IDEAS home Printed from https://ideas.repec.org/p/ake/iiepdt/202050.html
   My bibliography  Save this paper

Density estimation using bootstrap quantile variance and quantile-mean covariance

Author

Listed:
  • Gabriel Montes Rojas

    (Instituto Interdisciplinario de Economía Política de Buenos Aires - UBA - CONICET)

  • Andrés Sebastián Mena

    (Instituto Superior de Estudios Sociales - CONICET)

Abstract

We propose two novel bootstrap density estimators based on the quantile variance and the quantile-mean covariance. We review previous developments on quantile-density estimation and asymptotic results in the literature that can be applied to this case. We conduct Monte Carlo simulations for dierent data generating processes, sample sizes, and parameters. The estimators perform well in comparison to benchmark nonparametric kernel density estimator. Some of the explored smoothing techniques present lower bias and mean integrated squared errors, which indicates that the proposed estimator is a promising strategy.

Suggested Citation

  • Gabriel Montes Rojas & Andrés Sebastián Mena, 2020. "Density estimation using bootstrap quantile variance and quantile-mean covariance," Documentos de trabajo del Instituto Interdisciplinario de Economía Política IIEP (UBA-CONICET) 2020-50, Universidad de Buenos Aires, Facultad de Ciencias Económicas, Instituto Interdisciplinario de Economía Política IIEP (UBA-CONICET).
    • Handle: RePEc:ake:iiepdt:202050
    as

