Inference on the Minimum Effective Dose Using Binary Data

This article proposes a confidence interval procedure for an open question posted by Tamhane and Dunnett regarding the inference on the minimum effective dose of a drug for binary data. We use a partitioning approach in conjunction with a confidence interval procedure to provide a solution to this problem. Binary data frequently arise in medical investigations in connection with dichotomous outcomes such as the development of a disease or the efficacy of a drug. The proposed procedure not only detects the minimum effective dose of the drug, but also provides estimation information on the treatment effect of the closest ineffective dose. Such information benefits follow-up investigations in clinical trials. We prove that, when the confidence interval for the pairwise comparison has (or asymptotically controls) confidence level 1 ? α, the stepwise procedure strongly controls (or asymptotically controls) the familywise error rate at level α, which is a key criterion in dose finding. The new method is compared with other procedures in terms of power performance and coverage probability using simulations. The simulated results shed new light on the discernible features of the new procedure. An example on the investigation of acetaminophen is included.     

Minimum variance unbiased estimation in doubly type II censored samples from families of distributions involving two truncation parameters

In this paper we construct uniformly minimum variance unbiased estimators for U-estimable functions when the underlying family of distributions involves two unknown truncation parameters and the sample is doubly Type II censored. Previous relevant results for the complete sample case are obtained as special cases of our results.     

Accounting for uncertainty in the historical response rate of the standard treatment in single‐arm two‐stage designs based on Bayesian power functions

In phase II single‐arm studies, the response rate of the experimental treatment is typically compared with a fixed target value that should ideally represent the true response rate for the standard of care therapy. Generally, this target value is estimated through previous data, but the inherent variability in the historical response rate is not taken into account. In this paper, we present a Bayesian procedure to construct single‐arm two‐stage designs that allows to incorporate uncertainty in the response rate of the standard treatment. In both stages, the sample size determination criterion is based on the concepts of conditional and predictive Bayesian power functions. Different kinds of prior distributions, which play different roles in the designs, are introduced, and some guidelines for their elicitation are described. Finally, some numerical results about the performance of the designs are provided and a real data example is illustrated. Copyright © 2016 John Wiley & Sons, Ltd.     

我国最低工资统计测算模型研究

 最低工资统计测算模型研究，历来是各国政府极为重视的问题之一。它涉及到运用统计调查方法、经济计量模型、计算机辅助测算等方法，对最低工资测算、劳动者生存质量，以及对制度法规等问题进行定性定量分析的跨学科研究的问题，由于该课题在我国研究的时间较短，特别是统计学者介入研究不够，导致各级劳动和社会保障部门虽然亟需解决最低工资统计测算模型问题，但囿于统计技术问题，其发展极为缓慢。这也是本课题组亟力推动研究之动力。     

Stochastic approximation methods and their use in bioassay and phase i clinical trials

Stochastic approximation procedures are sequential estimation methods which provide estimates for the point at which a general regression function attains a given value. The application of such methods to the problem of estimating the median effective does in bioassay and to the problem of estimating the maximally tolerated does in phase I clinical trials is discussed. it is argued that these methods could be very useful in practice.     

Bounded Estimation in the Presence of Nuisance Parameters

The aim of this paper is to extend in a natural fashion the results on the treatment of nuisance parameters from the profile likelihood theory to the field of robust statistics. Similarly to what happens when there are no nuisance parameters, the attempt is to derive a bounded estimating function for a parameter of interest in the presence of nuisance parameters. The proposed method is based on a classical truncation argument of the theory of robustness applied to a generalized profile score function. By means of comparative studies, we show that this robust procedure for inference in the presence of a nuisance parameter can be used successfully in a parametric setting.     

Estimation of Population Mean in the Presence of Linear Trend

The present article deals with some methods for estimation of finite populations means in the presence of linear trend among the population values. As a result, we provided a strategy for the selection of sampling interval k for the case of circular systematic sampling, which ensures better estimator for the population mean compared to other choices of the sampling interval. This has been established based on empirical studies. Further we more, applied multiple random starts methods for selecting random samples for the case of linear systematic sampling and diagonal systematic sampling schemes. We also derived the explicit expressions for the variances and their estimates. The relative performances of simple random sampling, linear systematic sampling and diagonal systematic sampling schemes with single and multiple random starts are also assessed based on numerical examples.     

