Reading assignments and collected reading list for nonparametric statistics
Contents
Reading assignments and collected reading list for nonparametric statistics#
Collected readings#
Inequalities (including some probability inequalities)#
Beckenbach, E.F., and R. Bellman, 1983. Inequalities, Springer.
Boucheron, S. G. Lugosi, and P. Massart, 2013. Concentration Inequalities: A Nonasymptotic Theory of Independence, Oxford U. Press. 10.1093/acprof:oso/9780199535255.003.0001
Hardy, G., J.E. Littlewood, and G. Polya, 1952. Inequalities, 2nd edition, Cambridge.
Marshall, A.W., I. Olkin, and B.C. Arnold, 2011. Inequalities: Theory of Majorization and its Applications, Springer.
Maurer, A. and M. Pontil, 2009. Empirical Bernstein Bounds and Sample Variance Penalization, COLT. https://www.cs.mcgill.ca/~colt2009/papers/012.pdf#page=1
Convexity, convex analysis, optimization#
Anderson, E.J., and P. Nash, 1987. Linear Programming in Infinite-Dimensional Spaces, Wiley.
Luenberger, D.G., 1969. Optimization by Vector Space Methods, Wiley.
Rockafellar, R.T., 1970. Convex Analysis, Princeton U. Press.
Shor, N.Z., ???? Nondifferentiable Optimization, Springer.
Probability and stochastic processes#
Breiman, L., 1992. Probability, SIAM.
Durrett, R., 2016. Essentials of Stochastic Processes, 3rd edition, Springer.
Feller, W., 1971. An Introduction to Probability Theory and Its Applications, v.2, Wiley.
Permutation tests#
Lehmann, E., 2006. Nonparametrics: Statistical Methods Based on Ranks, Springer.
Pesarin, F. and L. Salmaso, 2010. Permutation Tests for Complex Data: Theory, Applications, and Software, Wiley
Romano, J.P., 1988. A bootstrap revival of some nonparametric distance tests, J. Amer. Stat. Assoc., 83, 698–708.
Romano, J.P., 1989. Bootstrap and randomization tests of some nonparametric hypotheses, Ann. Stat., 17, 141–159.
Walther, G., 1997. Absence of correlation between the solar neutrino flux and the sunspot number, Phys. Rev. Lett. 79, 4522–4524.
Walther, G., 1999. On the solar-cycle modulation of the Homestake solar neutrino capture rate and the shuffle test, Ap. J. 513, 990–996.
Phipson, B., and G.K. Smyth, 2010. Permutation P-values Should Never Be Zero: Calculating Exact P-values When Permutations Are Randomly Drawn, Statistical Applications in Genetics and Molecular Biology, https://doi.org/10.2202/1544-6115.1585
The Jackknife and the Bootstrap#
Beran, R., 1995. Stein confidence sets and the bootstrap, Stat. Sinica, 5, 109–127
Beran, R., 1990. Calibrating predictions regions, J. Amer. Stat. Assoc., 85, 715–723
Beran, R., 1990. Refining bootstrap simultaneous confidence sets, J. Amer. Stat. Assoc., 85, 417-426
Beran, R., 1987. Prepivoting to reduce level error of confidence sets, Biometrika, 74, 457–468
Efron, B., 1982. The Jackknife, the bootstrap, and other resampling plans, SIAM, Philadelphia.
\(E\)-values#
Vovk, V. and R. Ruodu Wang, 2021. E-values: Calibration, combination and applications, Ann. Statist. 49 (3) 1736-1754. https://doi.org/10.1214/20-AOS2020
Lecture notes by V. Vovk. https://www.isibang.ac.in/~statmath/pcm2020/talk1.pdf, https://www.isibang.ac.in/~statmath/pcm2020/talk2.pdf,
Supermartingale-based inference and sequential tests:#
Kaplan, H., 1987. A Method of One-Sided Nonparametric Inference for the Mean of a Nonnegative Population, The Amer. Statistician, 41, 157-158. https://www.tandfonline.com/doi/abs/10.1080/00031305.1987.10475470?journalCode=utas20
Howard, Steven R., Aaditya Ramdas, Jon McAuliffe, Jasjeet Sekhon, 2021. Time-uniform, nonparametric, nonasymptotic confidence sequences, Ann. Statist. 49(2), 1055-1080, 10.1214/20-AOS1991
Ramdas, A., P. Grunwald, V. Vovk, and G. Shafer, 2022. Game-Theoretic Statistics and Safe Anytime-Valid Inference, https://arxiv.org/pdf/2210.01948v1.pdf
Spertus, J. and P.B. Stark, 2023. Sweeter than SUITE, https://arxiv.org/abs/2207.03379
Stark, P.B., 2023. ALPHA: Audit that Learns from Previously Hand-Audited ballots, Ann. Appl. Stat., 17(1): 641-679. DOI: 10.1214/22-AOAS1646 https://projecteuclid.org/journalArticle/Download?urlId=10.1214/22-AOAS1646
Wald, A., 1945. Sequential Tests of Statistical Hypotheses, Ann. Math. Statist. 16(2), 117-186. 10.1214/aoms/1177731118
Waudby-Smith, I. and A. Ramdas, 2022. Estimating means of bounded random variables by betting, https://arxiv.org/abs/2010.09686
Conformal prediction#
Schafer, G., and V. Vovk, 2008. A tutorial on conformal prediction, Journal Machine Learning Res., 9, 371-421.
