On Estimating from a More General Time-Series Cum Cross-Section Data Structure

iance matrix ft by 'trial, error and generali zation', and obtains best quadratic unbiased (BQU) estimators of the variance compo nents. This, in turn, provides a feasible GLS estimator of the regression parameters. This note uses the results of Wansbeek and Kap teyn [15, 17] to derive the spectral decom position of ft. This allows a systematic and straightforward derivation of ft-1 and ft~v\ The latter matrix is used to simplify the com putation of GLS by reducing it into a weighted least squares (WLS) procedure. In addition, alternative BQU estimators of the variance components are proposed based on residual variances of least squares regressions. These OLS regressions are performed on the original model after it has been pre-multiplied by matrices of eigenvectors of ft. In summary, Ghosh's [4] results are reanalyzed in a brief and concise manner. Moreover, the compu tation of GLS is simplified and alternative BQU estimators of the variance components are derived.

[1]  S. R. Searle,et al.  Dispersion Matrices for Variance Components Models , 1979 .

[2]  S S Arora,et al.  The Exact Finite Sample Properties of the Estimators of Coefficients in the Error Components Regression Models , 1972 .

[3]  Tom Wansbeek,et al.  A simple way to obtain the spectral decomposition of variance components models for balanced data , 1982 .

[4]  T. Wansbeek,et al.  A Note on Spectral Decomposition and Maximum Likelihood Estimation in ANOVA Models with Balanced Data , 1983 .

[5]  Samuel Kotz,et al.  Eigenvalue-eigenvector analysis for a class of patterned correlation matrices with an application , 1984 .

[6]  F. Graybill,et al.  Theorems Concerning Eisenhart's Model II , 1961 .

[7]  Marc Nerlove,et al.  A Note on Error Components Models , 1971 .

[8]  Takeshi Amemiya,et al.  The Estimation of the Variances in a Variance-Components Model , 1971 .

[9]  Charles R. Henderson,et al.  Comment on 'The Use of Error Components Models in Combining Cross Section with Time Series Data' , 1971 .

[10]  Wayne A. Fuller,et al.  Estimation of linear models with crossed-error structure , 1974 .

[11]  Tom Wansbeek Eigenvalue-Eigenvector analysis for a class of patterned correlation matrices with an application: A comment , 1985 .

[12]  Pietro Balestra Best quadratic unbiased estimators of the variance-covariance matrix in normal regression , 1973 .

[13]  Tom Wansbeek,et al.  A Class of Decompositions of the Variance-Covariance Matrix of a Generalized Error Components Model , 1982 .

[14]  J. Hausman Specification tests in econometrics , 1978 .

[15]  Sukesh K. Ghosh Estimating from a More General Time-Series Cum Cross-Section Data Structure , 1976 .

[16]  M. Nerlove A note on error components models, and, Further evidenece on the estimation of dynamic economic relations from a time series of cross sections , 1971 .

[17]  Ashiq Hussain,et al.  The Use of Error Components Models in Combining Cross Section with Time Series Data , 1969 .