STAT 583: Advanced Theory of Statistical Inference

Spring Quarter 1998

Potential Topics, with some Selected and Random References

The following list is meant to be suggestive, and certainly does not exhaust all possible topics. Within any of these general topics, you will need to narrow the focus of your talk and project. I would be glad to talk with you about your choice of a topic for the project.

1. Bootstrap Methods
2. Inference for Dependent Data
3. Model Selection Problems
4. Multiple Comparisons
5. Nonparametric Maximum Likelihood Estimation
6. Nonparametric Density and Regression Function Estimation
7. Rates of Convergence via Empirical Processes
8. Robustness
9. Semiparametric Models: Estimation
10. Semiparametric Models: Testing
11. Sequential Analysis
12. Inverse problems
13. Estimation for multiphase and case-cohort designs
14. Algorithms and computational issues

1. Bootstrap Methods
   • Beran, R. (1987). Prepivoting to reduce level error of confidence sets. Biometrika, 74, 457 - 468.

   • Beran, R. (1988). Prepivoting test statistics: a bootstrap view of asymptotic refinements. J. Amer. Statist. Assoc. 83, 687 - 697.

   • Beran, R. (1995). Stein confidence sets and the bootstrap. Statist. Sinica 5, 109-127.

   • Hu, F. and Zidek, J. V. (1995). A bootstrap based on the estimating equations of the linear model. Biometrika 82, 263 - 275.

   • Newton, M. A. and Geyer, C. J. (1994). Bootstrap recycling: a monte-carlo alternative to the nested bootstrap J. Amer. Statist. Assoc. 89, 905-912.

   • Politis, D. N. and Romano, J. P. (1994). Large sample confidence regions based on subsamples under minimal assumptions. Ann. Statist. 22, 2031 - 2050.

   • Scholz, F. W. (1993). On exactness of the parametric double bootstrap. Boeing Computer Services Technical Report 93-052.

   • Scholz, F. W. (1993). The bootstrap small sample properties. Boeing Computer Services Technical Report 93-051.

2. Inference for Dependent Data.
   • Anderson, T. W. (1993). Goodness of fit tests for spectral distributions. Ann. Statist. 21, 830 - 847.

   • Basawa, I. V. and Rao, B.L.S. (1980). Statistical Inference for Stochastic Processes. Academic Press, New York.

   • Basawa, I. V. and Scott, D. J. (1983). Asymptotic Optimal Inference for Non-ergodic Models Lecture Notes in Statistics 17. Springer-Verlag, New York.

   • Beran, J. (1992). Statistical Methods for Data with Long-Range Dependence Statistical Science 7, 404 - 427.

   • Billingsley, P. (1961). Statistical Inferences for Markov Processes. University of Chicago Press, Chicago.

   • Ibragimov, A. (1963). Estimation of the spectral function of a stationary Gaussian process. Theory of Prob. 8, 366 - 401.

   • Levit, B. Ya. and Samarov, A. M. Estimation of spectral functions. Problems of Information Transmission 14, 120 - 124.

   • Wang, Yazhen (1996). Function estimation via wavelet shrinkage for long-memory data. Ann. Statist. 24, 466 - 484.

   • Wang, Yazhen (1997). Minimax estimation via wavelets for indirect long-memory data. J. Statist. Plann. Inference 64, 45 - 55.

3. Model Selection.
   • Knight, K. (1989). Consistency of Akaike's information crierion for infinite variance autoregressive processes. Ann. Statist. 17, 824 - 840.

   • Linhart, H. and Zucchini, W. (1986). Model Selection. Wiley, New York.

   • Schwarz, G. (1978). Estimating the dimension of a model. Ann. Statist. 6, 461 - 464.

   • Woodroofe, M. (1982). On model selection and the arcsine laws. Ann. Statist. 10, 1182 - 1194.

4. Multiple Comparisons.
   • Johansen, S. and Johnstone, I. (1990). Hotelling's theorem on the volume of tubes: some illustrations in simultaneous inference and data analysis. Ann. Statist. 18, 652 - 684.

   • Knowles, M. and Siegmund, D. (1989). On Hotelling's approach to testing for a nonlinear parameter in regression. Int. Statist. Rev. 57, 205 - 220.

   • Miller, R. G. (1981). Simultaneous Statistical Inference. Springer-Verlag, New York.

   • Owen, A. B. (1995). Nonparametric likelihood confidence bands for a distribution function. J. Amer. Statist. Assoc. 90, 516 - 521.