An Analysis of Two-Dimensional Agricultural Field Trials in the Presence of Outliers and Fertility Jumps

This paper proposes a model for outliers and fertility jumps in agricultural field trials when the fertility is correlated in two directions. Uncertainty concerning the occurrence of these anomalies can be substantial, especially when outliers occur near a fertility jump. The proposed estimation technique can take this uncertainty into account rather than condition on a particular set of anomalies. Diagnostics for the detection of these anomalies are also discussed. The procedures are illustrated with a wheat trial.     

A sequential design for maximizing the probability of a favourable response

Consider the situation in which subjects arrive sequentially for a treatment and in which there are two distinct ways in which the treatment may fail. Treatments are given at different dosages, and the probabilities of the two failure types vary with dose. Assuming that decreasing the chances of one failure type increases the chances of the other, we say the failures oppose each other. Also assume that one failure type is primary in that, if it occurs, it censors the trial, so that observation of the secondary failure type is contingent on no failure of the primary type. We are interested in designs that provide information about the dose that maximizes the probability of success, i.e., the optimal dose, while treating very few subjects at dosages that have high risks of failure. Assuming that dosages belong to a discrete set, we show that a randomized version of the Pólya urn scheme causes dose selection to be progressively biased so as to favour those doses that produce success with higher probability.     

Estimation and Prediction in the Presence of Spatial Confounding for Spatial Linear Models

In studies that produce data with spatial structure, it is common that covariates of interest vary spatially in addition to the error. Because of this, the error and covariate are often correlated. When this occurs, it is difficult to distinguish the covariate effect from residual spatial variation. In an i.i.d. normal error setting, it is well known that this type of correlation produces biased coefficient estimates, but predictions remain unbiased. In a spatial setting, recent studies have shown that coefficient estimates remain biased, but spatial prediction has not been addressed. The purpose of this paper is to provide a more detailed study of coefficient estimation from spatial models when covariate and error are correlated and then begin a formal study regarding spatial prediction. This is carried out by investigating properties of the generalized least squares estimator and the best linear unbiased predictor when a spatial random effect and a covariate are jointly modelled. Under this setup, we demonstrate that the mean squared prediction error is possibly reduced when covariate and error are correlated.     

Quantile Estimation in the Presence of Auxiliary Information under Negatively Associated Samples

In this article, we apply the empirical likelihood technique to propose a new class of quantile estimators in the presence of some auxiliary information under negatively associated samples. It is shown that the proposed quantile estimators are asymptotically normally distributed with smaller asymptotic variances than those of the usual quantile estimators. It is also shown that blocking technique is an useful tool in estimating asymptotic variance under negatively associated samples, which makes it possible to construct normal approximation based confidence intervals for quantiles.     

Empirical Bayes Estimation of Small Area Means under a Nested Error Linear Regression Model with Measurement Errors in the Covariates

Abstract.  Previously, small area estimation under a nested error linear regression model was studied with area level covariates subject to measurement error. However, the information on observed covariates was not used in finding the Bayes predictor of a small area mean. In this paper, we first derive the fully efficient Bayes predictor by utilizing all the available data. We then estimate the regression and variance component parameters in the model to get an empirical Bayes (EB) predictor and show that the EB predictor is asymptotically optimal. In addition, we employ the jackknife method to obtain an estimator of mean squared prediction error (MSPE) of the EB predictor. Finally, we report the results of a simulation study on the performance of our EB predictor and associated jackknife MSPE estimators. Our results show that the proposed EB predictor can lead to significant gain in efficiency over the previously proposed EB predictor.     

Efficient Estimation of the Seemingly Unrelated Regression Cointegration Model and Testing for Purchasing Power Parity

Abstract

This paper studies the efficient estimation of seemingly unrelated linear models with integrated regressors and stationary errors. We consider two cases. The first one has no common regressor among the equations. In this case, we show that by adding leads and lags of the first differences of the regressors and estimating this augmented dynamic regression model by generalized least squares using the long-run covariance matrix, we obtain an efficient estimator of the cointegrating vector that has a limiting mixed normal distribution. In the second case we consider, there is a common regressor to all equations, and we discuss efficient minimum distance estimation in this context. Simulation results suggests that our new estimator compares favorably with others already proposed in the literature. We apply these new estimators to the testing of the proportionality and symmetry conditions implied by purchasing power parity (PPP) among the G-7 countries. The tests based on the efficient estimates easily reject the joint hypotheses of proportionality and symmetry for all countries with either the United States or Germany as numeraire. Based on individual tests, our results suggest that Canada and Germany are the most likely countries for which the proportionality condition holds, and that Italy and Japan for the symmetry condition relative to the United States.     

