In sampling, arisen data with probability proportional to its length is called Length-bised. Nonparametric density estimation in length-biased sampling is more difficult than other states. One of the famous estimators in this context is the one introduced by Jones (1991). In this paper, we calculate the bandwidth parameter of this estimator by Bayes'method. The strong consistency of this estimator have been proved with a random Bandwidth. We have compared the performance of Bayes'method with cross validation by using simulation studies.
Ajami M, Fakoor V, Jomhoori S. Bayesian and Cross Validation Estimation Bandwidth of Kernel Density Function Estimator for Length-biased Data. JSS 2011; 5 (1) :41-60 URL: http://jss.irstat.ir/article-1-123-en.html