The Living Thing / Notebooks : Nonparametric statistics

Regression of rather wiggly lines. estimates of squidgy densities. Regularisation and sparsification. Splines, kernel density estimates, other fancy techniques. Less a field than a tag attached to other statistics.

Finite mixture models could sort of fit here, for example.

See also functional regression, convolution kernels.

I’m particularly curious about nonparametric estimates of conditional densities.

I want to read Bosq98 next.

Battey, H., & Linton, O. (2014) Nonparametric estimation of multivariate elliptic densities via finite mixture sieves. Journal of Multivariate Analysis, 123, 43–67. DOI.
Beirlant, J., Dudewicz, E. J., Györfi, L., & van der Meulen, E. C.(1997) Nonparametric entropy estimation: An overview. Journal of Mathematical and Statistical Sciences, 6(1), 17–39.
Bergsma, W. (2011) Nonparametric testing of conditional independence by means of the partial copula. arXiv:1101.4607.
Bhattacharya, A., & Bhattacharya, R. (2008) Nonparametric statistics on manifolds with applications to shape spaces. . ProQuest
Bjørnstad, O. N., & Falck, W. (2001) Nonparametric spatial covariance functions: Estimation and testing. Environmental and Ecological Statistics, 8, 53–70. DOI.
Bosq, D. (1998) Nonparametric statistics for stochastic processes: estimation and prediction. (2nd ed.). New York: Springer
Buckley, M. J., Eagleson, G. K., & Silverman, B. W.(1988) The estimation of residual variance in nonparametric regression. Biometrika, 75(2), 189–199. DOI.
Chao, A., & Shen, T.-J. (2003) Nonparametric estimation of Shannon?s index of diversity when there are unseen species in sample. Environmental and Ecological Statistics, 10(4), 429–443. DOI.
Chaudhuri, P. (1991) Nonparametric Estimates of Regression Quantiles and Their Local Bahadur Representation. The Annals of Statistics, 19(2), 760–777. DOI.
Chen, S. X., & Huang, T.-M. (2007) Nonparametric estimation of copula functions for dependence modelling. Canadian Journal of Statistics, 35(2), 265–282. DOI.
Comminges, L., & Dalalyan, A. (2011) Tight conditions for consistent variable selection in high dimensional nonparametric regression. arXiv:1102.3616 [math, Stat].
Duvenaud, D., Lloyd, J. R., Grosse, R., Tenenbaum, J. B., & Ghahramani, Z. (2013) Structure Discovery in Nonparametric Regression through Compositional Kernel Search. arXiv:1302.4922 [cs, Stat].
Efron, B. (1981) Nonparametric estimates of standard error: The jackknife, the bootstrap and other methods. Biometrika, 68(3), 589–599. DOI.
Fan, J. (1991) On the Optimal Rates of Convergence for Nonparametric Deconvolution Problems. The Annals of Statistics, 19(3), 1257–1272. DOI.
Fan, J., & Yao, Q. (2003) Nonlinear time series: nonparametric and parametric methods. . New York: Springer
Fisher III, J. W., Ihler, A. T., & Viola, P. A.(n.d.) Learning Informative Statistics: A Nonparametric Approach. . Citeseer
Girdhar, Y., Cho, W., Campbell, M., Pineda, J., Clarke, E., & Singh, H. (2015) Anomaly Detection in Unstructured Environments using Bayesian Nonparametric Scene Modeling. arXiv:1509.07979 [cs].
Good, I. J., & Gaskins, R. A.(1971) Nonparametric roughness penalties for probability densities. Biometrika, 58(2), 255–277. DOI.
Györfi, L. (Ed.). (2002) A distribution-free theory of nonparametric regression. . New York: Springer
Hall, P. (1992) On Bootstrap Confidence Intervals in Nonparametric Regression. The Annals of Statistics, 20(2), 695–711.
Hjort, N. L., & Jones, M. C.(1996) Locally parametric nonparametric density estimation. The Annals of Statistics, 24(4), 1619–1647. DOI.