Data splitting#
Fithian, W., D.L. Sun, and J. Taylor, 2017. Optimal inference after model selection, https://arxiv.org/pdf/1410.2597.pdf
Wasserman, L., Aaditya Ramdas, and Sivaraman Balakrishnan, 2020. Universal Inference. PNAS, 117, 29, 16880-16890 https://www.pnas.org/doi/10.1073/pnas.1922664117
Randomized experiments#
Aronow, P.M., H. Chang, and P. Lopatto, 2022?. Fast computation of exact confidence intervals for randomized experiments with binary outcomes. https://lopat.to/permutation.pdf
Caughey, D., A. Dafoe, X. Li, and L. Miratrix, 2021. Randomization Inference beyond the Sharp Null: Bounded Null Hypotheses and Quantiles of Individual Treatment Effects https://arxiv.org/abs/2101.09195
Ding, P., 2017. A Paradox from Randomization-Based Causal Inference, Statist. Sci. 32, 331-345. 10.1214/16-STS571
Fisher, R.A., 1935. The Design of Experiments, Hafner.
Li, X. and P. Ding, 2016. Exact confidence intervals for the average causal effect on a binary outcome, Statistics in Medicine, 35, 6, 957-960. 10.1002/sim.6764
Wu and Ding, 2021. Randomization Tests for Weak Null Hypotheses in Randomized Experiments, JASA, 116. https://www.tandfonline.com/doi/abs/10.1080/01621459.2020.1750415
Density estimation and inference about probability densities#
Daubechies, I. 1992. Ten lectures on wavelets, SIAM, Philadelphia, PA.
Donoho, D.L., 1988. One-Sided Inference about Functionals of a Density, Ann. Statist. 16(4): 1390-1420 10.1214/aos/1176351045
G. Kerkyacharian, and D. Picard, 1993. Density estimation by kernel and wavelets methods: Optimality of Besov spaces, Stat. Prob. Lett., 18, 4, 327-336. https://doi.org/10.1016/0167-7152(93)90024-D
Hengartner, N.W., and P.B. Stark, 1995. Finite-Sample Confidence Envelopes for Shape-Restricted Densities Ann. Statist. 23(2): 525-550 10.1214/aos/1176324534
Silverman, B.W., 1990. Density Estimation for Statistics and Data Analysis, Chapman and Hall, London.
Inverse problems#
Donoho, D., 1995. Nonlinear Solution of Linear Inverse Problems by Wavelet–Vaguelette Decomposition, Applied and Computational Harmonic Analysis, 2, 101-126. 10.1006/acha.1995.1008
Evans, S.N., and P.B. Stark, 2002. Inverse problems as statistics, Inverse Problems, 18, 4 10.1088/0266-5611/18/4/201
Kuusela, M. and P.B. Stark, 2017. Shape-constrained uncertainty quantification in unfolding steeply falling elementary particle spectra, Ann. Appl. Stat. 11, 3, 1671-1710. 10.1214/17-AOAS1053
Stark, P.B., 1992. Inference in infinite-dimensional inverse problems: duality and discretization, J. Geophys. Res., 97, 14055-14082. https://doi.org/10.1029/92JB00739
Stark, P.B., 2008. Generalizing resolution, Inverse Problems, _Inverse Problems, 24, 034014. 10.1088/0266-5611/24/3/034014
Pseudo-random number generation and pseudo-random sampling#
Knuth, D., 1997 The Art of Computer Programming, V.II: Seminumerical methods, 3rd edition, Addison-Wesley, Boston.
L’Ecuyer, P. and R. Simard, 2007. TestU01: A C Library for Empirical Testing of Random Number Generators, ACM Trans. Math. Softw., 33, http://doi.acm.org/10.1145/1268776.1268777
Marsaglia, G., 1968. Random Numbers Fall Mainly in the Planes, PNAS, 61, 25–28.
Matsumoto, M., and T. Nishimura, 1998. 8). Mersenne twister: a 623-dimensionally equidistributed uniform pseudo-random number generator, ACM Transactions on Modeling and Computer Simulation, 8, 3–30. doi:10.1145/272991.272995
McCullough, B.D., 2008. Microsoft’s ‘Not the Wichmann-Hill’ random number generator. Computational Statistics and Data Analysis, 52 (10), 4587–4593. http://dx.doi.org/10.1016/j.csda.2008.03.006
NIST Computer Security Division, Random Number Generation http://csrc.nist.gov/groups/ST/toolkit/rng/
Ottoboni, K., and P.B. Stark, 2018. Random problems with R. https://arxiv.org/abs/1809.06520
Stark, P.B., and K. Ottoboni, 2018. Random sampling: practice makes imperfect. https://arxiv.org/abs/1810.10985
Vitter, J.S., 1985. Random Sampling with a Reservoir, ACM Transactions on Mathematical Software, 11, 37–57.