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.

BaLi14
Battey, H., & Linton, O. (2014) Nonparametric estimation of multivariate elliptic densities via finite mixture sieves. Journal of Multivariate Analysis, 123, 43–67. DOI.
BDGM97
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.
Berg11
Bergsma, W. (2011) Nonparametric testing of conditional independence by means of the partial copula. arXiv:1101.4607.
BhBh08
Bhattacharya, A., & Bhattacharya, R. (2008) Nonparametric statistics on manifolds with applications to shape spaces. . ProQuest
BjFa01
Bjørnstad, O. N., & Falck, W. (2001) Nonparametric spatial covariance functions: Estimation and testing. Environmental and Ecological Statistics, 8, 53–70. DOI.
Bosq98
Bosq, D. (1998) Nonparametric statistics for stochastic processes: estimation and prediction. (2nd ed.). New York: Springer
BuES88
Buckley, M. J., Eagleson, G. K., & Silverman, B. W.(1988) The estimation of residual variance in nonparametric regression. Biometrika, 75(2), 189–199. DOI.
ChSh03
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.
Chau91
Chaudhuri, P. (1991) Nonparametric Estimates of Regression Quantiles and Their Local Bahadur Representation. The Annals of Statistics, 19(2), 760–777. DOI.
ChHu07
Chen, S. X., & Huang, T.-M. (2007) Nonparametric estimation of copula functions for dependence modelling. Canadian Journal of Statistics, 35(2), 265–282. DOI.
CoDa11
Comminges, L., & Dalalyan, A. (2011) Tight conditions for consistent variable selection in high dimensional nonparametric regression. arXiv:1102.3616 [math, Stat].
DLGT13
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].
Efro81
Efron, B. (1981) Nonparametric estimates of standard error: The jackknife, the bootstrap and other methods. Biometrika, 68(3), 589–599. DOI.
Fan91
Fan, J. (1991) On the Optimal Rates of Convergence for Nonparametric Deconvolution Problems. The Annals of Statistics, 19(3), 1257–1272. DOI.
FaYa03
Fan, J., & Yao, Q. (2003) Nonlinear time series: nonparametric and parametric methods. . New York: Springer
FiIV00
Fisher III, J. W., Ihler, A. T., & Viola, P. A.(n.d.) Learning Informative Statistics: A Nonparametric Approach. . Citeseer
GCCP15
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].
GoGa71
Good, I. J., & Gaskins, R. A.(1971) Nonparametric roughness penalties for probability densities. Biometrika, 58(2), 255–277. DOI.
Györ02:
Györfi, L. (Ed.). (2002) A distribution-free theory of nonparametric regression. . New York: Springer
Hall92
Hall, P. (1992) On Bootstrap Confidence Intervals in Nonparametric Regression. The Annals of Statistics, 20(2), 695–711.
HjJo96
Hjort, N. L., & Jones, M. C.(1996) Locally parametric nonparametric density estimation. The Annals of Statistics, 24(4), 1619–1647. DOI.
HoLi05
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.
HoWh05
Hong, Y., & White, H. (2005) Asymptotic Distribution Theory for Nonparametric Entropy Measures of Serial Dependence. Econometrica, 73(3), 837–901. DOI.
HuST98
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.
ImKo00
Imoto, S., & Konishi, S. (n.d.) Estimation of B-spline Nonparametric Regression Models using Information.
LaWa08
Lafferty, J., & Wasserman, L. (2008) Rodeo: Sparse, greedy nonparametric regression. The Annals of Statistics, 36(1), 28–63. DOI.
Lair78
Laird, N. (1978) Nonparametric Maximum Likelihood Estimation of a Mixing Distribution. Journal of the American Statistical Association, 73(364), 805–811. DOI.
LaMP15
Lavergne, P., Maistre, S., & Patilea, V. (2015) A significance test for covariates in nonparametric regression. Electronic Journal of Statistics, 9, 643–678. DOI.
LeMo11
Lewis, E., & Mohler, G. (2011) A nonparametric EM algorithm for multiscale Hawkes processes. Preprint.
LuRo14
Lunardon, N., & Ronchetti, E. (2014) Composite likelihood inference by nonparametric saddlepoint tests. Computational Statistics & Data Analysis, 79, 80–90. DOI.
MaKr00
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.
Niko12
Nikolov, S. (2012) Trend or no trend : a novel nonparametric method for classifying time series (Thesis). . Massachusetts Institute of Technology
OpWY01
Opsomer, J., Wang, Y., & Yang, Y. (2001) Nonparametric Regression with Correlated Errors. Statistical Science, 16(2), -134–153.
PaKo12
Panaretos, V. M., & Konis, K. (2012) Nonparametric Construction of Multivariate Kernels. Journal of the American Statistical Association, 107(499), 1085–1095. DOI.
Robi83
Robinson, P. M.(1983) Nonparametric Estimators for Time Series. Journal of Time Series Analysis, 4(3), 185–207. DOI.
RyRy10
Ryabko, D., & Ryabko, B. (2010) Nonparametric Statistical Inference for Ergodic Processes. IEEE Transactions on Information Theory, 56(3), 1430–1435. DOI.
Saga05
Sagara, N. (2005) Nonparametric maximum-likelihood estimation of probability measures: existence and consistency. Journal of Statistical Planning and Inference, 133(2), 249–271. DOI.
SaGu92
Sampson, P. D., & Guttorp, P. (1992) Nonparametric estimation of nonstationary spatial covariance structure. Journal of the American Statistical Association, 87(417), 108–119.
ScFe02
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
SzVZ13
Szabo, B., van der Vaart, A., & van Zanten, H. (2013) Frequentist coverage of adaptive nonparametric Bayesian credible sets. arXiv:1310.4489 [math, Stat].
TASL14
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].
Toda11
Toda, A. A.(2011) An Information-Theoretic Approach to Nonparametric Estimation, Model Selection, and Goodness of Fit. arXiv:1103.4890 [math, Stat].
Viel06
Viele, K. (2006) Nonparametric Estimation of Kullback-Leibler Information Illustrated by Evaluating Goodness of Fit. Bayesian Analysis, 1(1), 1–42.
ZhGr14
Zhang, Z., & Grabchak, M. (2014) Nonparametric Estimation of Küllback-Leibler Divergence. Neural Computation, 26(11), 2570–2593. DOI.