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Exponential Series Estimator of multivariate densities

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  • Wu, Ximing

Abstract

We present an Exponential Series Estimator (ESE) of multivariate densities, which has an appealing information-theoretic interpretation. For a d dimensional random variable with density p0, the ESE takes the form , where are some real-valued, linearly independent functions defined on the support of p0. We derive the convergence rate of the ESE in terms of the Kullback-Leibler Information Criterion, the integrated squared error and some other metrics. We also derive its almost sure uniform convergence rate. We then establish the asymptotic normality of . We undertake two sets of Monte Carlo experiments. The first experiment examines the ESE performance using mixtures of multivariate normal densities. The second estimates copula density functions. The results demonstrate the efficacy of the ESE. An empirical application on the joint distributions of stock returns is presented.

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  • Wu, Ximing, 2010. "Exponential Series Estimator of multivariate densities," Journal of Econometrics, Elsevier, vol. 156(2), pages 354-366, June.
    • Handle: RePEc:eee:econom:v:156:y:2010:i:2:p:354-366
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    2. Yichen Gao & Yu Zhang & Ximing Wu, 2015. "Penalized exponential series estimation of copula densities with an application to intergenerational dependence of body mass index," Empirical Economics, Springer, vol. 48(1), pages 61-81, February.
    3. Federico Zincenko, 2023. "Nonparametric estimation of conditional densities by generalized random forests," Papers 2309.13251, arXiv.org, revised May 2024.
    4. Zincenko, Federico, 2018. "Nonparametric estimation of first-price auctions with risk-averse bidders," Journal of Econometrics, Elsevier, vol. 205(2), pages 303-335.
    5. Perloff, Jeffrey M. & Schlenker, Wolfram & Sears, Molly & Wu, Ximing, 2020. "Crop Failures from Temperature and Precipitation Shocks: Implications for U.S. Crop Insurance," 2020 Annual Meeting, July 26-28, Kansas City, Missouri 304540, Agricultural and Applied Economics Association.
    6. Ximing Wu & Andreas Savvides & Thanasis Stengos, 2008. "The Global Joint Distribution of Income and Health," Working Paper series 25_08, Rimini Centre for Economic Analysis.
    7. Jesse B. Tack & David Ubilava, 2015. "Climate and agricultural risk: measuring the effect of ENSO on U.S. crop insurance," Agricultural Economics, International Association of Agricultural Economists, vol. 46(2), pages 245-257, March.
    8. Lee Tae-Hwy & Mao Millie Yi & Ullah Aman, 2021. "Maximum Entropy Analysis of Consumption-based Capital Asset Pricing Model and Volatility," Journal of Econometric Methods, De Gruyter, vol. 10(1), pages 1-19, January.
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    10. Juan Lin & Ximing Wu, 2015. "Smooth Tests of Copula Specifications," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 33(1), pages 128-143, January.
    11. Xu, Xingbai & Lee, Lung-fei, 2018. "Sieve maximum likelihood estimation of the spatial autoregressive Tobit model," Journal of Econometrics, Elsevier, vol. 203(1), pages 96-112.
    12. Jenny Farmer & Donald Jacobs, 2018. "High throughput nonparametric probability density estimation," PLOS ONE, Public Library of Science, vol. 13(5), pages 1-29, May.

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