Showing papers in "Sankhya in 2012"
TL;DR: In this paper, the authors define pivotal or approximate pivotal statistics based on estimating functions and propose asymptotic approximations as well as estimating function bootstrap (EFB) methods based on resampling the estimated terms in the estimating functions.
Abstract: Suppose that inference about parameters of interest is to be based on an unbiased estimating function that is U-statistic of degree 1 or 2. We define pivotal or approximate pivotal statistics based on such estimating functions and propose asymptotic approximations as well as estimating function bootstrap (EFB) methods based on resampling the estimated terms in the estimating functions. These methods are justified asymptotically and lead to confidence intervals produced directly from the estimating function based quantities that are pivotal or asymptotically pivotal. Particular examples in this class of estimating functions arise in least-squares regression, robust L
a
estimation (1 ≤ a < 2), Wilcoxon rank regression and other related estimation problems. The proposed methods are evaluated in simulations and applied to a real data set. When compared with existing asymptotic and resampling methods, the EFB method is found to be more accurate in small sample situations and robust to violation of model assumptions.
3 citations
TL;DR: This work first shows that the frequently used Chao-Lee estimator can in fact be obtained by Bayesian methods with a Dirichlet prior, and then uses such clarification to develop a new estimator that is more flexible than existing ones.
Abstract: We consider the classic problem of estimating T, the total number of species in a population, from repeated counts in a simple random sample. We first show that the frequently used Chao-Lee estimator can in fact be obtained by Bayesian methods with a Dirichlet prior, and then use such clarification to develop a new estimator; numerical tests and some real experiments show that the new estimator is more flexible than existing ones, in the sense that it adapts to changes in the normalized interspecies variance γ
2. Our method involves simultaneous estimation of T, γ
2, and of the parameter λ in the Dirichlet prior, and the only limitation seems to come from the required convergence of the prior which imposes the restriction γ
2 ≤ 1. We also obtain confidence intervals for T and an estimation of the species’ distribution. Some numerical examples are given, together with applications to sampling from a Census database closely following Benford’s law, showing good performances of the new estimator, even beyond γ
2 = 1. Tests on confidence intervals show that the coverage frequency appears to be in good agreement with the desired confidence level.
3 citations
TL;DR: In this paper, a characterization of the convolution of Gaussian and Poisson laws in the set of infinitely divisible distributions is provided, where Gaussian laws are defined as Gaussian distributions.
Abstract: A characterization of the convolution of Gaussian and Poisson laws in the set of infinitely divisible distributions is provided.
3 citations
TL;DR: In this paper, it was shown that the existence of a probability P such that Pn converges weakly to Pn in a Polish space is a strong predictor of weak convergence.
Abstract: We show that in a Polish space if {Pn} is a sequence of probability measures then the existence of \(\displaystyle \lim_n \int f dP_n\) for every bounded continuous function guarantees the existence of a probability P such that Pn converges weakly to P.
TL;DR: A histogram estimator of hazard rate may not be as appealing as in the case of density estimation, nevertheless it still provides an easy to compute estimator which is simple enough to display and summarize failure time data as discussed by the authors.
Abstract: A histogram estimator of hazard rate may not be as appealing as in the case of density estimation, nevertheless it still provides an easy to compute estimator which is simple enough to display and summarize failure time data Surprisingly there is no investigation into the properties of the simple histogram estimator of hazard rate In this article we study its mean square error properties and discuss the choice of bin width