Mathematics – Statistics Theory
Scientific paper
2004-06-25
Annals of Statistics 2004, Vol. 32, No. 3, 1137-1161
Mathematics
Statistics Theory
Scientific paper
10.1214/009053604000000300
The concept of biased data is well known and its practical applications range from social sciences and biology to economics and quality control. These observations arise when a sampling procedure chooses an observation with probability that depends on the value of the observation. This is an interesting sampling procedure because it favors some observations and neglects others. It is known that biasing does not change rates of nonparametric density estimation, but no results are available about sharp constants. This article presents asymptotic results on sharp minimax density estimation. In particular, a coefficient of difficulty is introduced that shows the relationship between sample sizes of direct and biased samples that imply the same accuracy of estimation. The notion of the restricted local minimax, where a low-frequency part of the estimated density is known, is introduced; it sheds new light on the phenomenon of nonparametric superefficiency. Results of a numerical study are presented.
No associations
LandOfFree
Density estimation for biased data does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Density estimation for biased data, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Density estimation for biased data will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-206487