THE EFFECT OF DISCRETIZATION ERROR ON BANDWIDTH SELECTION FOR KERNEL DENSITY-ESTIMATION

• 成果类型: Article
• 署名作者: CHIU, ST
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• 发表日期: 1991
• 页码: 436441
• 关键词: squares cross-validation

摘要

It is well known that the cross-validation score function of discretized data often tends to - infinity as the bandwidth tends to zero. This disturbing property causes some difficulty in applying cross-validation to discretized data. Since all data are rounded to some degree, the phenomenon limits the application of cross-validation in practice. Based on characteristic functions, the cause of the difficulty is explained, and a simple modification is suggested. Under some conditions, it is shown that the bandwidth selected by the proposed procedure is asymptotically equivalent to the bandwidth selected by cross-validation of the original unrounded data. The advantages of the proposed procedure are demonstrated in two examples.