On some non parametric estimators of the quantile density function for a stationary associated process

References

• Babu, G. J., and C. Radhakrishna Rao. 1990. Estimation of the reciprocal of the density quantile function at a point. Journal of Multivariate Analysis 33 (1):106–24. doi: 10.1016/0047-259X(90)90008-6.
   Web of Science ®Google Scholar
• Babu, G. J., A. J. Canty, and Y. P. Chaubey. 2002. Application of Bernstein polynomials for smooth estimation of a distribution and density function. Journal of Statistical Planning and Inference 105 (2):377–92. doi: 10.1016/S0378-3758(01)00265-8.
   Web of Science ®Google Scholar
• Bagai, I., and B. L. S. Prakasa Rao. 1995. Kernel-type density and failure rate estimation for associated sequences. Annals of the Institute of Statistical Mathematics 47 (2):253–66. doi: 10.1007/BF00773461.
   Web of Science ®Google Scholar
• Chaubey, Y. P., I. Dewan, and J. Li. 2011. Smooth estimation of survival and density functions for a stationary associated process using Poisson weights. Statistics & Probability Letters 81 (2):267–76. doi: 10.1016/j.spl.2010.10.010.
   Web of Science ®Google Scholar
• Chaubey, Y. P., I. Dewan, and J. Li. 2021. On some smooth estimators of the quantile function for a stationary associated process. Sankhya B 83 (S1):114–39. doi: 10.1007/s13571-020-00242-x.
   Google Scholar
• Cheng, C. 1995. Uniform consistency of generalized kernel estimators of quantile density. Annals of Statistics 23 (6):2285–91.
   Web of Science ®Google Scholar
• Cheng, C., and E. Parzen. 1997. Unified estimators of smooth quantile and quantile density functions. Journal of Statistical Planning and Inference 59 (2):291–307. doi: 10.1016/S0378-3758(96)00110-3.
   Web of Science ®Google Scholar
• Dewan, I., and B. L. S. Prakasa Rao. 1999. A general method of density estimation for associated random variables. Journal of Nonparametric Statistics 10 (4):405–20. doi: 10.1080/10485259908832769.
   Web of Science ®Google Scholar
• Esary, J. D., F. Proschan, and D. W. Walkup. 1967. Association of random variables, with applications. The Annals of Mathematical Statistics 38 (5):1466–74. doi: 10.1214/aoms/1177698701.
   Google Scholar
• Falk, M. 1986. On the estimation of the quantile density function. Statistics & Probability Letters 4 (2):69–73. doi: 10.1016/0167-7152(86)90020-9.
   Web of Science ®Google Scholar
• Harrell, F. E., and C. E. Davis. 1982. A new distribution-free quantile estimator. Biometrika 69 (3):635–40. doi: 10.1093/biomet/69.3.635.
   Web of Science ®Google Scholar
• Jones, M. C. 1992. Estimating densities, quantiles, quantile densities and density quantiles. Annals of the Institute of Statistical Mathematics 44 (4):721–7. doi: 10.1007/BF00053400.
   Web of Science ®Google Scholar
• Jones, M. C. 1993. Simple boundary correction for kernel density estimation. Statistics and Computing 3 (3):135–46. doi: 10.1007/BF00147776.
   Web of Science ®Google Scholar
• Karunamuni, R. J., and T. Alberts. 2005. A generalized reflection method of boundary correction in kernel density estimation. Canadian Journal of Statistics 33 (4):497–509. doi: 10.1002/cjs.5550330403.
   Web of Science ®Google Scholar
• Maritz, J. S., and R. G. Jarrett. 1978. A note on estimating the variance of the sample median. Journal of the American Statistical Association 73 (361):194–6. doi: 10.1080/01621459.1978.10480027.
   Web of Science ®Google Scholar
• Muller, H. G. 1993. On the boundary kernel method for non-parametric curve estimation near end points. Scandinavian Journal of Statistics 20:313–28.
   Web of Science ®Google Scholar
• Padgett, W. J. 1986. A kernel-type estimator of a quantile function from right-censored data. Journal of the American Statistical Association 81 (393):215–22. doi: 10.1080/01621459.1986.10478263.
   Web of Science ®Google Scholar
• Parzen, E. 1979. Nonparametric statistical data modeling. Journal of the American Statistical Association 74 (365):105–21. doi: 10.1080/01621459.1979.10481621.
   Web of Science ®Google Scholar
• Prakasa Rao, B. L. S. 2012. Associated sequences, demimartingales and nonparametric inference. Basel: Springer.
   Google Scholar
• Prakasa Rao, B. L. S., and I. Dewan. 2001. Associated sequences and related inference problems, In Handbook of statistics, ed. D. N. Shanbhag and C. R. Rao, 693–731. Holland: Elsevier Science.
   Google Scholar
• Roussas, G. G. 2000. Asymptotic normality of the kernel estimate of a probability density function under association. Statistics & Probability Letters 50 (1):1–12. doi: 10.1016/S0167-7152(00)00072-9.
   Web of Science ®Google Scholar
• Soni, P., I. Dewan, and K. Jain. 2012. Nonparametric estimation of quantile density function. Computational Statistics & Data Analysis 56 (12):3876–86. doi: 10.1016/j.csda.2012.04.014.
   Web of Science ®Google Scholar
• Tukey, J. W. 1965. Which part of the sample contains the information?. Proceedings of the National Academy of Sciences of the United States of America 53 (1):127–34. 16578583 doi: 10.1073/pnas.53.1.127.
   PubMed Web of Science ®Google Scholar
• Wei, L., D. Wang, and A. D. Hutson. 2015. An investigation of quantile function estimators relative to quantile confidence interval coverage. Communications in Statistics: theory and Methods 44 (10):2107–35. 26924881 doi: 10.1080/03610926.2013.775304.
   PubMed Web of Science ®Google Scholar
• Wu, X. 2019. Robust likelihood cross-validation for kernel density estimation. Journal of Business & Economic Statistics 37 (4):761–70. doi: 10.1080/07350015.2018.1424633.
   Web of Science ®Google Scholar
• Yang, S.-S. 1985. A smooth nonparametric estimator of a quantile function. Journal of the American Statistical Association 80 (392):1004–11. doi: 10.1080/01621459.1985.10478217.
   Web of Science ®Google Scholar