Hong, Y., & Li, H. (2005) Nonparametric Specification Testing for Continuous-Time Models with Applications to Term Structure of Interest Rates. Review of Financial Studies, 18(1), 37–84. DOI.
Hong, Y., & White, H. (2005) Asymptotic Distribution Theory for Nonparametric Entropy Measures of Serial Dependence. Econometrica, 73(3), 837–901. DOI.
Hurvich, C. M., Simonoff, J. S., & Tsai, C.-L. (1998) Smoothing Parameter Selection in Nonparametric Regression Using an Improved Akaike Information Criterion. Journal of the Royal Statistical Society. Series B (Statistical Methodology), 60(2), 271–293.
Imoto, S., & Konishi, S. (n.d.) Estimation of B-spline Nonparametric Regression Models using Information.
Lafferty, J., & Wasserman, L. (2008) Rodeo: Sparse, greedy nonparametric regression. The Annals of Statistics, 36(1), 28–63. DOI.
Laird, N. (1978) Nonparametric Maximum Likelihood Estimation of a Mixing Distribution. Journal of the American Statistical Association, 73(364), 805–811. DOI.
Lavergne, P., Maistre, S., & Patilea, V. (2015) A significance test for covariates in nonparametric regression. Electronic Journal of Statistics, 9, 643–678. DOI.
Lewis, E., & Mohler, G. (2011) A nonparametric EM algorithm for multiscale Hawkes processes. Preprint.
Lunardon, N., & Ronchetti, E. (2014) Composite likelihood inference by nonparametric saddlepoint tests. Computational Statistics & Data Analysis, 79, 80–90. DOI.
Markovitch, N. M., & Krieger, U. R.(2000) Nonparametric estimation of long-tailed density functions and its application to the analysis of World Wide Web traffic. Performance Evaluation, 42(2-3), 205–222. DOI.
Nikolov, S. (2012) Trend or no trend : a novel nonparametric method for classifying time series (Thesis). . Massachusetts Institute of Technology
Opsomer, J., Wang, Y., & Yang, Y. (2001) Nonparametric Regression with Correlated Errors. Statistical Science, 16(2), -134–153.
Panaretos, V. M., & Konis, K. (2012) Nonparametric Construction of Multivariate Kernels. Journal of the American Statistical Association, 107(499), 1085–1095. DOI.
Robinson, P. M.(1983) Nonparametric Estimators for Time Series. Journal of Time Series Analysis, 4(3), 185–207. DOI.
Ryabko, D., & Ryabko, B. (2010) Nonparametric Statistical Inference for Ergodic Processes. IEEE Transactions on Information Theory, 56(3), 1430–1435. DOI.
Sagara, N. (2005) Nonparametric maximum-likelihood estimation of probability measures: existence and consistency. Journal of Statistical Planning and Inference, 133(2), 249–271. DOI.
Sampson, P. D., & Guttorp, P. (1992) Nonparametric estimation of nonstationary spatial covariance structure. Journal of the American Statistical Association, 87(417), 108–119.
Scaillet, O., & Fermanian, J.-D. (2002) Nonparametric Estimation of Copulas for Time Series (SSRN Scholarly Paper No. ID 372142). . Rochester, NY: Social Science Research Network
Szabo, B., van der Vaart, A., & van Zanten, H. (2013) Frequentist coverage of adaptive nonparametric Bayesian credible sets. arXiv:1310.4489 [math, Stat].
Tang, M., Athreya, A., Sussman, D. L., Lyzinski, V., & Priebe, C. E.(2014) A nonparametric two-sample hypothesis testing problem for random dot product graphs. arXiv:1409.2344 [math, Stat].
Toda, A. A.(2011) An Information-Theoretic Approach to Nonparametric Estimation, Model Selection, and Goodness of Fit. arXiv:1103.4890 [math, Stat].
Viele, K. (2006) Nonparametric Estimation of Kullback-Leibler Information Illustrated by Evaluating Goodness of Fit. Bayesian Analysis, 1(1), 1–42.
Zhang, Z., & Grabchak, M. (2014) Nonparametric Estimation of Küllback-Leibler Divergence. Neural Computation, 26(11), 2570–2593. DOI.