The Estimation of Food Expenditures From Household Budget Data in the Presence of Bulk Purchases

The aim of this article is the estimation of annual food expenditures with limited information about bulk purchases with data from a Spanish household-budget survey for 1990—1991. Three alternatives are compared. The first, currently used for official purposes, does not use all the information. The second uses all the available information in a rough way. The third assumes a formal model for the unknown frequency of purchases. The three alternatives are compared by a regression model that should be homogeneous with respect to the dummy variables that represent the partial information of the groups and should show a distinct pattern of outliers under each alternative. Finally, we study the effect of the official and the best alternative on food inflation and inequality measures. We find that they lead to similar inflation rates but to different inequality estimates.     

Estimation of Population Mean Using Known Coefficient of Variation of the Study Character in the Presence of Non Response

Using the known coefficient of variation of the study character, generalized and regression-type estimators for the population mean using two phase sampling in the presence of non response were proposed and their properties have been studied. The conditions under which the proposed estimators are more efficient than the relevant estimators have been obtained. The empirical studies were given in the support of the problems in the case of positive and negative correlation between the study and the auxiliary characters which show the increase in the efficiency of the proposed estimators using known coefficient of variation of the study character with respect to the relevant estimators.     

A New Estimation Method Based on Order Statistics in the Families of Symmetric Location-scale Distributions

In this study, new unbiased and nonlinear estimators based on order statistics are proposed for the family of symmetric location-scale distributions and these estimators can be computed from both uncensored and symmetric doubly Type II censored samples. In addition, other relevant unbiased estimators are proposed to estimate standard deviations of these new estimators. A simulation study has been performed to evaluate the performance of the new estimators compared to BLU estimators for small sample sizes. As a result of the simulation study, the new estimators proposed for the location-scale family in general performed nearly as good as BLU estimators. Furthermore, the computational advantage of the proposed estimators over BLU and ML estimators are worthy of notice. In addition, these new estimators have been applied to real data, and the estimation results obtained have been compatible with those of BLUE methods.     

A monte carlo study of the f test and three tests based on ranks of treatment effects in randomized block designs

The F test is compared with three procedures based on ranks for testing treatment effects in the randomized complete block, fixed effects, model with one observation per cell.     

Local Estimation of the Second-Order Parameter in Extreme Value Statistics and Local Unbiased Estimation of the Tail Index

We develop and study in the framework of Pareto-type distributions a class of nonparametric kernel estimators for the conditional second order tail parameter. The estimators are obtained by local estimation of the conditional second order parameter using a moving window approach. Asymptotic normality of the proposed class of kernel estimators is proven under some suitable conditions on the kernel function and the conditional tail quantile function. The nonparametric estimators for the second order parameter are subsequently used to obtain a class of bias-corrected kernel estimators for the conditional tail index. In particular it is shown how for a given kernel function one obtains a bias-corrected kernel function, and that replacing the second order parameter in the latter with a consistent estimator does not change the limiting distribution of the bias-corrected estimator for the conditional tail index. The finite sample behavior of some specific estimators is illustrated with a simulation experiment. The developed methodology is also illustrated on fire insurance claim data.     

Efficient crossover designs in the presence of interactions between direct and carry-over treatment effects

Crossover designs, or repeated measurements designs, are used for experiments in which t treatments are applied to each of n experimental units successively over p time periods. Such experiments are widely used in areas such as clinical trials, experimental psychology and agricultural field trials. In addition to the direct effect on the response of the treatment in the period of application, there is also the possible presence of a residual, or carry-over, effect of a treatment from one or more previous periods. We use a model in which the residual effect from a treatment depends upon the treatment applied in the succeeding period; that is, a model which includes interactions between the treatment direct and residual effects. We assume that residual effects do not persist further than one succeeding period.A particular class of strongly balanced repeated measurements designs with n=t² units and which are uniform on the periods is examined. A lower bound for the A-efficiency of the designs for estimating the direct effects is derived and it is shown that such designs are highly efficient for any number of periods p=2,…,2t.