Density Estimation

Density Estimation

2004 | Simon J. Sheather
This paper provides a practical description of density estimation using kernel methods, aiming to encourage statisticians to apply these techniques. It discusses implementations in R, S-PLUS, and SAS. Key topics include kernel density estimation, bandwidth selection, local likelihood density estimates, and data sharpening. The paper explains the basic properties of kernel density estimators, emphasizing the importance of bandwidth selection. It describes methods for selecting the bandwidth, including rules of thumb, cross-validation, and plug-in methods. Recent improvements to kernel methods, such as local likelihood density estimates and data sharpening, are also discussed. The paper compares the performance of various methods using data from the U.S. PGA tour. It concludes with recommendations for density estimation, suggesting the use of multiple bandwidth values and the Sheather–Jones plug-in bandwidth for its good performance. The paper also highlights the importance of plotting cross-validation functions and using higher-order sharpened estimates for multi-modal density estimates.This paper provides a practical description of density estimation using kernel methods, aiming to encourage statisticians to apply these techniques. It discusses implementations in R, S-PLUS, and SAS. Key topics include kernel density estimation, bandwidth selection, local likelihood density estimates, and data sharpening. The paper explains the basic properties of kernel density estimators, emphasizing the importance of bandwidth selection. It describes methods for selecting the bandwidth, including rules of thumb, cross-validation, and plug-in methods. Recent improvements to kernel methods, such as local likelihood density estimates and data sharpening, are also discussed. The paper compares the performance of various methods using data from the U.S. PGA tour. It concludes with recommendations for density estimation, suggesting the use of multiple bandwidth values and the Sheather–Jones plug-in bandwidth for its good performance. The paper also highlights the importance of plotting cross-validation functions and using higher-order sharpened estimates for multi-modal density estimates.
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[slides and audio] Density Estimation