Density estimation for biased data
By Sam Efromovich. 2004
50 citations recorded by the source corpus.
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.
Subfields: Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/1025b6b9044f31f5f6efbf1afd3aff64612dc091
How researchers see this paper
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In Statistics and Probability
- Ahmed M. Alaa
- Mihaela van der Schaar
- P. Ramírez
- B. Vidakovic
- Sam Efromovich
- Ioana Bica
- James Jordon
- Craig Lambert
Citations in the corpus
- Bayesian Nonparametric Causal Inference: Information Rates and Learning Algorithms (2017, result): “The fact that selection bias does not impair the optimal information rate for causal inference is consistent with previous results on minimax-optimal kernel density estimation under selection bias or length bias [37]–[40].”
- Wavelet density estimation for stratified size-biased sample (2010, methodology): “According to Efromovich (2004b) this naive estimator is rate inadmissible whenever the biasing function is not as smooth as the underlying density fX .”
- Estimation of the density of regression errors (2005, background): “For instance, Van Keilegom and Veraverbeke [38] considered the problem of consistent error density estimation in a censored regression; using [4, 15, 18], it is reasonable to conjecture that optimal nonparametric results can be obtained for censored and biased regression models.”