Inference on log-linear regression model parameters with composite autocorrelated errors

Abstract

The log-normal distribution arises in many different domains such as finance, stock prices, risk assessments, in motor and health insurance analysis, soil aggregate size distributions (in agriculture), lifetime distributions (quality engineering and survival analysis), telecommunications and traffic engineering, and was introduced to model inherently positive, continuous random phenomena. Positive observations from a continuous random variable (with constant variance) are generally analyzed either by log-normal or gamma models. However, in practice, the variance is not constant always. For handling non-constant variance in the log-normal process random variable distribution, some concomitant variables are included as regressor variables. In the present article, the response distribution is assumed to be log-normal, and the errors under the process are assumed to have a first-order autocorrelated structure. A log-linear composite autocorrelated errors regression model has been developed. The best linear unbiased estimators of all the regression coefficients have been derived except for the intercept which is often unimportant in practice. Autocorrelation coefficient has been estimated by iterative method. A testing procedure for any set of linear hypotheses regarding the unknown regression coefficients has been developed. Confidence intervals of an estimable function and confidence ellipsoids of a set of estimable functions of regression coefficients have been developed. An index of fit for the fitted regression model has also been developed. An example (with simulated data) illustrates the results derived in this report.