分层抽样下的样本轮换理论研究

讨论用于回归估计的二相抽样理论在分层抽样下样本轮换后估计量的构造及其精度问题,并在构造的估计量的基础上计算了分层抽样下的最优样本轮换率,这对于深入研究分层抽样理论,使其估计量的精度提高,从而更好地实现抽样调查的目标有积极意义。     

Non-parametric Bayesian Inference for Integrals with respect to an Unknown Finite Measure

Abstract.  We consider the problem of estimating a collection of integrals with respect to an unknown finite measure μ from noisy observations of some of the integrals. A new method to carry out Bayesian inference for the integrals is proposed. We use a Dirichlet or Gamma process as a prior for μ , and construct an approximation to the posterior distribution of the integrals using the sampling importance resampling algorithm and samples from a new multidimensional version of a Markov chain by Feigin and Tweedie. We prove that the Markov chain is positive Harris recurrent, and that the approximating distribution converges weakly to the posterior as the sample size increases, under a mild integrability condition. Applications to polymer chemistry and mathematical finance are given.     

Binomial sampling plans for estimatingBemisia tabaci populations in cantaloupes

Early season infestations of the sweet potato whitefly,Bemisia tabaci (Gennadius), on cantaloupes,Cucumis melo L., were determined by counts of the number of adults per leaf in fields near Yuma, Arizona. We used these data to develop binomial sampling plans based on the relationship between mean densities of whiteflies per leaf,m, and proportion of leaves infested with more thanI whiteflies,P _I, according to the empirical model lnm=a′+b′ ln[−ln(1−P _I)]. The models were developed for the presence-absence approach (I=0) and for a cutoff value of three whiteflies per leaf (I=3). Four independent data sets were used to evaluate the models. Both methods yielded reliable predictions at low infestation levels, but some of the higherm values were overestimated. As the tentative economic threshold forB. tabaci is three adults per leaf, which corresponds to lowP _I values, results of the binomial sampling were satisfactory for pest management purposes.     

On constructing almost unbiased estimators of finite population mean using transformed auxiliary variable

${\overline y}$ , ratio _R and Tracy et al. (1999) estimators. Received: October 12, 1999; revised version: April 25, 2000     

Integrated statistical and decision models for multi-stage health care audit sampling

Health care audits are crucial in managing the government insurance programs that are estimated to have losses amounting to billions of dollars every year. Statistical methods such as sampling have long been used to handle their size and complexity. Sampling from health care claims data can benefit from multi-stage approaches, especially when the evaluation of the tradeoffs between precision and cost is important. The use of decision models could facilitate health care auditors and policy makers make the best use of these sampling outputs. This paper proposes an integrated multi-stage sampling and decision-making framework that enables auditors address the tradeoffs between audit costs and expected overpayment recovery. We illustrate the framework and discuss insights utilizing a variety of overpayment scenarios for payment populations including U.S. Medicare Part B claims payment data.     

Bias‐Corrected Estimation in Continuous Sampling Plans

Continuous sampling plans (CSPs) are algorithms used for monitoring and maintaining the quality of a production line. Although considerable work has been done on the development of CSPs, to our knowledge, there has been no corresponding effort in developing estimators with good statistical properties for data arising from a CSP inspection process. For example, information about the failure rate of the process will affect the management of the process, both in terms of selecting appropriate CSP parameters to keep the failure rate after inspection at a suitable level, and in terms of policy, for example, whether the process should be completely inspected, or shut down. The motivation for this exercise was developing sampling protocols for Australia's Department of Agriculture and Water Resources for monitoring the biosecurity compliance of incoming goods at international borders. In this study, we show that maximum likelihood estimation of the failure rate under a sampling scheme can be biased depending on when estimation is performed, and we provide explicit expressions for the main contribution of the bias under various CSPs. We then construct bias‐corrected estimators and confidence intervals, and evaluate their performance in a numerical study.     

Estimation of Nonparametric Conditional Moment Models With Possibly Nonsmooth Generalized Residuals

This paper studies nonparametric estimation of conditional moment restrictions in which the generalized residual functions can be nonsmooth in the unknown functions of endogenous variables. This is a nonparametric nonlinear instrumental variables (IV) problem. We propose a class of penalized sieve minimum distance (PSMD) estimators, which are minimizers of a penalized empirical minimum distance criterion over a collection of sieve spaces that are dense in the infinite‐dimensional function parameter space. Some of the PSMD procedures use slowly growing finite‐dimensional sieves with flexible penalties or without any penalty; others use large dimensional sieves with lower semicompact and/or convex penalties. We establish their consistency and the convergence rates in Banach space norms (such as a sup‐norm or a root mean squared norm), allowing for possibly noncompact infinite‐dimensional parameter spaces. For both mildly and severely ill‐posed nonlinear inverse problems, our convergence rates in Hilbert space norms (such as a root mean squared norm) achieve the known minimax optimal rate for the nonparametric mean IV regression. We illustrate the theory with a nonparametric additive quantile IV regression. We present a simulation study and an empirical application of estimating nonparametric quantile IV Engel curves.     

Nonparametric Instrumental Variable Estimation of Structural Quantile Effects

We study the asymptotic distribution of Tikhonov regularized estimation of quantile structural effects implied by a nonseparable model. The nonparametric instrumental variable estimator is based on a minimum distance principle. We show that the minimum distance problem without regularization is locally ill‐posed, and we consider penalization by the norms of the parameter and its derivatives. We derive pointwise asymptotic normality and develop a consistent estimator of the asymptotic variance. We study the small sample properties via simulation results and provide an empirical illustration of estimation of nonlinear pricing curves for telecommunications services in the United States.