Автор |
Bowman, Adrian W. |
Дата выпуска |
1985 |
dc.description |
Some practical approaches to the problem of choosing parameters which control the smoothness of kernel-based density estimators are investigated. Fixed and variable kernels are considered, and particularly simple approaches are investigated in the latter case. The performances of a wide range of estimators are compared in a simulation study. |
Формат |
application.pdf |
Издатель |
Gordon and Breach Science Publishers |
Копирайт |
Copyright Taylor and Francis Group, LLC |
Тема |
Cross-validation |
Тема |
density estimation |
Тема |
kernels |
Тема |
nearest neighbour |
Тема |
smoothing |
Тема |
variable kernels |
Название |
A comparative study of some kernel-based nonparametric density estimators |
Тип |
research-article |
DOI |
10.1080/00949658508810822 |
Electronic ISSN |
1563-5163 |
Print ISSN |
0094-9655 |
Журнал |
Journal of Statistical Computation and Simulation |
Том |
21 |
Первая страница |
313 |
Последняя страница |
327 |
Аффилиация |
Bowman, Adrian W.; Statistical Laboratory, Department of Mathematics, University of Manchester |
Выпуск |
3-4 |
Библиографическая ссылка |
Abramowitz, M. and Stegun, I.A. 1965. Handbook of Mathematical Functions, New York: Dover. |
Библиографическая ссылка |
Anderson, T.W. and Darling, D.A. 1952. Asymptotic theory of certain "goodness- of-fit" criteria based on stochastic processes. Ann. Math. Statist, 23: 193–212. |
Библиографическая ссылка |
Bean, S. and Tsokos, C.P. 1982. Bandwidth selection procedures for kernel density estimates. Comm. Stat. Theory & Method, 11: 1045–1069. |
Библиографическая ссылка |
Bowman, A.W. 1981. “Some aspects of density estimation by the kernel method”. In Ph.D.thesis, University of Glasgow. |
Библиографическая ссылка |
Bowman, A.W. 1984. An alternative method of cross-validation for the smoothing of density estimates. Biometrika, 71: 353–360. |
Библиографическая ссылка |
Breiman, L., Meisel, W. and Purcell, E. 1977. Variable kernel estimates of multivariate densities. Technometrics, 19: 135–144. |
Библиографическая ссылка |
Chow, Y.S., Geman, S. and Wu, L.D. 1983. Consistent cross-validated density estimation. Ann.Statist, 11: 25–38. |
Библиографическая ссылка |
Copas, J.B. and Fryer, M.J. 1980. Density estimation and suicide risks in psychiatric treatment. J.R. Statist. Soc. Ser. A, 143: 167–176. |
Библиографическая ссылка |
Diggle, P.J. and Grattan, R.J. 1984. Monte Carlo methods of inference for implicit statistical models. J.R. Statist. Soc. Ser. B, 46: 193–227. with discussion |
Библиографическая ссылка |
Duin, R.P.W. 1976. On the choice of smoothing parameters for Parzen estimators of probability density functions. IEEE Trans, on Computers, C-25: 1175–1179. |
Библиографическая ссылка |
Fryer, M.J. 1976. Some errors associated with the non-parametric estimation of density functions. J. Inst. Maths. Applics, 18: 371–380. |
Библиографическая ссылка |
Fryer, M.J. 1977. A review of some non-parametric methods of density estimation. J. Inst. Math. Applies, 20: 335–354. |
Библиографическая ссылка |
Good, I.J. and Gaskins, R.A. 1980. Density estimation and bump-hunting by the penalised likelihood method exemplified by scattering and meteorite data. J Amer Statist Assoc, 75: 42–55. |
Библиографическая ссылка |
Habbema, J.D.F., Hermans, J. and Van Den Broek, K. A stepwise discriminant analysis program using density estimation. Proceedings in Computational Statistics. Wien: Physica Verlag. COMPSTAT |
Библиографическая ссылка |
