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For a linear regression model with first-order autocorrelated disturbances, a variety of estimators for the regression coefficients have been proposed in the literature. One of the most commonly used estimators for this situation has been the Cochrane-Orcutt (1949) estimator (CO) due to its intuitive and computational simplicity. Since its introduction, several alternative estimators have also been proposed and their efficiency properties have been investigated. For example, Kadiyala (1968) showed that ordinary least squares (OLS) is a better estimator than CO for known autocorrelation coefficient g in 0 < ϱ ≤ 1 for the model containing only an intercept. 1 , 2 Maeshiro (1976), then showed that OLS is better than CO with known ϱ for all ϱ > 0 in a similar model where the matrix of explanatory variables contains an intercept and a strongly trended variable, even for sample sizes of t = 100. In addition, OLS is vindicated by Harvey and McAvinchey (1978), who suggest that it performs acceptably when the variable is trended; by Spitzer (1979), who recommends its use when the absolute value of the autocorrelation coefficient is ≤ 0.2; and by Kramer (1980), who proves that the efficiency (when measured by the trace of the variancecovariance matrix) of OLS with respect to the generalized least squares (GLS) approaches one as ϱ approaches one when the model includes a constant term. However, recently Taylor (1981) has pointed out that Maeshiro’s result only applies to a special case: very strong trends in the explanatory variable, and where this variable is fixed, as opposed to the Monte Carlo studies of Griliches and Rao (1969) and Spitzer (1979) in which the explanatory variable is drawn from a prespecified stochastic process. In this latter case, the first observation no longer remains as important for large t, hence the improved performance of CO.

Carbon stock distribution in different tropical forest types in India is rarely studied although India is a country with mega-diversity. The present study estimates the biomass and carbon stock of major tropical forest types in India, and attempts to identify suitable interpolation techniques for mapping carbon stock. Empirically derived allometric equations and carbon conversion coefficients were used to estimate the aboveground biomass and carbon stock, respectively. The point estimates were interpolated to spatial surface using different interpolation techniques. Two main modelling approaches were implemented: deterministic modelling and stochastic modelling. Deterministic modelling was to interpolate point information using similarities between measured points (inverse distance weighted (IDW) interpolation), and fitting a smoothing curve along the measured points (polynomial interpolation). In stochastic modelling, ordinary kriging (OK) was employed using parameters derived from semivariograms. The re...

In this article, we consider the estimation of a population mean when some observations on the study characteristic are missing in the bivariate sample data. In all, five estimators are presented and their efficiency properties are discussed. One estimator arises from the the amputation of incomplete observations while the remaining four estimators are formulated using imputed values obtained by the ratio method of estimation.

This paper discusses the estimation of coefficients in a linear regression model when there are some missing observations on an explanatory variable and the study variable individually as well as simultaneously. The first order regression method of imputation is followed and the least squares procedure is applied. Efficiency properties of estimators are then investigated employing the large sample asymptotic theory.

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.

SYNOPTIC ABSTRACTThis paper deals with the application of the weighted mixed regression estimation of the coefficients in a linear model when some values of some of the regressors are missing. Taking the weight factor as an arbitrary scalar, the performance of weighted mixed regression estimator in relation to the conventional least squares and mixed regression estimators is analyzed and the choice of scalar is discussed. Then taking the weight factor as a specific matrix, a family of estimators is proposed and its performance properties under the criteria of bias vector and mean squared error matrix are analyzed.

This paper considers the estimation of coefficients in a linear regression model with missing observations in the independent variables and introduces a modification of the standard first order regression method for imputation of missing values. The modification provides stochastic values for imputation and, as an extension, makes use of the principle of weighted mixed regression. The proposed procedures are compared with two popular procedures-one which utilizes only the complete observations and the other which employs the standard first order regression imputation method for missing values. A simulation experiment to evaluate the gain in efficiency and to examine interesting issues like the impact of varying degree of multicollinearity in explanatory variables is proceeded. Some work on the case of discrete regressor variables is in progress and will be reported in a future article to follow.

This paper considers the estimation of the ratio of population means when some observations are missing. Four estimators are presented and their bias and mean square error properties are studied.

This paper presents a comparative study of the performance properties of one unbiased and two Stein-type estimators for combining the estimates of coefficients in a linear regression model when data sets are available from replicated experiments conducted at possibly different stations.

Despite the now widespread use of nonlinear estimators, their finite-sample properties have received very little attention in either the statistics or econometrics literature. We partially redress this problem by deriving and examining the second-order bias and mean squared error of a fairly wide class of nonlinear estimators which includes Nonlinear Least Squares, Maximum Likelihood, and many Generalized Method of Moments estimators as special cases. A number of examples are provided. The results from a Monte Carlo exercise demonstrate how the results can be applied for improved inferences.

