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.
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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.
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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
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