Abstract.
This paper investigates the problem of density estimation for absolutely regular observations. In a first part, we state two important results: a new variance inequality and a Rosenthal type inequality. This allows us to study the ? p -integrated risk, p≧ 2, of a large class of density estimators including kernel or projection estimators. Under the summability condition on the mixing coefficients ∑ k≧ 0 (k+1) p− 2 β k <∞, the rates obtained are those known to be optimal in the independent setting.
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Received: 17 October 1995 / In revised form: 26 October 1996
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Viennet, G. Inequalities for absolutely regular sequences: application to density estimation. Probab Theory Relat Fields 107, 467–492 (1997). https://doi.org/10.1007/s004400050094
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DOI: https://doi.org/10.1007/s004400050094