This article considers a misspecified linear regression model in which misspecification relates to the inclusion of some explanatory variables. Assuming the distribution of disturbances to be not necessarily normal, this paper investigates the efficiency properties of predictions arising from ordinary least squares and Stein-rule when the aim is to predict either the actual value or the mean value of the study variable.

This paper considers Zellner's two estimators in a seemingly unrelated regression equations (SURE) model. Efficiency properties of the two estimators are analyzed by asymptotic expansions and Monte Carlo experiments under non-normal disturbances. It is shown that the two estimators have the same efficiency up to the second-order terms of O(T − 1 2 ) , and that non-normality influences the rate of convergency to normality of the estimators.

This article presents a comparative study of the efficiency properties of the coefficient of determination and its adjusted version in linear regression models when disturbances are not necessarily normal.

There is an extensive literature on the Stein-rule estimation of the parameters in a regression model. An important result in this literature is that the Stein-rule does not dominate the least squares estimator in the lower mean squared error sense when there are two or less regressors in the model. However, we note that not much is known about the Stein-rule estimation in dynamic models. This paper is a modest attempt in this direction and it shows that Stein-rule estimation of the lagged coefficient does not dominate the least square indicating that the result of regresion model goes through in the dynamic case.

This paper provides guidance in choosing k1 andk2 of the double k-class (KK) estimator such that it will improve upon both the ordinary least squares (OLS) and Stein-rule (SR) estimators in predictive mean squared error (PMSE). Asymptotic bias and mean squared error (MSE) results are derived for nonnormal and other cases. A simulation compares the KK estimator with the OLS and SR estimators.

The least squares estimation of the slope parameter of a simple linear regression is biased if the regressor variable is measured with random errors. This bias as well as the mean squared error is computed up to the order of 1/T without assuming normality for the error variable. They depend on the fourth moment of the error variable.

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.

This paper considers the choice of scalars characterizing the double k-class estimators of the coefficients in a linear regression model. We demonstrate the existence of a double k-class estimator that dominates the least squares and Stein-rule estimators and we give feasible values for the characterizing scalars which nearly minimize the risk of the estimator.

For estimating the coefficients in a linear regression model, the Stein-rule estimators are considered and their performance is studied according to the criterion of Pitman closeness. For this purpose, an asymptotic approximation for the criterion is derived and analyzed.

Determining the specification of a regression model according to the regressors' significance leads to a pre-test strategy. The exact sampling distribution of such a preliminary-test estimator is derived in this paper.

This article derives an unbiased estimator of the covariance matrix of the “mixed regression” estimator suggested by Theil and Goldberger for combining prior information with the sample information in regression analysis. This derivation facilitates the construction of finite-sample standard errors for the mixed estimators of the individual regression coefficients. Comparisons are made between the unbiased covariance estimator, the conventional consistent estimator based on the generalized least squares formula, and a simple modification of the latter, which is found to approximate the unbiased estimator well in practical situations.

The paper derives an exact unbiased estimator of the mean squared error of the feasible generalised ridge regression estimator for a linear regressioncoefficient. This provides the basis for calculating the standard error of such an estimator in a meaningful way.

Stein-rule estimation is a well-known method to improve the unbiased OLSE in the sense of smaller Mean-Square-Error. The paper is investigating the behaviour of this efficiency relation in case of misspecification of the linear model caused by inclusion of superfluous variables

For the estimation of the mean μ of a normal population with unknown variance σ2, Searles (1964) provides the minimum mean squared (MMSE) estimator (1 + σ2/(nμ2))−1 x in the class of all estimators of the type x . This MMSE estimator however is not computable in practice if σ/μ is unknown. Srivastava (1980) showed that the corresponding computable estimator t = (1 + s2/(n x 2)) x is more efficient than the usual estimator x whenever σ2/(nμ2) is at least 0.5. However, the gain in efficiency is a function of μ and σ2, and therefore remains unknown. This note provides a uniformly minimum variance unbiased estimate of the exact efficiency ratio E(t − μ)2/E( x − μ)2 to help determine the usefulness of t over x in practice.

In this note we furnish a set-up under which the Stein-rule estimator turns out to be a feasible version of the minimum risk estimator.

The purpose of this note is to spell out the conditions for the existence of the mean of the coefficient; estimator in seemingly unrelated regressions.

