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Using bimodal kernel for inference in nonparametric regression with correlated errors

Author

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  • Kim, Tae Yoon
  • Park, Byeong U.
  • Moon, Myung Sang
  • Kim, Chiho

Abstract

For nonparametric regression model with fixed design, it is well known that obtaining a correct bandwidth is difficult when errors are correlated. Various methods of bandwidth selection have been proposed, but their successful implementation critically depends on a tuning procedure which requires accurate information about error correlation. Unfortunately, such information is usually hard to obtain since errors are not observable. In this article a new bandwidth selector based on the use of a bimodal kernel is proposed and investigated. It is shown that the new bandwidth selector is quite useful for the tuning procedures of various other methods. Furthermore, the proposed bandwidth selector itself proves to be quite effective when the errors are severely correlated.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:100:y:2009:i:7:p:1487-1497
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    References listed on IDEAS

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    1. Chiu, Shean-Tsong, 1989. "Bandwidth selection for kernel estimate with correlated noise," Statistics & Probability Letters, Elsevier, vol. 8(4), pages 347-354, September.
    2. Byeong U. Park & Young Kyung Lee & Tae Yoon Kim & Cheolyong Park, 2006. "A Simple Estimator of Error Correlation in Non‐parametric Regression Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 33(3), pages 451-462, September.
    3. Tae Yoon Kim, 2004. "Nonparametric detection of correlated errors," Biometrika, Biometrika Trust, vol. 91(2), pages 491-496, June.
    4. Peter Hall & Ingrid Van Keilegom, 2003. "Using difference‐based methods for inference in nonparametric regression with time series errors," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(2), pages 443-456, May.
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    Cited by:

    1. Scholz, Michael & Sperlich, Stefan & Nielsen, Jens Perch, 2016. "Nonparametric long term prediction of stock returns with generated bond yields," Insurance: Mathematics and Economics, Elsevier, vol. 69(C), pages 82-96.
    2. Huan Wang & Mary C. Meyer & Jean D. Opsomer, 2013. "Constrained spline regression in the presence of AR(p) errors," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 25(4), pages 809-827, December.
    3. repec:grz:wpaper:2012-10 is not listed on IDEAS
    4. K De Brabanter & F Cao & I Gijbels & J Opsomer, 2018. "Local polynomial regression with correlated errors in random design and unknown correlation structure," Biometrika, Biometrika Trust, vol. 105(3), pages 681-690.
    5. 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.

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