Asymptotic Properties of Error Density Estimator in Regression Model Under α-Mixing Assumptions

This paper aims at working out economic groupscreening plans to sort out defective items from a population which consists of tems with unequal a-priori probabilities of being defective. It is shown that in the case of group-screening from a population with unequal a-priori probabilities of factors being defective, the number of obseruations needed on the average is considerably smaller than that required in the case of a population with factors having the same a-priori probability of being defective. Tables at the end give some group-screening plans as illustrations.     

Optimum two stage group-screening with unequal group sizes and with errors in decisions

In this paper, the formula for the expected number of incorrect decisions has been obtained. It is assumed that the factors are defective with different a-priori probabilities. Group-screening designs have been described which minimise (i) the expected number of runs for a fixed value of the expected number of incorrect decisions, (ii) the expected total cost.     

Step-wise group screening designs with errors in observations

The performance of step-wise group screening In terms of the expected number of runs and the expected number of incorrect decisions, Is considered. A method for obtaining optimal step-wise designs Is presented, for the cases in which the direction of each defective factor is assumed to be known a-priori and the observations are subject to error.     

Group-testing,halving procedures,and binary search ∗

Group-testing procedures for minimizing the expected number of tests needed to classify N units as either good or bad are described, The units are assumed to have come independently from a binomial population with common probability p of being defective and q = 1-p of being good, Special consideration is given to comparing certain halving procedures with the correspending optimal procedures for the problem of finding one defective if it exists, and the problem of finding all the defectives.     

Step-wise group screening with equal prior probabilities and no errors in observations

This paper introduces a screening procedure called step-wise group screening for isolating defective factors from a population consisting of defective (or important) and non-defective     

A computer program for the design of group testing experiments

This paper describes a computer program GTEST for designing group testing experiments for classifying each member of a population of items as “good” or “defective”. The outcome of a test on a group of items is either “negative” (if all items in the group are good) or “positive” (if at least one of the items is defective, but it is not known which). GTEST is based on a Bayesian approach. At each stage, it attempts to maximize (nearly) the expected reduction in the “entropy”, which is a quantitative measure of the amount of uncertainty about the state of the items. The user controls the procedure through specification of the prior probabilities of being defective, restrictions on the construction of the test group, and priorities that are assigned to the items. The nominal prior probabilities can be modified adaptively, to reduce the sensitivity of the procedure to the proportion of defectives in the population.     

Defective data in the analysis of variance

Several kinds of defective data are considered, the first being that of data completely missing. General expressions for block designs are given for the variances of treatment contrasts. Sometimes even a moderate loss of data will seriously increase an important variance. A similar defect arises when some plots receive the wrong treatment. Again the consequences can be serious though, if the correct form of analysis used, variances of contrasts may be much better estimated than if defective data are regarded as missing. Finally, the problem of the mixed-up plots is considered, the total value for certain plots being known but not the individual data. Formulae are presented for dealing with such a case. Again the correct form of analysis can sometimes retain useful information that would be lost if affected plots are regarded as missing. Finally some considerations are set out for dealing with defective data in general.     

Group Testing,the Pooled Hypergeometric Distribution,and Estimating the Number of Defectives in Small Populations

The testing of combined bacteriological samples – or “group testing” – was introduced to reduce the cost of identifying defective individuals in populations containing small proportions of defectives. It may also be applied to plants, animals, or food samples to estimate proportions infected, or to accept or reject populations. Given the proportion defective in the population, the number of positive combined samples is approximately binomial when the population is large: we find the exact distribution when groups include the same number of samples. We derive some properties of this distribution, and consider maximum-likelihood and Bayesian estimation of the number defective.     

“Faulty inspeciton” distributions

The distribution of the number of items observed to be defective in samples from a finite population. When detection of defectiveness is not certain, is obtained. The distribution of waiting time all a specified number of defective items is observed is also considered.

