| Abstract: | ABSTRACT The goal of this article is to address the problem of fixed-precision estimation of parameters in a linear regression setup with stochastic regressors. First in the case of a linear regression model where the regressor variable and the random errors have independent Gaussian distributions, sequential sampling schemes are proposed for fixed proportional accuracy estimation and fixed-width interval estimation of the regression-slope based on a Chebyshev inequality approach. The asymptotic second-order efficiency of these procedures is then established using the techniques developed in Aras and Woodroofe (1993)2] Aras, G. and Woodroofe, M. 1993. Asymptotic Expansions for the Moments of a Randomly Stopped Average. Ann. Statist., 21: 503–519. Crossref], Web of Science ®] , Google Scholar]. Asymptotic second-order expansions are derived for a lower bound of P (relative error < preassigned bound) in the fixed proportional accuracy estimation case and that of the coverage-probability in the interval-estimation case. In both cases, the possibility of relaxing the Gaussian assumption is explored, leading to a reconsideration of Martinsek's (1995)15] Martinsek, A.T. 1995. Estimating a Slope Parameter in Regression with Prescribed Proportional Accuracy. Statistics and Decisions, 13: 363–377. Google Scholar] fixed proportional accuracy estimation and a detailed discussion of a stochastic multiple linear regression model with distribution-free errors and regressors. In this distribution-free multiple regression scenario, construction of fixed-size confidence regions for the vector of regression-parameters is considered and an asymptotically second-order efficient sequential methodology is put forward. Moderate sample-size performances of some of these procedures are investigated via simulation-studies. |
