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A Localized Neural Network with Dependent Data: Estimation and Inference

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  • Jiti Gao
  • Bin Peng
  • Yanrong Yang

Abstract

In this paper, we propose a localized neural network (LNN) model and then develop the LNN based estimation and inferential procedures for dependent data in both cases with quantitative/qualitative outcomes. We explore the use of identification restrictions from a nonparametric regression perspective, and establish an estimation theory for the LNN setting under a set of mild conditions. The asymptotic distributions are derived accordingly, and we show that LNN automatically eliminates the dependence of data when calculating the asymptotic variances. The finding is important, as one can easily use different types of wild bootstrap methods to obtain valid inference practically. In particular, for quantitative outcomes, the proposed LNN approach yields closed-form expressions for the estimates of some key estimators of interest. Last but not least, we examine our theoretical findings through extensive numerical studies.

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  • Jiti Gao & Bin Peng & Yanrong Yang, 2023. "A Localized Neural Network with Dependent Data: Estimation and Inference," Papers 2306.05593, arXiv.org.
    • Handle: RePEc:arx:papers:2306.05593
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    References listed on IDEAS

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    3. Andrew J. Patton & Kevin Sheppard, 2015. "Good Volatility, Bad Volatility: Signed Jumps and The Persistence of Volatility," The Review of Economics and Statistics, MIT Press, vol. 97(3), pages 683-697, July.
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