     

Estimation of the Proportion of Defective Units by Using Group Testing Under the Existence of a Threshold of Detection

Group testing procedures, in which groups containing several units are tested without testing each unit, are widely used as cost-effective procedures in estimating the proportion of defective units in a population. A problem arises when we apply these procedures to the detection of genetically modified organisms (GMOs), because the analytical instrument for detecting GMOs has a threshold of detection. If the group size (i.e., the number of units within a group) is large, the GMOs in a group are not detected due to the dilution even if the group contains one unit of GMOs. Thus, most people conventionally use a small group size (which we call conventional group size) so that they can surely detect the existence of defective units if at least one unit of GMOs is included in the group. However, we show that we can estimate the proportion of defective units for any group size even if a threshold of detection exists; the estimate of the proportion of defective units is easily obtained by using functions implemented in a spreadsheet. Then, we show that the conventional group size is not always optimal in controlling a consumer's risk, because such a group size requires a larger number of groups for testing.     

Improved Empirical Bayes Estimation in Group Testing Procedure for Small Proportions

Group testing has been long recognized as an efficient method to classify all the experimental units into two mutually exclusive categories: defective or not defective. In recent years, more attention has been brought to the estimation of the population prevalence rate p of a disease, or of some property, using group testing. In this article, we propose two scaled squared-error loss functions, which improve the Bayesian approach to estimating p in terms of minimizing the mean squared error (MSE) of the Bayes estimators of p for small p. We show that the new estimators are preferred over the estimator from the usual squared-error loss function and the maximum likelihood estimator (MLE) for small p.     

Multi-stage step-wise group screening

Step-wise group screening experiments for classifying members of a population as either good or defective are generalised to more than two stages. An expression for the expected number of tests is obtained and optimum 2, 3 and 4-stage designs are tabulated. By assuming p to be small, an approximation to the expected number of tests is derived which is minimized with respect to the number of groups in each stage. Finally, a new bifurcation technique, seen to be a special case of multi-stage step-wise group screening, is discussed.     

Simulated and unbiased reliability sampling plans

Statistical estimation and hypothesis testing are two ways in which the data of a sample can be made to yield information concerning the parameters of the population from which the sample is drawn. The most important applications of these two ways is the acceptance sampling methods used in industrial quality control, systems reliability and failure detection. The use of these sampling methods is connected with the risk of unnecessary rejection of satisfactory lots and the risk of acceptance of lots with defective units, these decisions can occur when selecting biased samples containing most defective units or no defective units despite the fact that the lot has the contrary. The aim of this research is to make this kind of decision an improbable or impossible event. The parameters and techniques determining the sampling methods must be correctly chosen. The formulation of an optimised statistical model of these problems is the basic condition of obtaining objective results. By the essence of statistical simulation the process of functioning of the complex system was used to represent a mathematically formulated model which was isomorphic in all essential aspects of the research objectives. This model was repeatedly tested to determine the required statistical characteristics, based on the complex stochastic process.     

Measurement Error Correction by Exploiting Gene–Environment Independence in Family‐Based Case–Control Studies

Abstract. Family‐based case–control designs are commonly used in epidemiological studies for evaluating the role of genetic susceptibility and environmental exposure to risk factors in the etiology of rare diseases. Within this framework, it is often reasonable to assume genetic susceptibility and environmental exposure being conditionally independent of each other within families in the source population. We focus on this setting to explore the situation of measurement error affecting the assessment of the environmental exposure. We correct for measurement error through a likelihood‐based method. We exploit a conditional likelihood approach to relate the probability of disease to the genetic and the environmental risk factors. We show that this approach provides less biased and more efficient results than that based on logistic regression. Regression calibration, instead, provides severely biased estimators of the parameters. The comparison of the correction methods is performed through simulation, under common measurement error structures.     

Repeated screening with inspection error and no false positive results with application to pharmaceutical pill production

Summary.  Repeated screening is a 100% sampling inspection of a batch of items followed by removal of the defective items and further iterations of inspection and removal. The reason for repeating the inspection is that the detection of a defective item happens with probability p <1. A missed defective item is a false negative result. The no false positive result is contemplated in this paper, which is motivated by a problem coming from the production of pharmaceutical pills. Bayesian posterior distributions for the quality of the lot are obtained for the case of both p known and p unknown. Batch rejection and batch acceptance control limits for the number of defective items at subsequent iterations can then be calculated. Theoretical connections to the problem of estimating the number-of-trials parameter of a binomial distribution are drawn.     

