On ratio estimators in two phase sampling under size stratification and estimation over two successive occasions

Adopting size stratification when the auxiliary character is approximated by a continuous uniform distribution, a double sampling ratio strategy has been suggested. this sampling strategy has been compared with some of the known sampling strategies. the applicability of this strategy to sampling on two successive occasions has also been investigated     

REGRESSION DIAGNOSTICS FOR THE LEAST ABSOLUTE DEVIATIONS AND THE MINIMAX METHODS

Abstract

In this article, we extend the concept of univariate frailty to a bivariate case to quantify and visualize the loss of efficiency of the log-rank test when a dependence structure between failure and censoring times is being ignored. We assume that an unobservable frailty influences the risk of failure and the other affects the risk of censoring, and those two frailties are correlated. Under the model being compared as a benchmark, the dependence structure between failure and censoring times is assumed to be completely observed. Under the model where the log-rank test is constructed without considering the dependency between failure and censoring times, it is assumed that the unobservable dependence structure has been absorbed into the baseline distributions. We note in our particular example that the loss of efficiency is minimal under the proportional hazards model even when the correlation between potential failure and censoring times is strong unless the dependence censorship induces a severe nonproportionality.     

Efficient initial designs for binary response data

In this paper we introduce a binary search algorithm that efficiently finds initial maximum likelihood estimates for sequential experiments where a binary response is modeled by a continuous factor. The problem is motivated by switching measurements on superconducting Josephson junctions. In this quantum mechanical experiment, the current is the factor controlled by the experimenter and a binary response indicating the presence or the absence of a voltage response is measured. The prior knowledge on the model parameters is typically poor, which may cause the common approaches of initial estimation to fail. The binary search algorithm is designed to work reliably even when the prior information is very poor. The properties of the algorithm are studied in simulations and an advantage over the initial estimation with equally spaced factor levels is demonstrated. We also study the cost-efficiency of the binary search algorithm and find the approximately optimal number of measurements per stage when there is a cost related to the number of stages in the experiment.     

Maximum-likelihood estimation and presentation for the interaction between treatments in observational studies with a dichotomous outcome

In observational studies for the interaction between treatments, one needs to estimate and present both the treatment effects and the interaction to learn the significance of the interaction to the treatment effects. In this article, we estimate the treatment effects and the interaction jointly by using only one logistic model and based on maximum-likelihood. We present the interaction by (1) point estimate and confidence interval of the interaction, (2) point estimate and confidence region of (treatment effect, interaction), and (3) point estimate and confidence interval of the interaction when the maximum-likelihood estimate of one treatment effect falls into specified range.     

Notes on estimation of the proportion ratio in the presence of carryover effects under the AB/BA crossover trial

The authors focus discussion on estimation of the proportion ratio (PR) in the presence of residual effects under the AB/BA design. Under a random effects multiplicative risk model, we develop three point estimators and three interval estimators accounting for residual effects for the PR. Using Monte Carlo simulations, we compare the performance of these point (or interval) estimators with point (or interval) estimators assuming no residual effects with respect to the bias and mean-squared-error (or the coverage probability and average length). The authors use the data taken from an AB/BA trial comparing two new inhalation devices to illustrate the use of these estimators.     

Nonparametric Estimation of the Conditional Distribution at Regression Boundary Points

Abstract

Nonparametric regression is a standard statistical tool with increased importance in the Big Data era. Boundary points pose additional difficulties but local polynomial regression can be used to alleviate them. Local linear regression, for example, is easy to implement and performs quite well both at interior and boundary points. Estimating the conditional distribution function and/or the quantile function at a given regressor point is immediate via standard kernel methods but problems ensue if local linear methods are to be used. In particular, the distribution function estimator is not guaranteed to be monotone increasing, and the quantile curves can “cross.” In the article at hand, a simple method of correcting the local linear distribution estimator for monotonicity is proposed, and its good performance is demonstrated via simulations and real data examples. Supplementary materials for this article are available online.     

Formulating robust regression estimation as an optimum allocation problem

The Mallows-type estimator, one of the most reasonable bounded influence estimators, often downweights leverage points regardless of the magnitude of the corresponding residual, and this could imply a loss of efficiency. In this article, we consider whether the efficiency of this bounded influence estimator could be improved by regarding both the robust x -distance and the residual size. We develop a new robust procedure based on the ideas of the Mallows-type estimator and the general robust recipe, where data been cleaned by pulling outliers towards their fitted values. Our basic idea is to formulate the robust estimation as an allocation problem, where the objective function is a Huber-type "loss" function, but the pulling resource is restricted. Using a mathematical programming technique, the pulling resource is optimally allocated to influential points <$>({x}_i, y_i)<$> with respect to residual size and given weights, <$>w({x}_i)<$>. Three previously published approaches are compared to our proposal via simulated experiments. In the case of contaminated data by regression outliers and "good" leverage points, the proposed robust estimator is a reasonable bounded influence estimator concerning both efficiency and norm of bias. In addition, the proposed approach offers the potential to establish constraints for the regression parameters and also may potentially provide insight regarding outlier detection.     

股市周期转换与国债利率期限结构——基于MS—VAR的分析

本文以2003—2008期间的国债数据为样本,采用Nelson-Siegel模型对反映国债利率期限结构的三个模型参数：水平因子、斜率因子和曲率因子进行了估计。在此基础上,假设三个参数序列构成的时间序列向量的演变过程受某潜在变量的支配,且该潜在变量服从二区制马尔科夫链转换过程。本文构建了反映潜在变量影响利率期限结构变化的MS—VAR模型,并用此模型实证检验了该潜在变量转换对国债利率期限结构的影响。结果表明：该潜在变量是股市周期,我国股市周期的转换对国债利率期限结构的变化存在着显著的影响。     

Regional Risk Assessment for Point Source Pollution Based on a Water Quality Model of the Taipu River,China

Point source pollution is one of the main threats to regional environmental health. Based on a water quality model, a methodology to assess the regional risk of point source pollution is proposed. The assessment procedure includes five parts: (1) identifying risk source units and estimating source emissions using Monte Carlo algorithms; (2) observing hydrological and water quality data of the assessed area, and evaluating the selected water quality model; (3) screening out the assessment endpoints and analyzing receptor vulnerability with the Choquet fuzzy integral algorithm; (4) using the water quality model introduced in the second step to predict pollutant concentrations for various source emission scenarios and analyzing hazards of risk sources; and finally, (5) using the source hazard values and receptor vulnerability scores to estimate overall regional risk. The proposed method, based on the Water Quality Analysis Simulation Program (WASP), was applied in the region of the Taipu River, which is in the Taihu Basin, China. Results of source hazard and receptor vulnerability analysis allowed us to describe aquatic ecological, human health, and socioeconomic risks individually, and also integrated risks in the Taipu region, from a series of risk curves. Risk contributions of sources to receptors were ranked, and the spatial distribution of risk levels was presented. By changing the input conditions, we were able to estimate risks for a range of scenarios. Thus, the proposed procedure may also be used by decisionmakers for long‐term dynamic risk prediction.     

Unbiased Estimation of Central Moments by using U-statistics

We obtain an estimator of the r th central moment of a distribution, which is unbiased for all distributions for which the first r moments exist. We do this by finding the kernel which allows the r th central moment to be written as a regular statistical functional. The U-statistic associated with this kernel is the unique symmetric unbiased estimator of the r th central moment, and, for each distribution, it has minimum variance among all estimators which are unbiased for all these distributions.