The risks of estimators incorporating the correction to the sample mean in the spirit of Stein and Lindley are approximated in the case of small disturbances.

In this paper we have derived the large sample asymptotic approximation for the variance-covariance matrix of the two stage Prais-Winston estimator of the regression coefficients. The efficiency properties of this estimator with respect to ordinary least squares, and generalized least squares with a known autocorrelation coefficient are then analysed numerically. The results are useful for the practitioners dealing with moderate size sample data.

The present paper investigates the properties of the sampling distribution of an operational general ridge estimator. Exact expression are given for the moments and their approximations are worked out when non-centrality parameter is large. These approximations are used to study the skewness and kurtosis of the sampling distribution.

This paper presents a fairly general and sufficiently weak condition on the observation matrix for the asymptotic normality of the least squares estimator of coefficient vector in a linear regression model. The asymptotic distribution of a statistic for testing the nullity of coefficient vector is also considered.

In the estimation of a linear regression model with random coefficients, sometimes negative estimates of variances of random coefficients are obtained–an undesirable feature. In this paper we have obtained the asymptotic bounds of the probability of obtaining negative estimators. A simple illustration is also provided for the purpose.

The paper presents a comparative study of product estimators proposed byRobson [1957] andMurthy [1964]. It is seen that the Robson's estimator gives a better performance.

In this paper we develop small-σ and large-T asymptotic expansions of the distribution functions of a family of adaptive shrinkage estimators and theirF-ratios. We demonstrate that the small-σ approximation is much more accurate than the large-T approximation. The small-σ approximate distribution function of the improvedF-ratio is a weighted sum of centralF distribution functions with varying degrees of freedom. This result is useful for forming confidence intervals and testing hypotheses using shrinkage estimators.

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

This paper presents a brief survey of the developments in the estimation of seemingly unrelated regression equation models covering a period of one and a half decades, including some of the recent results by the authors.

In this article the authors have investigated the situations in which the single-equation least squares estimator is identical with the generalized least squares estimator in the seemingly unrelated regression model. The condition obtained turned out to be advantageous from an empirical point of view as it permits one to decide whether to go for a single-equation least squares method or Zellner's method with estimated disturbance variance covariance matrix for estimating the coefficients in the model.

An estimator for the mean of a Normal population is presented and its properties are analyzed. The efficiency with respect to the conventional sample mean is also examined.

This paper derives the exact expressions for the first two moments of a generalized ridge estimator employing the initial choice of characterizing scalars as recommended by Hoer1 and Kermard (1970a). A numerical comparison of relative bias, relative mean squared error and efficiency with respect to the ordinary least squares estimator is also presented.

Small-disturbance approximations for the bias vector and mean squared error matrix of the mixed regression estimator for the coefficients in a linear regression model are derived and efficiency with respect to least squares estimator is examined.

summary This paper discusses a pre-test regression estimator which uses the least squares estimate when it is “large” and a ridge regression estimate for “small” regression coefficients, where the preliminary test is applied separately to each regression coefficient in turn to determine whether it is “large” or “small.” For orthogonal regressors, the exact finite-sample bias and mean squared error of the pre-test estimator are derived. The latter is less biased than a ridge estimator, and over much of the parameter space the pre-test estimator has smaller mean squared error than least squares. A ridge estimator is found to be inferior to the pre-test estimator in terms of mean squared error in many situations, and at worst the latter estimator is only slightly less efficient than the former at commonly used significance levels.

This paper considers a class of recently developed biased estimators of regression coefficients and studies its sampling properties when the disturbances are not normally distributed. It has been found that the conditions of dominance of these estimators over the least squares estimator, under non-normality, are quite different than their well-known dominance conditions under normality. Some implications of the results are also discussed.

Regression coefficients are regarded as stochastic variables in order to account for this kind of variability. This is needed, because differences in responses at successive doses vary generally and thus the assumption of constancy of regression coefficients is violated.

Employing the small-disturbance approach, I study the bias and mean squared error of a class of estimators of the variance of the disturbances in a simultaneous linear stochastic equation model. The estimator considered is the residual sum of squares after estimation of the structural parameters by a k-class estimator, divided by an arbitrary scalar. The scalar which minimizes the mean squared error is (T—n+2), regardless of which k-class estimator is used, where T is the number of observations and n is the number of structural parameters estimated. Using the scalar (T—n+2), the member of the k-class that minimizes the mean squared error is classical least squares.

This paper presents a class of estimators for the mean of a normal population and determines the conditions on characterizing scalars under which the class of estimators uniformly dominates over the conventional sample mean according to the mean-square-error criterion.