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Complete Convergence for Acceptable Partial sums with Application to Autoregressive Model AR(1)

Ikhlasse Chebbab, Samir Benaissa


The concentration inequalities, or probability bounds, plays a basic role in the analysis of machine learning algorithms and in statistics. In this work, we found a new concentration inequality for acceptable random variables of partial sums which enable us to show the complete convergence for the estimator of the coefficient of first order AR model. Using these inequalities, a confidence interval is obtained.


acceptable random variables, autoregressive process, confidence interval, complete convergence, exponential inequality.

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