there are no gauging sites in the basin or adjacent basins with a longer period of streamflow data. Hence rainfall data of a nearby raingauge station are used. Five regressionmodels, namely, runoff coefficient model, single linearregression, monthly linearregression, monthly linearregression with stochastic description for residuals, and a double regressed model are used. The results show that the monthly linear regression model with stochastic description for the residuals is best suited for the purpose when applied to a case study.
Estimation in the presence of censoring is an important problem. In the linearmodel, the Buckley-James method proceeds iteratively by estimating the censored values than re-estimating the regression coefficients. A l...
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Estimation in the presence of censoring is an important problem. In the linearmodel, the Buckley-James method proceeds iteratively by estimating the censored values than re-estimating the regression coefficients. A large-scale Monte Carlo simulation technique has been developed to test the performance of the Buckley-James (denoted B-J) estimator. One hundred and seventy two randomly generated data sets, each with three thousand replications, based on four failure distributions, four censoring patterns, three sample sizes and four censoring rates have been investigated, and the results are presented. It is found that, except for Type II censoring, the B-J estimator is essentially unbiased, even when the data sets with small sample sizes are subjected to a high censoring rate. The variance formula suggested by Buckley and James (1979) is shown to be sensitive to the failure distribution. If the censoring rate is kept constant along the covariate line, the sample variance of the estimator appears to be insensitive to the censoring pattern with a selected failure distribution. Oscillation of the convergence values associated with the B-J estimator is illustrated and thoroughly discussed.
A generalized class of shrinkage estimators in linearregression is proposed, the risk associated with the class is derived under a general quadratic loss function when the disturbances are not normal and a comparativ...
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A generalized class of shrinkage estimators in linearregression is proposed, the risk associated with the class is derived under a general quadratic loss function when the disturbances are not normal and a comparative study with some new estimators from the class has been provided with the existing ones.
This paper considers the application of Stein-type estimation procedure for the coefficients in a linear regression model when data are available from replicated experiment. Two families of estimators characterized by...
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This paper considers the application of Stein-type estimation procedure for the coefficients in a linear regression model when data are available from replicated experiment. Two families of estimators characterized by a single scalar are proposed and their large sample asymptotic properties are derived. These are utilized for comparing the performances of the two estimators along with the conventional estimator and conditions for the superiority of one estimator over the other are deduced.
Several adaptive versions of the minimum mean squared error estimator of the coefficient vector, in a linear regression model are proposed in the literature. Some of these are compared here, and another estimator is a...
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Several adaptive versions of the minimum mean squared error estimator of the coefficient vector, in a linear regression model are proposed in the literature. Some of these are compared here, and another estimator is also proposed.
In the usual linearmodel Y(i) = x(i)'beta0 + e(i), i = 1, .... , n, denote by beta(n) the L1 estimate of beta0. Under some general conditions on {e(i)}, it is shown that SIGMA(i)infinity = \\x(i)\\ = infinity is ...
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In the usual linearmodel Y(i) = x(i)'beta0 + e(i), i = 1, .... , n, denote by beta(n) the L1 estimate of beta0. Under some general conditions on {e(i)}, it is shown that SIGMA(i)infinity = \\x(i)\\ = infinity is a necessary condition for the consistency of beta(n).
We consider the problem of estimating the parameter vector in the linearmodel when the observations on the independent variables are partially missing. The new quasi minimax approach, which uses prior restrictions on...
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We consider the problem of estimating the parameter vector in the linearmodel when the observations on the independent variables are partially missing. The new quasi minimax approach, which uses prior restrictions on the exogenous variables, is compared to the Maximum Likelihood method with respect to the (empirical) mean square error.
We consider the problem of estimating the parameter vector in the linearmodel when observations on the independent variables are partially missing or incorrect. A new estimator is developed which systematically combi...
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We consider the problem of estimating the parameter vector in the linearmodel when observations on the independent variables are partially missing or incorrect. A new estimator is developed which systematically combines prior restrictions on the exogenous variables with the incomplete data. We compare this method with the alternative strategy of deleting missing values.
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