The role of the copula density function in the estimation of the conditional density function

Shirazi, Esmaeil

doi:10.22075/ijnaa.2025.34631.5178

The role of the copula density function in the estimation of the conditional density function

Articles in Press

Document Type : Research Paper

Author

Esmaeil Shirazi

Faculty of Science, Gonbad Kavous University, Gonbad Kavous, Iran

10.22075/ijnaa.2025.34631.5178

Abstract

In this article, a new wavelet-based method for estimating the conditional density function using the wavelet method is investigated. Based on this method, we will explain how to obtain an estimate with the optimal convergence rate for the conditional density function based on the information in the quantiles and using the copula density function. We also discuss the convergence rate of the new estimator.

Keywords

Hard thresholding estimator

Copula function

Conditional density

Quantiles

Wavelets

[1] D. Bosq, Nonparametric Statistics for Stochastic Processes, second edition, Springer, New York, 1998.

[2] C. Chesneau and H. Doosti, A note on the adaptive estimation of a conditional continuous‑discrete multivariate density by wavelet methods, Chinese J. Math. 2 (2016), 1-8.

[3] O.P. Faugeras, A quantile‑copula approach to conditional density estimation, J. Multivar. Anal. 100 (2009), 2083-2099.

[4] H. Joe, Multivariate Models and Dependence Concepts, Chapman & Hall, London, 1997.

[5] G. Lugosi and L. Devroye, Combinatorial Methods in Density Estimation, Springer‑Verlag, New York, 1987.

[6] S. Mallat, A Wavelet Tour of Signal Processing, the Sparse Way, third edition, Academic Press, 2009.

[7] D. Picard, A. Tsybakov, W. Hardle, and G. Kerkyacharian, Wavelets, approximations, and statistical applications, Lecture Notes in Statistics, Springer‑Verlag, Berlin, 1998.

[8] E. Shirazi and Y.P. Chaubey, Non‑negative density estimation via wavelet block thresholding for biased data, J. Statist. Theory Pract. 11 (2019), 13.

[9] E. Shirazi and O.P. Faugeras, A new wavelet‑based estimation of conditional density via block threshold method, Commun. Statist. Theory Meth. 53 (2024), no. 22, 8155-8165.

[10] E. Shirazi, B. Ghanbari, and M. Yarmohammadi, Wavelet block thresholding for copula density estimation under biased sampling, J. Statist. Comput. Simul. 93 (2023), no. 14, 2512-2533.

[11] A. Sklar, Fonctions de répartition à n dimensions et leurs marges, Publ. Inst. Statist. Univ. Paris 8 (1959), 229-231.

[12] Q. Yao and J. Fan, Nonlinear Time Series, Springer, New York, 2005.