Optimal acceptance sampling policy considering Bayesian risks

In this paper, we propose a sampling policy considering Bayesian risks. Various definitions of producer's risk and consumer's risk have been made. Bayesian risks for both producer and consumer are proven to give better information to decision-makers than classical definitions of the risks. So considering the Bayesian risk constraints, we seek to find optimal acceptance sampling policy by minimizing total cost, including the cost of rejecting the batch, the cost of inspection, and the cost of defective items detected during the operation. Proper distributions to construct the objective function of the model are specified. In order to demonstrate the application of the proposed model, we illustrate a numerical example. Furthermore, the results of the sensitivity analysis show that lot size, the cost of inspection, and the cost of one defective item are key factors in sampling policies. The acceptable quality level, the lot tolerance proportion defective, and Bayesian risks also affect the sampling policy, but variations of acceptable quality level and producer Bayesian risks, for values more than a specified value, cause no changes in sampling policy.     

A Multi-Stage Two-Machines Replacement Strategy Using Mixture Models,Bayesian Inference,and Stochastic Dynamic Programming

If at least one out of two serial machines that produce a specific product in manufacturing environments malfunctions, there will be non conforming items produced. Determining the optimal time of the machines' maintenance is the one of major concerns. While a convenient common practice for this kind of problem is to fit a single probability distribution to the combined defect data, it does not adequately capture the fact that there are two different underlying causes of failures. A better approach is to view the defects as arising from a mixture population: one due to the first machine failures and the other due to the second one. In this article, a mixture model along with both Bayesian inference and stochastic dynamic programming approaches are used to find the multi-stage optimal replacement strategy. Using the posterior probability of the machines to be in state λ₁, λ₂ (the failure rates of defective items produced by machine 1 and 2, respectively), we first formulate the problem as a stochastic dynamic programming model. Then, we derive some properties for the optimal value of the objective function and propose a solution algorithm. At the end, the application of the proposed methodology is demonstrated by a numerical example and an error analysis is performed to evaluate the performances of the proposed procedure. The results of this analysis show that the proposed method performs satisfactorily when a different number of observations on the times between productions of defective products is available.     

A likelihood ratio test for the equality of proportions of two normal populations

In sampling inspection by variables, an item is considered defective if its quality characteristic Y falls below some specification limit L₀. We consider switching to a new supplier if we can be sure that the proportion of defective items for the new supplier is smaller than the proportion defective for the present supplier.

Assume that Y has a normal distribution. A test for comparing these proportions is developed. A simulation study of the performance of the test is presented.     

中国各地区人口特征和房价波动的动态关系

本文分析了人口特征、金融市场和房地产市场三者的相互影响机制，基于2002-2015年中国大陆31个省市自治区直辖市的年度数据，建立了面板平滑转换模型，将人口密度作为异质变量构建计量模型来研究房地产市场的非线性影响因素，研究中国省市人口特征对房价波动的影响机制。实证结果表明：人均GDP对房价的影响随人口密度增加呈现非线性提升效应；人口密度小的城市房地产价格上涨比人口密度大的城市更像是“货币现象”；当人口密度较小时，地区中老年人口占比越大，房价有下降趋势，反映了房地产“年轻人推动房价上涨”的直观趋势，但是极少人口密度比较大城市例外。     

基于函数性数据方法的艺术品网上拍卖竞买者出价水平影响因素研究

在分析互联网艺术品拍卖中竞买者出价水平特有影响因素的基础上,运用函数性相平面图与线性回归方法,探究出价水平及各影响因素在整个拍卖期间的动态变化情况。结果表明,在拍卖的不同阶段,推动竞买者出价水平变化的影响因素各有不同,且作用大小与作用方向在整个拍卖期间不断变化。特别指出,拍卖次序在整个拍卖期间对出价水平具有正向影响,且作用程度随着拍卖的进行逐渐增强,即序号越大、越晚参与竞拍的艺术品的最终成交金额越大。