Accession Number : AD0248651

Title :   A CENTRAL LIMIT THEOREM FOR SYSTEMS OF REGRESSIONS

Corporate Author : NORTH CAROLINA UNIV AT CHAPEL HILL DEPT OF STATISTICS

Personal Author(s) : HANNAN, E.J.

Report Date : MAR 1960

Pagination or Media Count : 1

Abstract : The theory of regression on fixed variables, when the residuals are generated by a stationary process, was illuminated by the introduction of certain restrictions on the regressor vectors. These restrictions are designed to concentrate attention on cases where consistent estimates of the regression coefficients exist and the asymptotic properties of these estimates may be investigated by Fourier methods. The restric(over) tions are satisfied in most cases of regression on functions of time as well as in cases where the fixed variable is generated by some stationary process for which the sample serial correlations converge with probably one. Conditions are shown which are (together with certain restrictions on the nature of the process generating the residuals) sufficient to ensure that the estimates of the regression coefficients are asymptotically normal. (Author)

Descriptors :   FOURIER ANALYSIS, MATRICES(MATHEMATICS), PROBABILITY, STATISTICAL FUNCTIONS, STATISTICAL PROCESSES.

Distribution Statement : APPROVED FOR PUBLIC RELEASE