A Large Deviation Inequality for β-mixing Time Series and its Applications to the Functional Kernel Regression Model

2017/01/19 by Johannes Krebs, Krebs, Johannes T. N. · 1 citation
Mathematics · #37A25 (Primary) #62G09 (Secondary) #62G20 #62M10 #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Statistical Methods and Bayesian Inference #Statistical Methods and Inference #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.1701.05380

openalex publication_date 2017/01/19 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

We give a new large deviation inequality for sums of random variables of the form Z_k = f(X_k,X_t) for k,t∈ ℕ, t fixed, where the underlying process X is β-mixing. The inequality can be used to derive concentration inequalities. We demonstrate its usefulness in the functional kernel regression model of Ferraty et al. (2007) where we study the consistency of dynamic forecasts.

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