Estimation of regression parameters with correlated residuals, part 1
by
Rabindra Nath Das
Department of Statistics, Burdwan University, Burdwan, West Bengal, India

One of the standard assumptions in the regression model is that the error terms ui and uj , associated with the ith and jth observations, are uncorrelated. Correlation in the error terms suggests that there is additional explanatory information in the data that has not been exploited in the current model or observations sampled from adjacent experimental plots or areas tend to have residuals that are correlated since they are affected by similar external conditions. When the observations have a natural sequential order, the correlation is referred to as autocorrelation.

In this paper we have considered regression models when errors in observations have intra-class structure, inter-class structure and compound symmetry structure. In general, the form of the correlation structure is known for a given situation of data set but the correlation parameter or parameters that are involved in the correlation structure are always unknown. Here we have developed some methods for estimating the regression parameters, the correlation coefficient or coefficients and the error variance for the regression models with correlated residuals having intra-class structure, inter-class structure and compound symmetry structure.

Date received: May 26, 2003