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Central limit theorems for nonparametric estimators with real‐time random variables

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  • Tae Yoon Kim
  • Zhi‐Ming Luo

Abstract

In this article, asymptotic theories for nonparametric methods are studied when they are applied to real‐time data. In particular, we derive central limit theorems for nonparametric density and regression estimators. For this we formally introduce a sequence of real‐time random variables indexed by a parameter related to fine gridding of time domain (or fine discretization). Our results show that the impact of fine gridding is greater in the density estimation case in the sense that strong dependence due to fine gridding severely affects the major strength of nonparametric density estimator (or its data‐adaptive property). In addition, we discuss some issues about nonparametric regression model with fine gridding of time domain.

Suggested Citation

  • Tae Yoon Kim & Zhi‐Ming Luo, 2010. "Central limit theorems for nonparametric estimators with real‐time random variables," Journal of Time Series Analysis, Wiley Blackwell, vol. 31(5), pages 337-347, September.
    • Handle: RePEc:bla:jtsera:v:31:y:2010:i:5:p:337-347
    DOI: 10.1111/j.1467-9892.2010.00668.x
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    References listed on IDEAS

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    1. Tae Yoon Kim, 2004. "Nonparametric detection of correlated errors," Biometrika, Biometrika Trust, vol. 91(2), pages 491-496, June.
    2. Hall, Peter & Hart, Jeffrey D., 1990. "Nonparametric regression with long-range dependence," Stochastic Processes and their Applications, Elsevier, vol. 36(2), pages 339-351, December.
    3. P. M. Robinson, 1983. "Nonparametric Estimators For Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 4(3), pages 185-207, May.
    4. Kim, Tae Yoon & Park, Byeong U. & Moon, Myung Sang & Kim, Chiho, 2009. "Using bimodal kernel for inference in nonparametric regression with correlated errors," Journal of Multivariate Analysis, Elsevier, vol. 100(7), pages 1487-1497, August.
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