References
- Akritas, M. G., and I. Van Keilegom. 2003. Estimation of bivariate and marginal distributions with censored data. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 65 (2):457–71. doi:https://doi.org/10.1111/1467-9868.00396.
- Babu, G., A. Cantry, and Y. Chaubey. 2002. Application of Bernstein polynomials for smooth estimation of a distribution and density function. Journal of Statistical Planning and Inference 105:377–92.
- Babu, G. J., and Y. P. Chaubey. 2006. Smooth estimation of a distribution and density function on a hyper-cube using Bernstein polynomials for dependent random vectors. Statistics & Probability Letters 76 (9):959–69. doi:https://doi.org/10.1016/j.spl.2005.10.031.
- Belalia, M. 2016. On the asymptotic properties of the Bernstein estimator of the multivariate distribution function. Statistics and Probability Letters 110:249–56. doi:https://doi.org/10.1016/j.spl.2015.10.004.
- Bernstein, S. 1912. Démonstration du théorème de weierstrass fondée sur le calcul des probabilités. Communications of the Kharkov Mathematical Society 13:1–2.
- Dabrowska, D. M. 1988. Kaplan-Meier estimate on the plane. The Annals of Statistics 16 (4):1475–89. doi:https://doi.org/10.1214/aos/1176351049.
- Denuit, M., O. Purcaru, and I. Van Keilegom. 2006. Bivariate archimedean copula models for censored data in non-life insurance. Journal of Actuarial Practice 13:5–32.
- Frees, E., and E. A. Valdez. 1998. Understanding relationships using copulas. North American Actuarial Journal 2 (1):1–25. doi:https://doi.org/10.1080/10920277.1998.10595667.
- Gribkova, S., and O. Lopez. 2015. Non-parametric copula estimation under bivariate censoring. Scandinavian Journal of Statistics 42 (4):925–46. doi:https://doi.org/10.1111/sjos.12144.
- Janssen, P., J. Swanepoel, and N. Veraverbeke. 2012. Large sample behavior of the Bernstein copula estimator. Journal of Statistical Planning and Inference 142 (5):1189–97. doi:https://doi.org/10.1016/j.jspi.2011.11.020.
- Koyuncu, N., M. Hanif, S. Shahzadi, and U. Shahzad. 2018. On the adaptive nadaraya-watson kernel estimator for the discontinuity in the presence of jump size. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi 22:511–20. doi:https://doi.org/10.19113/sdufbed.70996.
- Leblanc, A. 2012. On estimating distribution functions using Bernstein polynomials. Annals of the Institute of Statistical Mathematics 64 (5):919–43. doi:https://doi.org/10.1007/s10463-011-0339-4.
- Leblanc, A. 2012. On the boundary properties of Bernstein polynomial estimators of density and distribution functions. Journal of Statistical Planning and Inference 142 (10):2762–78. doi:https://doi.org/10.1016/j.jspi.2012.03.016.
- Lopez, O., and P. Saint-Pierre. 2012. Bivariate censored regression relying on a new estimator of the joint distribution function. Journal of Statistical Planning and Inference 142 (8):2440–53. doi:https://doi.org/10.1016/j.jspi.2012.02.046.
- Lorentz, G. G. 1986. Bernstein polynomials. 2nd ed. New York, NY: Chelsea Publishing.
- Major, P., and L. Rejto. 1988. Strong embedding of the estimator of the distribution function under random censorship. The Annals of Statistics 16 (3):1113–32. doi:https://doi.org/10.1214/aos/1176350949.
- Silverman, B. 1986. Density estimation for statistics and data analysis. New York, NY: Chapman and Hall.
- Stute, W. 1993. Consistent estimation under random censorship when covariables are present. Journal of Multivariate Analysis 45 (1):89–103. doi:https://doi.org/10.1006/jmva.1993.1028.
- van der Laan, M. J. 1996. Efficient estimation in the bivariate censoring model and repairing npmle. The Annals of Statistics 24 (2):596–627. doi:https://doi.org/10.1214/aos/1032894454.
- Vitale, R. 1975. A Bernstein polynomial approach to density estimation. In Statistical Inference and Related Topics, ed. M. L. Puri, vol. 2, 87–99. New York, NY: Academic Press.
- Wand, M., and M. Jones. 1995. Kernel smoothing. New York, NY: Chapman and Hall.