   • Siegmund, D. and Zhang, H. (1993). The expected number of local maxima of a random field and the volume of tubes. Ann. Statist. 21, 1948 - 1966.

5. Nonparametric Maximum Likelihood Estimation
   • Gill, R. D. (1989). Non- and semiparametric maximum likelihood estimators and the von - Mises method (part I). Scand. J. Statist. 16, 97 - 128.

   • Gill, R. D. and van der Vaart, A. W. (1993). Non- and semiparametric maximum likelihood estimators and the von - Mises method (part II). Scand. J. Statist. 20, 271 - 288.

   • Groeneboom, P. and Wellner, J. A. (1992). Information Bounds and Nonparametric Maximum Likelihood Estimation. Birkhauser, New York.

   • Kiefer, J. and Wolfowitz, J. (1956). Consistency of the maximum likelihood estimator in the presence of infinitely many nuisance parameters. Ann. Math. Statist. 27, 887 - 906.

   • Boyles, R. A., Marshall, A. W., Proschan, F. (1985). Inconsistency of the maximum likelihood estimator of a distribution having increasing failure rate average. Ann. Statist. 13, 413 - 417.

   • Scholz, F. W. (1980). Towards a unified definition of maximum likelihood. Canad. J. Statist. 8, 193 - 203.

6. Nonparametric Density and Regression Function Estimation
   • Bickel, P. J. and Rosenblatt, M. (1973). On some global measures of the deviations of density function estimates. Ann. Statist. 1, 1071 - 1096.

   • Buja, A., Hastie, T., and Tibshirani, R. (1989). Linear smoothers and additive models (with discussion). Ann. Statist. 17, 453 - 555.

   • Devroye, L. (1983). The equivalence of weak, strong, and complete convergence in L-1 for kernel density estimates. Ann. Statist. 11, 896 - 904.

   • Devroye, L. (1987). A Course in Density Estimation. Progress in Probability 14, Birkhauser, Boston.

   • Devroye, L. and Gyorfi, L. (1985). Nonparametric Density Estimation: The L-1 View. Wiley, New York.

   • Hardle, W. (1990). Applied Nonparametric Regression. Cambridge University Press, Cambridge.

   • Hardle, W. (1991). Smoothing Techniques: with implementation in S. Springer-Verlag, New York.

   • Hastie, T. J. and Tibshirani, R. J. (1990). Generalized Additive Models. Chapman and Hall, London.

   • Izenman, A. J. (1991). Recent developments in nonparametric density estimation. J. Amer. Statist. Assoc. 86, 205 - 224.

   • Mallows, C. (1980). Some theory of nonlinear smoothers Ann. Statist. 8, 695 - 715.

   • Nolan, D. and Marron, J. S. (1989). Uniform consistency of automatic and location-adaptive delta-sequence estimators. Probab. Th. Rel. Fields 80, 619 - 632.

   • Rosenblatt, M. (1971). Curve estimates. Ann. Math. Statist. 42, 1815 - 1842.

   • Silverman, B. W. (1986). Density Estimation for Statistics and Data Analysis. Chapman and Hall, London

   • Stone, C. J. (1982). Optimal global rates of convergence for nonparametric regression Ann. Statist. 10, 1040 - 1053.

   • Stone, C. J. (1985). Additive regression and other nonparametric models. Ann. Statist. 13, 689 - 705.

   • Stone, C. J. (1986). The dimensionality reduction principle for generalized additive models Ann. Statist. 14, 590 - 606.

   • Van der Vaart, A. W. (1994). Weak convergence of smoothed empirical processes. Scand. J. Statist. 21, 501 - 504.

7. Rates of convergence via empirical processes
   Birge, L. and Massart, P. (1993). Rates of convergence for minimum contrast estimators. Probab. Theory Relat. Fields 97, 113 - 150.
   • Shen, X. and Wong, W. H. (1994). Convergence rate of sieve estimates. Ann. Statist. 22, 580 - 615.

   • van de Geer, S. (1993). Hellinger - consistency of certain nonparametric maximum likelihood estimators. Ann. Statist. 21, 14 - 44.

   • Wong, W. H. and Shen, X. (1995). Probability inequalities for likelihood ratios and convergence rates of sieve MLEs. Ann. Statist. 23, 339 - 362.

   • Van der Vaart, A. W. and Wellner, J. A. (1996). Weak Convergence and Empirical Processes, Chapter 3.4. Springer-Verlag, New York.

