Presentation of smoothers: the family approach

SummaryThe product of most statistical smoothing methods is a single curve estimate. A drawback of such methods is that what is learned varies with choice of the smoothing parameter. This paper proposes simultaneous display of all important features, through presentation of a family of smooths. Some suggestions are given as to how this should be done.

[1]  A. Cuevas,et al.  A comparative study of several smoothing methods in density estimation , 1994 .

[2]  J. Marron,et al.  SiZer for Exploration of Structures in Curves , 1999 .

[3]  B. Silverman,et al.  Nonparametric regression and generalized linear models , 1994 .

[4]  M. C. Jones,et al.  A reliable data-based bandwidth selection method for kernel density estimation , 1991 .

[5]  B. Silverman.  Density estimation for statistics and data analysis , 1986 .

[6]  M. Wand,et al.  An Effective Bandwidth Selector for Local Least Squares Regression , 1995 .

[7]  W. Härdle.  Applied Nonparametric Regression , 1992 .

[8]  J. Marron,et al.  Simultaneous Density Estimation of Several Income Distributions , 1992, Econometric Theory.

[9]  M. Wand,et al.  EXACT MEAN INTEGRATED SQUARED ERROR , 1992 .

[10]  W. Härdle.  Applied Nonparametric Regression , 1991 .

[11]  Bu. Park,et al.  Rejoinder to ``Practical performance of several data driven bandwidth selectors" , 1992 .

[12]  J. Marron,et al.  Simultaneous estimation of several size distributions of income , 1988 .

[13]  M. C. Jones,et al.  A Brief Survey of Bandwidth Selection for Density Estimation , 1996 .

[14]  David W. Scott,et al.  Multivariate Density Estimation: Theory, Practice, and Visualization , 1992, Wiley Series in Probability and Statistics.

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

[16]  K. Roeder.  Density estimation with confidence sets exemplified by superclusters and voids in the galaxies , 1990 .

[17]  James Stephen Marron,et al.  Comparison of data-driven bandwith selectors , 1988 .

[18]  G. Terrell.  The Maximal Smoothing Principle in Density Estimation , 1990 .

[19]  Jianqing Fan,et al.  Local polynomial modelling and its applications , 1994 .

[20]  T. Hassard,et al.  Applied Linear Regression , 2005 .

[21]  A. Izenman,et al.  Philatelic Mixtures and Multimodal Densities , 1988 .

[22]  J. Marron,et al.  Progress in data-based bandwidth selection for kernel density estimation , 1996 .

[23]  Jianqing Fan,et al.  Fast Implementations of Nonparametric Curve Estimators , 1994 .

[24]  J. Marron,et al.  SCALE SPACE VIEW OF CURVE ESTIMATION , 2000 .

[25]  G. Wahba.  Spline models for observational data , 1990 .

[26]  D. W. Scott,et al.  Multivariate Density Estimation, Theory, Practice and Visualization , 1992 .

[27]  M. C. Jones,et al.  Spline Smoothing and Nonparametric Regression. , 1989 .

[28]  D. W. Scott,et al.  The Mode Tree: A Tool for Visualization of Nonparametric Density Features , 1993 .

[29]  P. Diggle.  A Kernel Method for Smoothing Point Process Data , 1985 .

[30]  James Stephen Marron,et al.  Choosing a Kernel Regression Estimator , 1991 .

[31]  C. J. Stone,et al.  A study of logspline density estimation , 1991 .

[32]  James Stephen Marron,et al.  Transformations in Density Estimation , 1991 .