Modified Two-Stage Sampling Around the Mean of the First-Order Autoregressive Model

In this paper, a modified two-stage procedure in the Autoregressive model  AR(1) is considered, which investigates the point and the interval estimation of the mean based on the least-squares estimator. The modified two-stage procedure is as effective as the best fixed-sample size procedure. In this regard, the significant properties of the procedure, including asymptotic risk efficiency, first-order efficiency, consistent, and asymptotic distribution of the mean, are established. Then, a Monte Carlo simulation study is deduced to investigate the modified two-stage procedure. The performance of estimators and confidence intervals are evaluated utilizing a simulation study. Finally, real-time series data is considered to illustrate the applicability of the modified two-stage procedure.