The Annals of Statistics

Data-Driven Bandwidth Choice for Density Estimation Based on Dependent Data

Jeffrey D. Hart and Philippe Vieu

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The bandwidth selection problem in kernel density estimation is investigated in situations where the observed data are dependent. The classical leave-out technique is extended, and thereby a class of cross-validated bandwidths is defined. These bandwidths are shown to be asymptotically optimal under a strong mixing condition. The leave-one out, or ordinary, form of cross-validation remains asymptotically optimal under the dependence model considered. However, a simulation study shows that when the data are strongly enough correlated, the ordinary version of cross-validation can be improved upon in finite-sized samples.

Article information

Ann. Statist., Volume 18, Number 2 (1990), 873-890.

First available in Project Euclid: 12 April 2007

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


Primary: 65G05
Secondary: 62G20: Asymptotic properties 62M99: None of the above, but in this section 62M10: Time series, auto-correlation, regression, etc. [See also 91B84] 60G10: Stationary processes 60G35: Signal detection and filtering [See also 62M20, 93E10, 93E11, 94Axx]

Nonparametric density estimation kernel estimate bandwidth selection $\alpha$-mixing processes cross-validation


Hart, Jeffrey D.; Vieu, Philippe. Data-Driven Bandwidth Choice for Density Estimation Based on Dependent Data. Ann. Statist. 18 (1990), no. 2, 873--890. doi:10.1214/aos/1176347630.

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