A comparative study of some kernel-based nonparametric density estimators

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.

[1]  T. W. Anderson,et al.  Asymptotic Theory of Certain "Goodness of Fit" Criteria Based on Stochastic Processes , 1952 .

[2]  M. Rosenblatt Remarks on Some Nonparametric Estimates of a Density Function , 1956 .

[3]  E. Parzen On Estimation of a Probability Density Function and Mode , 1962 .

[4]  C. Quesenberry,et al.  A nonparametric estimate of a multivariate density function , 1965 .

[5]  Irene A. Stegun,et al.  Handbook of Mathematical Functions. , 1966 .

[6]  M. Woodroofe On Choosing a Delta-Sequence , 1970 .

[7]  E. Wegman Nonparametric probability density estimation , 1972 .

[8]  E. Nadaraya,et al.  On the Integral Mean Square Error of Some Nonparametric Estimates for the Density Function , 1974 .

[9]  M. Stone Cross‐Validatory Choice and Assessment of Statistical Predictions , 1976 .

[10]  T. Wagner,et al.  Nonparametric estimates of probability densities , 1975, IEEE Trans. Inf. Theory.

[11]  M. J. Fryer Some Errors Associated with the Non-parametric Estimation of Density Functions , 1976 .

[12]  Robert P. W. Duin,et al.  On the Choice of Smoothing Parameters for Parzen Estimators of Probability Density Functions , 1976, IEEE Transactions on Computers.

[13]  D. W. Scott,et al.  Kernel density estimation revisited , 1977 .

[14]  M. J. Fryer A Review of Some Non-parametric Methods of Density Estimation , 1977 .

[15]  L. Breiman,et al.  Variable Kernel Estimates of Multivariate Densities , 1977 .

[16]  B. Silverman,et al.  Choosing the window width when estimating a density , 1978 .

[17]  R. Hogg Statistical Robustness: One View of its use in Applications Today , 1979 .

[18]  M. Rosenblatt,et al.  Multivariate k-nearest neighbor density estimates , 1979 .

[19]  J. Remme,et al.  A simulative comparison of linear, quadratic and kernel discrimination , 1980 .

[20]  J. B. Copas,et al.  Density Estimation and Suicide Risks in Psychiatric Treatment , 1980 .

[21]  I. Good,et al.  Density Estimation and Bump-Hunting by the Penalized Likelihood Method Exemplified by Scattering and Meteorite Data , 1980 .

[22]  B. Silverman,et al.  Using Kernel Density Estimates to Investigate Multimodality , 1981 .

[23]  E. F. Schuster,et al.  On the Nonconsistency of Maximum Likelihood Nonparametric Density Estimators , 1981 .

[24]  David W. Scott,et al.  Monte Carlo Study of Three Data-Based Nonparametric Probability Density Estimators , 1981 .

[25]  Bandwidth selection procedures tor kernel density estimates , 1982 .

[26]  P. Hall Large Sample Optimality of Least Squares Cross-Validation in Density Estimation , 1983 .

[27]  S. Geman,et al.  Consistent Cross-Validated Density Estimation , 1983 .

[28]  P. Diggle,et al.  Monte Carlo Methods of Inference for Implicit Statistical Models , 1984 .

[29]  A. Bowman An alternative method of cross-validation for the smoothing of density estimates , 1984 .

[30]  C. J. Stone,et al.  An Asymptotically Optimal Window Selection Rule for Kernel Density Estimates , 1984 .