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Articles

Parametric embedding of nonparametric inference problems

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Pages 151-164 | Received 15 Sep 2016, Accepted 30 Oct 2017, Published online: 04 Dec 2017

References

  • Aalen, O. 1978. Nonparametric estimation of partial transition probabilities in multiple decrement models. Annals of Statistics 6 (3):534–45. doi:10.1214/aos/1176344198.
  • Alvo, M. 2016. Bridging the gap: A likelihood function approach for the analysis of ranking data. Communications in Statistics—Theory and Methods 45 (19):5835–47.
  • Alvo, M., and P. Cabilio. 1994. Rank test of trend when data are incomplete. Environmetrics 5:21–27. doi:10.1002/(ISSN)1099-095X.
  • Alvo, M., and P. L. H. Yu. 2014. Statistical methods for ranking data. New York, NY: Springer.
  • Andersen, P., O. Borgan, R. Gill, and N. Keiding. 1993. Statistical models based on counting processes. New York, NY: Springer.
  • Bhattacharya, P. K., H. Chernoff, and S. S. Yang. 1983. Nonparametric estimation of the slope of a truncated regression. Annals of Statistics 11 (2):505–14. doi:10.1214/aos/1176346157.
  • Bickel, P. J., C. A. J. Klaassen, Y. Ritov, and J. A. Wellner. 1993. Efficient and adaptive estimation for semiparametric models. Baltimore, MD: Johns Hopkins University Press.
  • Breslow, N. 1970. A generalized Kruskai-Wallis test for comparing K samples subject to unequal ppattern of censorship. Biometrika 57:579–94. doi:10.1093/biomet/57.3.579.
  • Cox, D. R. 1972. Regression models and life-tables. Journal of the Royal Statistical Society, Series B 34 (2):187–220.
  • Cox, D. R. 1975. Partial likelihood. Biometrika 62 (2):269–76. doi:10.1093/biomet/62.2.269.
  • Cuzick, J. 1985. Asymptotic properties of censored linear rank tests. Annals of Statistics 13 (1):133–41. doi:10.1214/aos/1176346581.
  • Friedman, M. 1937. The use of ranks to avoid the assumption of normality implicit in the analysis of variance. Journal of the American Statistical Association 32:675–701. doi:10.1080/01621459.1937.10503522.
  • Gehan, E. A. 1965. A generalized Wilcoxon test for comparing arbitrarily singly-censored samples. Biometrika 52 (1/2):203–23. doi:10.1093/biomet/52.1-2.203.
  • Gill, R. D. 1980. Censoring and stochastic integrals. Amsterdam, The Netherlands: Mathematical Centre.
  • Gu, M. G., T. L. Lai, and K. K. G. Lan. 1991. Rank tests based on censored data and their sequential analogues. American Journal of Mathematical & Management Sciences 11 (1–2):147–76.
  • Hajek, J. 1962. Asymptotically most powerful rank-order tests. Annals of Mathematical Statistics 33 (3):1124–47. doi:10.1214/aoms/1177704476.
  • Hajek, J. 1968. Asymptotic normality of simple linear rank statistics under alternatives. Annals of Mathematical Statistics 39:325–46. doi:10.1214/aoms/1177698394.
  • Hajek, J. 1970. A characterization of limiting distributions of regular estimates. Zeitschrift Für Wahrscheinlichkeitstheorie Und Verwandte Gebiete 14:323–30. doi:10.1007/BF00533669.
  • Hajek, J. 1972. Local asymptotic minimax and admissibility in estimation. In Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability, ed J. N. L. LeCam and E. Scott, Vol. 1, 175–94. Berkeley, CA: University of California Press.
  • Hajek, J., Z. Sidak, and P. K. Sen. 1999. Theory of statistics, 2nd ed. London, UK: Academic Press.
  • Hoeffding, W. 1951. Optimum non-parametric tests. In Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability, ed. J. Neyman, 83–92. Berkeley, CA: University of California Press.
  • Kalbfleisch, J. D., and R. L. Prentice. 1973. Marginal likelihoods based on Cox’s regression and life model. Biometrika 60 (2):267–78. doi:10.1093/biomet/60.2.267.
  • Lai, T. L., and Z. Ying. 1991. Rank regression methods for left-truncated and right-censored data. Annals of Statistics 19 (2):531–56. doi:10.1214/aos/1176348110.
  • Lai, T. L., and Z. Ying. 1992. Asymptotically efficient estimation in censored and truncated regression models. Statistica Sinica 2 (1):17–46.
  • LeCam, L. 1960. Locally asymptotically normal families of distributions. University California Publication Statistics 3:37–98.
  • LeCam, L. 1972. Limits of experiments. In Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, ed J. N. L. LeCam and E. Scott, Vol. 1, 245–61. Berkeley, CA: University of California Press.
  • Lehmann, E., and C. Stein. 1949. On the theory of some non-parametric hypotheses. Annals of Mathematical Statistics 20 (1):28–45. doi:10.1214/aoms/1177730089.
  • Mantel, N. 1966. Evaluation of survival data and two new rank order statistics arising in its consideration. Cancer Chemotherapy Reports 50 (3):163–70.
  • Neyman, J. 1937. Smooth test for goodness of fit. Skandinavisk Aktuarietidskrift 20:149–99.
  • Neyman, J., and E. Pearson. 1933. On the problem of the most efficient tests of statistical hypotheses. Philosophical Transactions of the Royal Social A 231:289–337. doi:10.1098/rsta.1933.0009.
  • Neyman, J., and E. Pearson. 1936. Contributions to the theory of testing statistical hypotheses. Statistics Researcher Memory 1 (1–37):2, 25–57.
  • Prentice, R. 1978. Linear rank tests with right censored data. Biometrika 65:167–79. doi:10.1093/biomet/65.1.167.
  • Stein, C. 1956. Efficient nonparametric testing and estimation. In Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability, ed. J. Neyman, Vol. 1, 187–95. Berkeley, CA: University of California Press.
  • Terry, M. 1952. Some rank order tests which are most powerful against specific parametric alternatives. Annals of Mathematical Statistics 23 (3):346–66. doi:10.1214/aoms/1177729381.
  • Van Der Vaart, A. 1998. Asymptotic statistics. New York, NY: Cambridge University Press.
  • Wald, A. 1949. Statistical decision functions. Annals of Mathematical Statistics 22 (2):165–205. doi:10.1214/aoms/1177730030.

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