Halkos, George and Kevork, Ilias (2006): Estimating population means in covariance stationary process.

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Abstract
In simple random sampling, the basic assumption at the stage of estimating the standard error of the sample mean and constructing the corresponding confidence interval for the population mean is that the observations in the sample must be independent. In a number of cases, however, the validity of this assumption is under question, and as examples we mention the cases of generating dependent quantities in Jackknife estimation, or the evolution through time of a social quantitative indicator in longitudinal studies. For the case of covariance stationary processes, in this paper we explore the consequences of estimating the standard error of the sample mean using however the classical way based on the independence assumption. As criteria we use the degree of bias in estimating the standard error, and the actual confidence level attained by the confidence interval, that is, the actual probability the interval to contain the true mean. These two criteria are computed analytically under different sample sizes in the stationary ARMA(1,1) process, which can generate different forms of autocorrelation structure between observations at different lags.
Item Type:  MPRA Paper 

Original Title:  Estimating population means in covariance stationary process 
Language:  English 
Keywords:  Jackknife estimation; ARMA; Longitudinal data; Actual confidence level 
Subjects:  C  Mathematical and Quantitative Methods > C5  Econometric Modeling C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C15  Statistical Simulation Methods: General 
Item ID:  31843 
Depositing User:  Nickolaos Tzeremes 
Date Deposited:  26. Jun 2011 10:18 
Last Modified:  23. Feb 2013 14:49 
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URI:  http://mpra.ub.unimuenchen.de/id/eprint/31843 