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On the asymptotic behaviour of the integrated square error of kernel density estimators with data-dependent bandwidth

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  • Tenreiro, Carlos

Abstract

In this paper, we consider the integrated square error where f is the common density function of the independent and identically distributed random vectors X1,...,Xn and is the kernel estimator with a data-dependent bandwidth. Using the approach introduced by Hall (J. Multivariate Anal. 14 (1984) 1), and under some regularity conditions, we derive the L2 consistency in probability of and we establish an asymptotic expansion in probability and a central limit theorem for Jn.

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  • Tenreiro, Carlos, 2001. "On the asymptotic behaviour of the integrated square error of kernel density estimators with data-dependent bandwidth," Statistics & Probability Letters, Elsevier, vol. 53(3), pages 283-292, June.
    • Handle: RePEc:eee:stapro:v:53:y:2001:i:3:p:283-292
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    References listed on IDEAS

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    1. Fan, Yanqin, 1994. "Testing the Goodness of Fit of a Parametric Density Function by Kernel Method," Econometric Theory, Cambridge University Press, vol. 10(2), pages 316-356, June.
    2. Hall, Peter, 1984. "Central limit theorem for integrated square error of multivariate nonparametric density estimators," Journal of Multivariate Analysis, Elsevier, vol. 14(1), pages 1-16, February.
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    Cited by:

    1. Carlos Tenreiro, 2022. "On automatic kernel density estimate-based tests for goodness-of-fit," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(3), pages 717-748, September.
    2. Yu-Ye Zou & Han-Ying Liang, 2020. "CLT for integrated square error of density estimators with censoring indicators missing at random," Statistical Papers, Springer, vol. 61(6), pages 2685-2714, December.
    3. Tenreiro, Carlos, 2003. "On the asymptotic normality of multistage integrated density derivatives kernel estimators," Statistics & Probability Letters, Elsevier, vol. 64(3), pages 311-322, September.
    4. Paul Deheuvels & David Mason, 2004. "General Asymptotic Confidence Bands Based on Kernel-type Function Estimators," Statistical Inference for Stochastic Processes, Springer, vol. 7(3), pages 225-277, October.

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