In this dissertation, improved statistical methods for time-series and lifetime data are developed. First, an improved trend test for time series data is presented. Then, robust parametric estimation methods based on system lifetime data with known system signatures are developed.
In the first part of this dissertation, we consider a test for the monotonic trend in time series data proposed by Brillinger (1989). It has been shown that when there are highly correlated residuals or short record lengths, Brillinger’s test procedure tends to have significance level much higher than the nominal level. This could be related to the discrepancy between the empirical distribution of the test statistic and the asymptotic normal distribution. Hence, different bootstrap-based procedures are proposed based on the Brillinger test statistic. The performances of proposed bootstrap test procedures are evaluated through an extensive Monte Carlo simulation study, and are compared to other trend test procedures in the literature.
In the second part of this dissertation, we consider the estimation of component reliability based on system lifetime data with known system signature using the minimum density divergence estimation method. Different estimation procedures based on the minimum density divergence estimation method are proposed. We also study the standard error estimation and interval estimation procedures for the proposed minimum density divergence estimator. Based on the proposed procedures, a Monte Carlo simulation study is used to evaluate the performance of these proposed procedures and compare these procedures with the maximum likelihood estimation under different contaminated mod- els. Then, a numerical example is presented to illustrate the minimum density divergence estimation method. In particular, we show that the proposed estimation procedures are robust to contamination and model misspecification.
Hon Keung Tony Ng
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Zhu, Xiaojie, "Improved Statistical Methods for Time-series and Lifetime Data" (2020). Statistical Science Theses and Dissertations. 19.