8. Robustness
   • Huber, P. (1964). Robust estimation of a location parameter. Ann. Math. Statist. 35, 73 - 101.

   • Davies, P. L. (1993). Aspects of robust linear regression. Ann. Statist. 21, 1843 - 1899.

   • Davies, P. L. (1992). The asymptotics of Rousseeuw's minimum volume ellipsoid estimator Ann. Statist. 20, 1828 - 1843.

   • Martin, R. D. and Zamar, R. H. (1993). Bias - robust estimation of scale. Ann. Statist. 21, 991 - 1017.

   • Martin, R. D. and Zamar, R. H. (1993). Efficiency constrained bias - robust estimation of location. Ann. Statist. 21, 338 - 354.

9. Semiparametric Models: Estimation
   • Bickel, P. J., Klaassen, C. A. J., Ritov, Y., and Wellner, J. A. (1993). Efficient and Adaptive Estimation for Semiparametric Models. Johns Hopkins University Press, Baltimore.

   • Bickel, P.J., Ritov, Y., and Wellner, J. A. (1991). Efficient estimation of linear functionals of a probability measure P with known marginal distributions. Ann. Statist. 19, 1316 - 1346.

   • Huang, J. (1998). Efficient estimation of the partly linear additive Cox model. Submitted to Ann. Statist.

   • Liang, K.-Y., Self, S. G., and Chang, Y.-C. (1993). Modelling marginal hazards in multivariate failure time data. J. R. Statist. Soc. B 55, 441 - 453.

   • Mammen, E. and Van de Geer, S. (1997). Penalized quasi-likelihood estimation in partial linear models. Ann. Statist. 25, 1014-1035.

   • Van der Vaart, A. W. (1996). Efficient maximum likelihood estimation in semiparametric mixture models. Ann. Statist. 24, 862-878.

   • Van der Vaart, A. W. (1995a). Efficiency of infinite dimensional M-estimators. Statistica Neerl. 49, 9 - 30.

10. Testing in Semiparametric Models:
    • Bickel, P. J. and Ritov, Y. (1992). Testing for goodness of fit: A new approach. Nonparametric Stat. and Related Topics; A. K. Md. E. Saleh; Elsevier, Amsterdam, 51-57.

    • Cox, D., Koh, E., Wahba, G., and Yandell, B. S. (1988). Testing the (parametric) null model hypothesis in (semiparametric) partial and generalized spline models. Ann. of Statistics 16, 113-119.

    • Giancarlo, Moschini (1991). Testing for preference change in consumer demand: An indirectly separable, semiparametric model. J. of Busn. and Economic Stat. 9, 111-117.

    • Horowitz, Joel L. and Neumann, George R. (1992). A generalized moments specification test of the proportional hazards model. J. Amer. Statist. Assoc. 87, 234-240.

    • Knowles, Mark and Siegmund, David (1989). On Hotelling's approach to testing for a nonlinear parameter in regression. International Statistical Review, 57, 205-220

    • Murphy, S. A. and Van der Vaart, A.W. (1995). Semiparametric likelihood ratio inference. Ann. Statist. 25, 1471 - 1509.

    • Peters, Simon and Richard J. Smith (1991). Distributional specification tests against semiparametric alternatives. J. of Econometrics 47, 175-194.

    • Rotnitzky, A. and Jewell, N. P. (1990). Hypothesis testing of regression parameters in semiparametric generalized linear models for cluster correlated data. Biometrika 77, 485-497.

11. Sequential Analysis
    • Bilias, Y., Gu, M., and Ying, Z. (1997). Towards a general asymptotic theory for Cox model with staggered entry. Ann. Statist. 25, 662 - 682.

    • Carlin, Bradley P., Chaloner, Kathryn, Church, Timothy, Louis, Thomas A., and Matts, John P. (1993). Bayesian approaches for monitoring clinical trials with an application to toxoplasmic encephalitis prophylaxis. The Statistician 42, 355-367.

    • Chernoff, Herman and Petkau, A. John (1981). Sequential medical trials involving paired data. Biometrika 68, 119-132.

    • Emerson, Scott S. and Fleming, Thomas R. (1989). Symmetric group sequential test designs. Biometrics 45, 905-923.

    • Emerson, Scott S. and Fleming, Thomas R. (1990). Parameter estimation following group sequential hypothesis testing. Biometrika 77, 875-892.

    • Fleming, Thomas R., Harrington, D. P., and O'Brien, P.C. (1984). Designs for group sequential tests. J. Controlled Clinical Trials 5, 348-361.

