On Second-Order A-, D- and E-Minimax Designs for Estimating Slopes in Extrapolation and Restricted Interpolation Regions

Summary

The concepts of D-, A- and E-minimax optimality criteria of designs for estimating the slopes of a response surface are considered for situations where the region of interest may not be identical to the experimental region. Optimal second-order designs are derived for the situation where the experimental region and the region of interest are both hyperspherical with a common centre. The dependence of the optimal design on the relative sizes of the regions is investigated. Further, the perfomance of designs optimal for one region in estimating slopes in other regions is also examined.     

VARIANCE ESTIMATION IN NONPARAMETRIC MULTIPLE REGRESSION

ABSTRACT

We consider the variance estimation in a general nonparametric regression model with multiple covariates. We extend difference methods to the multivariate setting by introducing an algorithm that orders the design points in higher dimensions. We also consider an adaptive difference estimator which requires much less strict assumptions on the covariate design and can significantly reduce mean squared error for small sample sizes.     

Some New Results on the Multinomial Randomized Response Model

ABSTRACT

The randomized response technique is an effective survey method designed to elicit sensitive information while ensuring the privacy of the respondents. In this article, we present some new results on the randomization response model in situations wherein one or two response variables are assumed to follow a multinomial distribution. For a single sensitive question, we use the well-known Hopkins randomization device to derive estimates, both under the assumption of truthful and untruthful responses, and present a technique for making pairwise comparisons. When there are two sensitive questions of interest, we derive a Pearson product moment correlation estimator based on the multinomial model assumption. This estimator may be used to quantify the linear relationship between two variables when multinomial response data are observed according to a randomized-response protocol.     

Tolerance‐based error reduction in multi‐agent bioassays

Some degree of error is inevitable in multi‐agent bioassays regardless of design or measurement technology. Estimation error can be reduced post facto by exploiting the matrix partial ordering of the bioassay survival estimates. The standard method for this is order‐restricted regression (ORR). If the joint action of the bioassay agents admits a tolerance‐based interpretation, additional structure beyond matrix partial ordering is available, leading to a new method of error reduction. This tolerance‐based error reduction (TBER) procedure almost always outperforms ORR. Like ORR, TBER applies to complete factorial bioassay designs and, using weighting, to incomplete designs.     

A Comparison of Three-level Orthogonal Arrays in the Presence of a Possible Correlation in Observations

When we want to compare two designs we usually assume the standard linear model with uncorrelated observations. In this paper we use the comparison method proposed by Ghosh & Shen (2006) to compare three level orthogonal arrays with 18, 27 and 36 runs under a possible presence of correlation in observations.     

Multistage sampling for latent variable models

I consider the design of multistage sampling schemes for epidemiologic studies involving latent variable models, with surrogate measurements of the latent variables on a subset of subjects. Such models arise in various situations: when detailed exposure measurements are combined with variables that can be used to assign exposures to unmeasured subjects; when biomarkers are obtained to assess an unobserved pathophysiologic process; or when additional information is to be obtained on confounding or modifying variables. In such situations, it may be possible to stratify the subsample on data available for all subjects in the main study, such as outcomes, exposure predictors, or geographic locations. Three circumstances where analytic calculations of the optimal design are possible are considered: (i) when all variables are binary; (ii) when all are normally distributed; and (iii) when the latent variable and its measurement are normally distributed, but the outcome is binary. In each of these cases, it is often possible to considerably improve the cost efficiency of the design by appropriate selection of the sampling fractions. More complex situations arise when the data are spatially distributed: the spatial correlation can be exploited to improve exposure assignment for unmeasured locations using available measurements on neighboring locations; some approaches for informative selection of the measurement sample using location and/or exposure predictor data are considered.     

Optimal design of clinical trials comparing several treatments with a control

Clinical trials are often designed to compare several treatments with a common control arm in pairwise fashion. In this paper we study optimal designs for such studies, based on minimizing the total number of patients required to achieve a given level of power. A common approach when designing studies to compare several treatments with a control is to achieve the desired power for each individual pairwise treatment comparison. However, it is often more appropriate to characterize power in terms of the family of null hypotheses being tested, and to control the probability of rejecting all, or alternatively any, of these individual hypotheses. While all approaches lead to unbalanced designs with more patients allocated to the control arm, it is found that the optimal design and required number of patients can vary substantially depending on the chosen characterization of power. The methods make allowance for both continuous and binary outcomes and are illustrated with reference to two clinical trials, one involving multiple doses compared to placebo and the other involving combination therapy compared to mono-therapies. In one example a 55% reduction in sample size is achieved through an optimal design combined with the appropriate characterization of power.     

我国可转换债券转股条款设计的实证研究

转股条款的灵活设计是实现可转债特定融资动因的重要途径之一,本文根据相关理论假说及其对证券条款设计的意义,设计了较为系统的实证分析框架和稳健的模型估计方法,对我国可转债的转股条款进行了较为严格意义上的实证检验。研究发现,高负债率、小规模和获取经营现金能力较差的公司明显倾向于设计较低的转股价格和较高的转换比率;信用记录较短（以上市年限代表）和收益不稳定的公司具有相同的倾向。国内可转债设计主要由财务危机假说解释,而制度性因素对条款设计具有重要影响。总体上,目前可转债的条款设计没有得到发行人的理性对待,本文就此提出了相关政策建议。     

互连网络拓扑优化设计

论述了互连网络拓扑优化设计问题,建立了必要的数学模型,该数学模型是一个非线性组合优化问题,它属于NP—完备类问题。采取拉格朗日松弛法、次梯度迭代算法和启发式算法,得出最优下确界和结论。