Access

You are not currently logged in.

Access your personal account or get JSTOR access through your library or other institution:

login

Log in to your personal account or through your institution.

If You Use a Screen Reader

This content is available through Read Online (Free) program, which relies on page scans. Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.

On the Optimal Rates of Convergence for Nonparametric Deconvolution Problems

Jianqing Fan
The Annals of Statistics
Vol. 19, No. 3 (Sep., 1991), pp. 1257-1272
Stable URL: http://www.jstor.org/stable/2241949
Page Count: 16
  • Read Online (Free)
  • Download ($19.00)
  • Subscribe ($19.50)
  • Cite this Item
Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
On the Optimal Rates of Convergence for Nonparametric Deconvolution Problems
Preview not available

Abstract

Deconvolution problems arise in a variety of situations in statistics. An interesting problem is to estimate the density f of a random variable X based on n i.i.d. observations from Y = X + ε, where ε is a measurement error with a known distribution. In this paper, the effect of errors in variables of nonparametric deconvolution is examined. Insights are gained by showing that the difficulty of deconvolution depends on the smoothness of error distributions: the smoother, the harder. In fact, there are two types of optimal rates of convergence according to whether the error distribution is ordinary smooth or supersmooth. It is shown that optimal rates of convergence can be achieved by deconvolution kernel density estimators.

Page Thumbnails

  • Thumbnail: Page 
1257
    1257
  • Thumbnail: Page 
1258
    1258
  • Thumbnail: Page 
1259
    1259
  • Thumbnail: Page 
1260
    1260
  • Thumbnail: Page 
1261
    1261
  • Thumbnail: Page 
1262
    1262
  • Thumbnail: Page 
1263
    1263
  • Thumbnail: Page 
1264
    1264
  • Thumbnail: Page 
1265
    1265
  • Thumbnail: Page 
1266
    1266
  • Thumbnail: Page 
1267
    1267
  • Thumbnail: Page 
1268
    1268
  • Thumbnail: Page 
1269
    1269
  • Thumbnail: Page 
1270
    1270
  • Thumbnail: Page 
1271
    1271
  • Thumbnail: Page 
1272
    1272