Better confidence intervals for the slope parameters of the quadratic regression model when the error term is not normally distributed

Abstract

When the error term is not normally distributed, the confidence intervals for the slope parameters of the quadratic regression model, based on the ordinary t-statistic, are not appropriate. In this paper, we consider the interval based on the ordinary t-statistic and the intervals based on the resampling methods. Further, we derive the Edgeworth expansion of the distribution of the t-statistic. Based on that expansion we propose a new transformation of the t-statistic which is used for the construction of the bootstrap-t confidence interval for the slope parameter beta(2). The obtained results for the Gamma, Weibull, and Exponential distributions and for the real data set show that the intervals based on the resampling methods and the interval based on the new transformation of the t-statistic provide better coverage accuracy than the interval based on the ordinary t-statistic.