Local Likelihood SiZer Map

The SiZer Map, proposed by Chaudhuri and Marron (1999), is a statistical tool for finding which features in noisy data are strong enough to be distinguished from background noise.In this paper, we propose the local likelihood SiZer map.Some simulation examples illustrate that the newly proposed SiZer map is more efficient in distinguishing features than the original one, because of the inferential advantage of the local likelihood approach.Some computational problems are addressed, with the result that the computational cost in constructing the local likelihood SiZer map is close to that of the original one.

[1]  R. W. Wedderburn.  Quasi-likelihood functions, generalized linear models, and the Gauss-Newton method , 1974 .

[2]  P. Bickel.  One-Step Huber Estimates in the Linear Model , 1975 .

[3]  C. A. Murthy,et al.  Thresholding in edge detection: a statistical approach , 2004, IEEE Transactions on Image Processing.

[4]  Jianqing Fan,et al.  Data‐Driven Bandwidth Selection in Local Polynomial Fitting: Variable Bandwidth and Spatial Adaptation , 1995 .

[5]  Tony Lindeberg,et al.  Scale-Space Theory in Computer Vision , 1993, Lecture Notes in Computer Science.

[6]  T. Gasser,et al.  A Flexible and Fast Method for Automatic Smoothing , 1991 .

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

[8]  Jianqing Fan,et al.  Local polynomial kernel regression for generalized linear models and quasi-likelihood functions , 1995 .

[9]  John A. Nelder,et al.  Generalized linear models. 2nd ed. , 1993 .

[10]  H. Müller,et al.  Local Polynomial Modeling and Its Applications , 1998 .

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

[12]  Probal Chaudhuri,et al.  Significance in Scale Space for Bivariate Density Estimation , 2002 .

[13]  Debasis Sengupta,et al.  Classification Using Kernel Density Estimates , 2006, Technometrics.

[14]  C. A. Murthy,et al.  On visualization and aggregation of nearest neighbor classifiers , 2005, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[15]  P. McCullagh,et al.  Generalized Linear Models , 1972, Predictive Analytics.

[16]  R. Tibshirani,et al.  Local Likelihood Estimation , 1987 .

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

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

[19]  J. Simonoff.  Smoothing Methods in Statistics , 1998 .

[20]  Jianqing Fan,et al.  One-step local quasi-likelihood estimation , 1999 .

[21]  Jianqing Fan,et al.  Efficient Estimation and Inferences for Varying-Coefficient Models , 2000 .

[22]  Wolfgang Härdle,et al.  Applied Nonparametric Regression , 1991 .

[23]  P. McCullagh,et al.  Generalized Linear Models, 2nd Edn. , 1990 .

[24]  Jianqing Fan,et al.  Local maximum likelihood estimation and inference , 1998 .