    • Fleming, Thomas R. and Watelet, Luc F. (1989). Approaches to monitoring clinical trials. J. of the National Cancer Inst. 81, 188-193.

    • Lee, Jae Won, and DeMets, D. L. (1991). Sequential comparison of changes with repeated measurements data J. Amer. Statist. Assn. 86, 757-762.

    • Lin, D. Y., Shen, L., Ying, Z. and Breslow, N. (1996). Group sequential designs for monitoring survival probabilities. Biometrics 52, 1033 - 1041.

    • Siegmund, D. O. (1985). Sequential Analysis: Tests and Confidence Intervals. Springer-Verlag, New York.

12. Inverse Problems
    • Van der Laan, M. J., Bickel, P. J., and Jewell, N. (1997). Singly and doubly censored current status data. Scand. J. Statist. 24, 289 - 307.

    • Groeneboom, P. and Jongbloed, G. (1995). Isotonic estimation and rates of convergence in Wicksell's problem. Ann. Statist. 23, 1518 - 1542.

    • Geskus, R., and Groeneboom, P. (1996) Asymptotically optimal estimation of smooth functionals for interval censoring, part1. Statistica Neerl. 50, 69 - 88.

    • Geskus, R., and Groeneboom, P. (1996) Asymptotically optimal estimation of smooth functionals for interval censoring, part 2. Statistica Neerl. 51, 201 - 219.

    • Jewell, N. P., Malani, H. M, and Vittinghoff, E. (1994). Nonparametric estimation for a form of doubly censored data with application to two problems in AIDS. Jour. Amer. Statist. Assoc. 89, 7 - 18.

    • Jongbloed, J. (1995). Three Statistical Inverse Problems. Ph.D. dissertation, Delft.

    • Mammen, E. (1991). (1991). Nonparametric regression under qualitative smoothness assumptions. Ann. Statist. 19, 741 - 759.

13. Estimation for multiphase and case-cohort designs.
    • Breslow, N. E. and Holubkov, R. (1997). Maximum likelihood estimation of logistic regression parameters under two-phase, outcome-dependent sampling. J. R. Statist. Soc. B 59, 447 - 461.

    • Lawless, J.F., Wild, C. J., and Kalbfleisch, J. D. (1997). Semiparametric methods for response-selective and missing data problems in regression. Preprint; submitted to JRSS?

    • Scott, A. J. and Wild, C. J. (1991). Fitting logistic models in stratified case-control studies. Biometrics 47, 497-510.

    • Scott, A. J. and Wild, C. J. (1997). Fitting regression models to case-control data by maximum likelihood. Biometrika 84, 57 - 84.

    • Prentice, R. L. (1986). A case-cohort design for epidemiologic cohort studies and disease prevention trials. Biometrika, 73, 1-11.

    • Self, S. G. and Prentice, R. L. (1988). Asymptotic distribution theory and efficiency results for case-cohort studies. Ann. Statist., 16, 64-81.

    • Goldstein, L. and Langholz, B. (1992). Asymptotic theory for nested case-control sampling in the Cox regression model. Ann. Statist., 20, 1903-1928.

14. Algorithms and computational issues
    • Böhning, D. (1995). A review of reliable maximum likelihood algorithms for semiparametric mixture models. J. Statistical Planning and Inference 47, 5 - 28.

    • Dempster, A. P., Laird, N. M., and Rubin, D. B. (1977). Maximum likelihood from incomplete data via the EM algorithm. J. Roy. Statist. Soc. B 39, 1 - 38.

    • Green, P. J. (1995). Reversible jump Markov chain Monte Carlo computation and Bayesian model determination. Biometrika 82, 711 - 732.

    • Jongbloed, G. (1995). Three Statistical Inverse Problems. Ph.D. dissertation, Delft University of Technology.

    • Jongbloed, G. (1998). The iterative convex minorant algorithm for nonparametric estimation. J. Comp. Graphical Statist., to appear.

    • Meilijson, I. (1989). A fast improvement to the EM algorithm on its own terms. J. Roy. Statist. Soc. 51, 127 - 138.

    • Satten, G. A. (1996). Rank-based inference in the proportional hazard model for interval censored data. Biometrika 83, 355-370.

    • Wellner, J. A. and Zhan, Y. (1997). A hybrid algorithm for computation of the nonparametric maximum likelihood estimator from censored data. J. Amer. Statist. Assoc. 92, 945 - 959.