Performance and Robustness Analysis of Sequential Hypotheses Testing for Time Series with Trend

Alexey Kharin, Ton That Tu


The problem of sequential testing of simple hypotheses for time series with a trend is considered. Analytic expressions and asymptotic expansions for error probabilities and expected numbers of observations are obtained. Robustness analysis is performed. Numerical results are given.

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Basseville M, Nikiforov I (1993). Detection of Abrupt Changes: Theory and Application. Prentice Hall.

Bilodeau M, Brenner D (1999). The Theory of Multivariate Statistics. Springer-Verlag.

Coope I (1996). On Matrix Trace Inequalities and Related Topics for Products of Hermitian Matrices. Journal of Mathematical Analysis and Applications, 188, 999-1001.

Cox D, Miller H (1965). The Theory of Stochastic Processes. John Wiley and Sons.

Govindarajulu Z (2004). Sequential Statistics. World Scientifc.

Gut A (2005). Probability: A graduate Course. Springer Science-Business Media Inc.

Hoffman J (2001). Numerical Methods for Engineers and Scientists. Marcel Dekker Inc.

Huber P (1981). Robust Statistics. John Wiley and Sons.

Kharin A (2005). Robust Bayesian Prediction under Distortions of Prior and Conditional Distributions. Journal of Mathematical Sciences, 126(1), 992-997.

Kharin A (2008). Robustness Evaluation in Sequential Testing of Composite Hypotheses. Austrian Journal of Statistics, 37(1), 51-60.

Kharin A (2011). Robustness Analysis for Bayesian Sequential Testing of Composite Hypotheses under Simultaneous Distortion of Priors and Likelihoods. Austrian Journal of Statistics, 40(1&2), 65-73.

Kharin A (2013). Robustness of Sequential Testing of Hypotheses on Parameters of M-valued Random Sequences. Journal of Mathematical Sciences, 189(6), 924-931.

Kharin A (2016). Performance and Robustness Evaluation in Sequential Hypotheses Testing. Communications in Statistics - Theory and Methods, 45(6), 1693-1709.

Kharin A, Kishylau D (2015). Robust Sequential Test for Hypotheses about Discrete Distributions in the Presence of ``Outliers"." Journal of Mathematical Sciences, 205(1), 68-73.

Kharin A, Ton T (2016). Sequential Statistical Hypotheses Testing on Parameters of Time Series with a Trend under Missing Values. Proceedings of the National Academy of Sciences of Belarus. Series of Physical-Mathematical Sciences, (3), 38-46.

Kharin Y (1997). Robustness of Clustering under Outliers. Lecture Notes in Computer Science, 1280, 501-512.

Maevskii V, Kharin Y (2002). Robust Regressive Forecasting under Functional Distortions in a Model. Automation and Remote Control, 63(11), 1803-1820.

Wald A (1947). Sequential Analysis. John Wiley and Sons.

Wald A, Wolfowitz J (1948). Optimum Character of the Sequential Probability Ratio Test. The Annals of Mathematical Statistics, 19(3), 326-339.



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