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Nonparametric estimation of ratios of noise to signal in stochastic regression

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  • Tong, Howell
  • Yao, Qiwei

Abstract

In this paper, we study three different types of estimates for the noise-to signal ratios in a general stochastic regression setup. The locally linear and locally quadratic regression estimators serve as the building blocks in our approach. Under the assumption that the observations are strictly stationary and absolutely regular, we establish the asymptotic normality of the estimates, which indicates that the residual-based estimates are to be preferred. Further, the locally quadratic regression reduces the bias when compared with the locally linear (or locally constant) regression without the concomitant increase in the asymptotic variance, if the same bandwidth is used. The asymptotic theory also paves the way for a fully data-driven under smoothing scheme to reduce the biases in estimation. Numerical examples with both simulated and real data sets are used as illustration.

Suggested Citation

  • Tong, Howell & Yao, Qiwei, 2000. "Nonparametric estimation of ratios of noise to signal in stochastic regression," LSE Research Online Documents on Economics 6324, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:6324
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    File URL: http://eprints.lse.ac.uk/6324/
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    Citations

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    Cited by:

    1. Holger Dette & Mareen Marchlewski & Jens Wagener, 2012. "Testing for a constant coefficient of variation in nonparametric regression by empirical processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(5), pages 1045-1070, October.
    2. Müller, Hans-Georg & Sen, Rituparna & Stadtmüller, Ulrich, 2011. "Functional data analysis for volatility," Journal of Econometrics, Elsevier, vol. 165(2), pages 233-245.
    3. Dette, Holger & Wieczorek, Gabriele, 2007. "Testing for a constant coefficient of variation in nonparametric regression," Technical Reports 2007,36, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    4. Hyndman, R.J. & Yao, Q., 1998. "Nonparametric Estimation and Symmetry Tests for Conditional Density Functions," Monash Econometrics and Business Statistics Working Papers 17/98, Monash University, Department of Econometrics and Business Statistics.
    5. Storlie, Curtis B. & Helton, Jon C., 2008. "Multiple predictor smoothing methods for sensitivity analysis: Example results," Reliability Engineering and System Safety, Elsevier, vol. 93(1), pages 55-77.
    6. Liitiäinen, Elia & Corona, Francesco & Lendasse, Amaury, 2010. "Residual variance estimation using a nearest neighbor statistic," Journal of Multivariate Analysis, Elsevier, vol. 101(4), pages 811-823, April.

    More about this item

    Keywords

    absolutely regular; asymptotic normality; local polynomial regression; noise to signal ratio.;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

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