ﻻ يوجد ملخص باللغة العربية
Consider a linear regression model and suppose that our aim is to find a confidence interval for a specified linear combination of the regression parameters. In practice, it is common to perform a Durbin-Watson pretest of the null hypothesis of zero first-order autocorrelation of the random errors against the alternative hypothesis of positive first-order autocorrelation. If this null hypothesis is accepted then the confidence interval centred on the Ordinary Least Squares estimator is used; otherwise the confidence interval centred on the Feasible Generalized Least Squares estimator is used. We provide new tools for the computation, for any given design matrix and parameter of interest, of graphs of the coverage probability functions of the confidence interval resulting from this two-stage procedure and the confidence interval that is always centred on the Feasible Generalized Least Squares estimator. These graphs are used to choose the better confidence interval, prior to any examination of the observed response vector.
We consider a linear regression model with regression parameter beta=(beta_1,...,beta_p) and independent and identically N(0,sigma^2) distributed errors. Suppose that the parameter of interest is theta = a^T beta where a is a specified vector. Define
We consider a general regression model, without a scale parameter. Our aim is to construct a confidence interval for a scalar parameter of interest $theta$ that utilizes the uncertain prior information that a distinct scalar parameter $tau$ takes the
Introductory texts on statistics typically only cover the classical two sigma confidence interval for the mean value and do not describe methods to obtain confidence intervals for other estimators. The present technical report fills this gap by first
Consider a linear regression model with n-dimensional response vector, regression parameter beta = (beta_1, ..., beta_p) and independent and identically N(0, sigma^2) distributed errors. Suppose that the parameter of interest is theta = a^T beta wher
We derive a computationally convenient formula for the large sample coverage probability of a confidence interval for a scalar parameter of interest following a preliminary hypothesis test that a specified vector parameter takes a given value in a ge