    Download full text from publisher

    File URL: http://iiep-baires.econ.uba.ar/uploads/publicaciones/519/archivos/1.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Javier Alejo & Anil Bera & Antonio Galvao & Gabriel Montes-Rojas & Zhijie Xiao, 2016. "Tests for normality based on the quantile-mean covariance," Stata Journal, StataCorp LP, vol. 16(4), pages 1039-1057, December.
    2. M. Jones, 1992. "Estimating densities, quantiles, quantile densities and density quantiles," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 44(4), pages 721-727, December.
    3. Chesneau, Christophe & Dewan, Isha & Doosti, Hassan, 2016. "Nonparametric estimation of a quantile density function by wavelet methods," Computational Statistics & Data Analysis, Elsevier, vol. 94(C), pages 161-174.
    4. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    5. Pagan,Adrian & Ullah,Aman, 1999. "Nonparametric Econometrics," Cambridge Books, Cambridge University Press, number 9780521355643.
    6. Bera Anil K. & Galvao Antonio F. & Wang Liang, 2014. "On Testing the Equality of Mean and Quantile Effects," Journal of Econometric Methods, De Gruyter, vol. 3(1), pages 47-62, January.
    7. K. Cheung & Stephen Lee, 2005. "Variance estimation for sample quantiles using them out ofn bootstrap," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 57(2), pages 279-290, June.
    8. Nora Saadi & Smail Adjabi & Lamia Djerroud, 2019. "On the estimation of the quantile density function by orthogonal series," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 48(21), pages 5265-5289, November.
    9. Mnatsakanov, Robert M. & Sborshchikovi, Aleksandre, 2018. "Recovery of quantile and quantile density function using the frequency moments," Statistics & Probability Letters, Elsevier, vol. 140(C), pages 53-62.
    10. Daniel Janas, 1993. "A smoothed bootstrap estimator for a studentized sample quantile," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 45(2), pages 317-329, June.
    11. Bera, Anil K. & Galvao, Antonio F. & Wang, Liang & Xiao, Zhijie, 2016. "A New Characterization Of The Normal Distribution And Test For Normality," Econometric Theory, Cambridge University Press, vol. 32(5), pages 1216-1252, October.
    12. A. D. Hutson & M. D. Ernst, 2000. "The exact bootstrap mean and variance of an L‐estimator," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(1), pages 89-94.
    13. Soni, Pooja & Dewan, Isha & Jain, Kanchan, 2012. "Nonparametric estimation of quantile density function," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 3876-3886.
    14. Huang, J. S., 1991. "Estimating the variance of the sample median, discrete case," Statistics & Probability Letters, Elsevier, vol. 11(4), pages 291-298, April.
    15. Cheng, Cheng, 1998. "A Berry-Esséen-type theorem of quantile density estimators," Statistics & Probability Letters, Elsevier, vol. 39(3), pages 255-262, August.
    16. Unknown, 1986. "Letters," Choices: The Magazine of Food, Farm, and Resource Issues, Agricultural and Applied Economics Association, vol. 1(4), pages 1-9.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Fabian Dunker & Stephan Klasen & Tatyana Krivobokova, 2017. "Asymptotic Distribution and Simultaneous Confidence Bands for Ratios of Quantile Functions," Papers 1710.09009, arXiv.org.
    2. Inanoglu, Hulusi & Jacobs, Michael, Jr. & Liu, Junrong & Sickles, Robin, 2015. "Analyzing Bank Efficiency: Are "Too-Big-to-Fail" Banks Efficient?," Working Papers 15-016, Rice University, Department of Economics.
    3. P.G. Sankaran & N.N. Midhu, 2017. "Nonparametric estimation of mean residual quantile function under right censoring," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(10), pages 1856-1874, July.
    4. Andriansyah, Andriansyah & Messinis, George, 2016. "Intended use of IPO proceeds and firm performance: A quantile regression approach," Pacific-Basin Finance Journal, Elsevier, vol. 36(C), pages 14-30.
    5. Chen, Xirong & Li, Degui & Li, Qi & Li, Zheng, 2019. "Nonparametric estimation of conditional quantile functions in the presence of irrelevant covariates," Journal of Econometrics, Elsevier, vol. 212(2), pages 433-450.
    6. Hu, Shuowen & Poskitt, D.S. & Zhang, Xibin, 2021. "Bayesian estimation for a semiparametric nonlinear volatility model," Economic Modelling, Elsevier, vol. 98(C), pages 361-370.
    7. Trede, Mark, 1998. "Making mobility visible: a graphical device," Economics Letters, Elsevier, vol. 59(1), pages 77-82, April.
    8. Joseph G. Altonji & Hidehiko Ichimura & Taisuke Otsu, 2012. "Estimating Derivatives in Nonseparable Models With Limited Dependent Variables," Econometrica, Econometric Society, vol. 80(4), pages 1701-1719, July.
    9. repec:wyi:journl:002108 is not listed on IDEAS
    10. Van Kerm, Philippe, 2006. "Comparisons of income mobility profiles," ISER Working Paper Series 2006-36, Institute for Social and Economic Research.
    11. Chesneau, Christophe & Dewan, Isha & Doosti, Hassan, 2016. "Nonparametric estimation of a quantile density function by wavelet methods," Computational Statistics & Data Analysis, Elsevier, vol. 94(C), pages 161-174.
    12. Ivana Komunjer & Michael T. Owyang, 2012. "Multivariate Forecast Evaluation and Rationality Testing," The Review of Economics and Statistics, MIT Press, vol. 94(4), pages 1066-1080, November.
    13. Hjalmarsson, Erik, 2005. "Predictive regressions with panel data," Working Papers in Economics 160, University of Gothenburg, Department of Economics.
    14. Joel L. Horowitz, 1998. "Bootstrap Methods for Median Regression Models," Econometrica, Econometric Society, vol. 66(6), pages 1327-1352, November.
    15. Long, Xiangdong & Su, Liangjun & Ullah, Aman, 2011. "Estimation and Forecasting of Dynamic Conditional Covariance: A Semiparametric Multivariate Model," Journal of Business & Economic Statistics, American Statistical Association, vol. 29(1), pages 109-125.
    16. Dong, Kangyin & Dong, Xiucheng & Ren, Xiaohang, 2020. "Can expanding natural gas infrastructure mitigate CO2 emissions? Analysis of heterogeneous and mediation effects for China," Energy Economics, Elsevier, vol. 90(C).
    17. Marcel, Bräutigam & Marie, Kratz, 2018. "On the Dependence between Quantiles and Dispersion Estimators," ESSEC Working Papers WP1807, ESSEC Research Center, ESSEC Business School.
    18. Chen, Xiaohong, 2007. "Large Sample Sieve Estimation of Semi-Nonparametric Models," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 76, Elsevier.
    19. Meiseberg, Brinja, 2016. "The Effectiveness of E-tailers’ Communication Practices in Stimulating Sales of Niche versus Popular Products," Journal of Retailing, Elsevier, vol. 92(3), pages 319-332.
    20. Gloria González-Rivera & Tae-Hwy Lee, 2007. "Nonlinear Time Series in Financial Forecasting," Working Papers 200803, University of California at Riverside, Department of Economics, revised Feb 2008.
    21. Pasha Andreyanov & Grigory Franguridi, 2021. "Nonparametric inference on counterfactuals in first-price auctions," Papers 2106.13856, arXiv.org, revised Jun 2022.

    More about this item

    Keywords

    Density Estimation; Quantile Variance; Quantile-Mean Covariance; Bootstrap;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:ake:iiepdt:202050. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: IIEP UBA-CONICET (email available below). General contact details of provider: https://edirc.repec.org/data/ieeubar.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.