Hall, P. 1983a. Large sample optimality of least squares cross-validation in density estimation. Ann. Statist, 4: 1156–1174. |
Библиографическая ссылка |
Hall, P. Asymptotic theory of minimum integrated square error for multivariate density estimation. Proceedings of the Multivariate Analysis Symposium. Pittsburgh, , U.S.A 1983 To appear |
Библиографическая ссылка |
Hogg, R.V. 1979. Statistical robustness: one view of its use in applications today. American Statistician, 33: 108–116. |
Библиографическая ссылка |
Loftsgaarden, F. and Quesenberry, C. 1965. A nonparametric estimate of a multivariate density function. Ann. Math. Statist, 36: 1049–1051. |
Библиографическая ссылка |
Mack, Y.P. and Rosenblatt, M. 1979. Multivariate k-nearest neighbour density estimates. J. Mult. Anal, 9: 1–15. |
Библиографическая ссылка |
Nadaraja, E.A. 1974. On the integral mean square error of some nonparametric estimates of a probability density. Theory Prob. Appl, 19: 133–141. |
Библиографическая ссылка |
Parzen, E. 1962. On estimation of a probability density dunction and mode. Ann. Math. Statist, 33: 1065–1076. |
Библиографическая ссылка |
Raatgever, J.W. and Duin, R.P.W. On the variable kernel model for multivariate nonparametric density estimation. Proceedings in Computational Statistics. Wien: Physica Verlag. COMPSTAT 1978 |
Библиографическая ссылка |
Raatgever, J.W., Habbema, J.D.F. and Hermans, J. 1979. Estimation of the kernel width in the variable kernel model, University of Leiden. Technical Report, Dept.of Medical Statistics |
Библиографическая ссылка |
Remme, J., Habbema, J.D.F. and Hermans, J. 1980. A simulative comparison of linear, quadratic and kernel discrimination. J. Stat. Comp. Simul, 11: 87–106. |
Библиографическая ссылка |
Rosenblatt, M. 1956. Remarks on some nonparametric estimates of a density function. Ann. Math. Statist, 27: 832–837. |
Библиографическая ссылка |
Rudemo, M. 1982. Empirical choice of density estimators. Scand. J. Statist, 9: 65–78. |
Библиографическая ссылка |
Schuster, E.F. and Gregory, G.G. On the nonconsistency of maximum likelihood nonparametric density estimators. 13th Annual Symposium on the Interface of Computer Science and Statistics. Edited by: Eddy, W.F. pp.295–298. New York: Springer-Verlag. |
Библиографическая ссылка |
Scott, D.W., Tapia, R.A. and Thompson, J.R. 1977. Kernel density estimation Revisited. Nonlinear Analysis: Theory, Methods and Applications, 1: 339–372. |
Библиографическая ссылка |
Scott, D.W. and Factor, L.E. 1981. Monte Carlo study of three data-based nonparametric probability density estimators. J. Amer. Statist. Assoc, 76: 9–15. |
Библиографическая ссылка |
Silverman, B.W. 1978. Choosing the window width when estimating a density. Biometrika, 65: 1–11. |
Библиографическая ссылка |
Silverman, B.W. 1981. Using kernel density estimates to investigate multimodality. J.R. Statist. Soc. Ser. B, 43: 97–99. |
Библиографическая ссылка |
Stone, C.J. 1984. An asymptotically optimal window selection rule for kernel density estimates. Ann. Statist, 12: 1285–1297. |
Библиографическая ссылка |
Stone, M. 1974. Cross-validatory choice and assessment of statistical predictions. J.R. Statist. Soc. Ser. B, 36: 111–147. |
Библиографическая ссылка |
Wagner, T.J. 1975. Nonparametric estimates of probability densities. IEEE Trans. information Theory IT, 21: 438–440. |
Библиографическая ссылка |
Wegman, E.J. 1972. Nonparametric probability density estimation.II.A comparison of density estimation methods. J. Stat. Comp. Simul, 1: 225–246. |
Библиографическая ссылка |
Woodroofe, M. 1970. On choosing a delta sequence. Ann. Math. Statist, 41: 1665–1671. |