Title:
Folded Variance Estimators for Stationary Time Series
Folded Variance Estimators for Stationary Time Series
Author(s)
Antonini, Claudia
Advisor(s)
Goldsman, David
Alexopoulos, Christos
Wilson, James R.
Alexopoulos, Christos
Wilson, James R.
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Abstract
This thesis is concerned with simulation output analysis. In particular, we are inter-
ested in estimating the variance parameter of a steady-state output process. The estimation
of the variance parameter has immediate applications in problems involving (i) the precision
of the sample mean as a point estimator for the steady-state mean and #956;X, and (ii) confidence
intervals for and #956;X. The thesis focuses on new variance estimators arising from Schrubens
method of standardized time series (STS). The main idea behind STS is to let such series
converge to Brownian bridge processes; then their properties are used to derive estimators
for the variance parameter. Following an idea from Shorack and Wellner, we study different
levels of folded Brownian bridges. A folded Brownian bridge is obtained from the standard
Brownian bridge process by folding it down the middle and then stretching it so that
it spans the interval [0,1]. We formulate the folded STS, and deduce a simplified expression
for it. Similarly, we define the weighted area under the folded Brownian bridge, and we
obtain its asymptotic properties and distribution. We study the square of the weighted area
under the folded STS (known as the folded area estimator ) and the weighted area under the
square of the folded STS (known as the folded Cram??von Mises, or CvM, estimator) as
estimators of the variance parameter of a stationary time series. In order to obtain results
on the bias of the estimators, we provide a complete finite-sample analysis based on the
mean-square error of the given estimators. Weights yielding first-order unbiased estimators
are found in the area and CvM cases. Finally, we perform Monte Carlo simulations to test
the efficacy of the new estimators on a test bed of stationary stochastic processes, including
the first-order moving average and autoregressive processes and the waiting time process in
a single-server Markovian queuing system.
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Date Issued
2005-04-19
Extent
849002 bytes
Resource Type
Text
Resource Subtype
Dissertation