Estimation of Variance Components When Errors Are Correlated by Autoregressive of Order One

Abstract

In the present investigation, expressions for estimating variance components of one-way classification random model are developed in case of correlated errors which follows autoregressive of order one i.e. AR(I). These expressions are further used to see the influence ofcorrelated errors on the estimate ofheritability by half-sib method. The expected mean sums ofsquare due to error and due to sire are overestimated and underestimated respectively when errors are negatively correlated. The former increases and the later decreases as the degree of correlation increases. When the correlation is positive, just reverse results are obtained for both the expected mean sums ofsquares. The heritability values obtained by neglecting the correlation present in errors are underestimated when they are negatively correlated. In contrast, heritability values are overestimated if the correlation is positive. These results are found to be consistent for all the levels of heritability. Also, heritability increases from zero to nearly four as the autoregressive coefficient increases from minus unity to approximately unity irrespective ofthe heritability values. Thus, when the coefficient ofAR(I) is positive and is very high, heritability value goes far beyond its actual upper limit (i.e. unity) but ifit is negatively correlated, it will never cross the actual minimum limit ofheritability even for maximum value of auto regression coefficient, and simply it matches to the minimum limit of heritability in such a situation.