Exact calculation of the Dodge-Romig LTPD single sampling plans for inspection by variables

In this paper we shall deal with the acceptance sampling plans when the remainder of rejected lots is inspected. We shall consider two types of LTPD plans- for inspection by variables and for inspection by variables and attributes (all items from the sample are inspected by variables, remainder of rejected lots is inspected by attributes). We shall report on an algorithm allowing the calculation of these plans when the non-central t distribution is used for the operating characteristic. The calculation is considerably difficult, algorithm for non-central t distribution takes several minutes. For the calculation we shall use an original method.     

Failure–censored reliability sampling plans for the exponential distribution

In this paper we examine the failure-censored sampling plans for the two–parameter exponential distri- bution based on m random samples, each of size n. The suggested procedure is based on exact results and only the first failure time of each sample is needed. The values of the acceptability constant are also tabulated for selected values of p _α ¹ p _β ¹, α and β. Further, a comparison of the proposed sampling plans with ordinary sampling plans using a sample of size mn is made. When compared to ordinary sampling plans, the proposed plan has an advantage in terms of shorter test-time and a saving of resources.     

Dodge-Romig AOQL single sampling plans for inspection by variables

Acceptance sampling plans for inspection by variables, which minimize the mean inspection cost per lot of process average quality (assuming that the remainder of rejected lots is inspected), are derived under the condition that the maximum value of the mean fraction defective after sampling inspection, replacing all defective items found by good ones, shall be equal top _L . These plans are tabulated for chosen values of the given parameters, and compared with the Dodge-Romig AOQL attribute sampling plans. From the comparison it follows that under the same protection of consumer the AOQL plans for inspection by variables are in some situations more economical than the corresponding Dodge-Romig plans.     

Double ASN Minimax sampling plans by variables when the standard deviation is unknown

We deal with the double sampling plans by variables proposed by Bowker and Goode (Sampling Inspection by Variables, McGraw–Hill, New York, 1952) when the standard deviation is unknown. Using the procedure for the calculation of the OC given by Krumbholz and Rohr (Allg. Stat. Arch. 90:233–251, 2006), we present an optimization algorithm allowing to determine the ASN Minimax plan. This plan, among all double plans satisfying the classical two-point-condition on the OC, has the minimal ASN maximum.     

Choice experiments for estimating main effects and interactions

Choice-based conjoint experiments are used when choice alternatives can be described in terms of attributes. The objective is to infer the value that respondents attach to attribute levels. This method involves the design of profiles on the basis of attributes specified at certain levels. Respondents are presented sets of profiles and asked to select the one they consider best. However if choice sets have too many profiles, they may be difficult to implement. In this paper we provide strategies for reducing the number of profiles in choice sets. We consider situations where only a subset of interactions is of interest, and we obtain connected main effect plans with smaller choice sets that are capable of estimating subsets of two-factor and three-factor interactions in 2ⁿ and 3ⁿ plans. We also provide connected main effect plans for mixed level designs.     

Acceptance sampling by variables when the remainder of rejected lots is inspected

Acceptance sampling plans for inspection by variables, which minimize the mean inspection cost per lot of process average quality (assuming that the remainder of rejected lots is, inspected), were derived under the condition that the probability of accepting a submitted lot of tolerance quality, shall be 0.1. These plans were tabulated for chosen values of the given parameters, and compared with the Dodge-Romig LTPD attribute sampling plans. From the comparison it follows that under the same protection of consumer the LTPD plans for inspection by variables are in many situations more economical than the corresponding Dodge-Romig plans. This result is valid especially for the large lots and for the small values of the tolerance fraction defective.     

Exact two-sided Lieberman-Resnikoff sampling plans

We deal sith sampling by variables with two-way-protection in the case of aN(μσ²) distributed characteristic with unknown σ². For the sampling plan by Lieberman and Resnikoff (1955), which is based on the MVU estimator of the percent defective, we prove a formula for the OC. If the sampling parametersp ₁ (AQL),p ₂ (LQ) and α, β (type I, II errors) are given, we are able to compute the true type I and II errors of the usual (one-sided) approximation plans. Furthermore it is possible to compute exact two-sided Lieberman-Resnikoff sampling plans.     

On a bounded bimodal two-sided distribution fitted to the Old-Faithful geyser data

In this paper, we shall develop a novel family of bimodal univariate distributions (also allowing for unimodal shapes) and demonstrate its use utilizing the well-known and almost classical data set involving durations and waiting times of eruptions of the Old-Faithful geyser in Yellowstone park. Specifically, we shall analyze the Old-Faithful data set with 272 data points provided in Dekking et al. [3]. In the process, we develop a bivariate distribution using a copula technique and compare its fit to a mixture of bivariate normal distributions also fitted to the same bivariate data set. We believe the fit-analysis and comparison is primarily illustrative from an educational perspective for distribution theory modelers, since in the process a variety of statistical techniques are demonstrated. We do not claim one model as preferred over the other.     

Main effect plan for 2m factorials which allow search and estimation of one unknown effect

In this paper, we discuss resolution III plans for 2^m factorial experiments which have an additional property. We relax the classical assumption that all the interactions are negligible by assuming that (at most) one of them may be nonnegligible. Which interaction is nonnegligible is unknown. We discuss designs which allow the search and estimation of this interaction, along with the estimation of the general mean and the main effects as in the classical resolution III designs.     

Sampling and empirical risk minimization

ABSTRACT

In certain situations that shall be undoubtedly more and more common in the Big Data era, the datasets available are so massive that computing statistics over the full samples is hardly feasible, if not unfeasible. A natural approach in this context consists in using survey schemes and substituting the ‘full data’ statistics with their counterparts based on the resulting random samples, of manageable size. It is the main purpose of this paper to investigate the impact of survey sampling on statistical learning methods based on empirical risk minimization through the standard binary classification problem, considered here as a ‘case in point’. Precisely, we prove that, in presence of auxiliary information, appropriate use of optimally coupled Poisson survey plans may not affect much the learning rates, while possibly reducing significantly the number of terms that must be averaged to compute the empirical risk functional with overwhelming probability. These striking results are next shown to extend to more general sampling schemes by means of a coupling technique, originally introduced by Hajek [Asymptotic theory of rejective sampling with varying probabilities from a finite population. Ann Math Stat. 1964;35(4):1491–1523].     

The implementation of the bayesian paradigm

Routine implementation of the Bayesian paradigm requires an efficient approach to the calculation and display of posterior or predictive distributions for given likelihood and prior specifi- cations. In this paper we shall review some of the analytic and numerical approaches currently available, describing in detail a numerical integration strategy based on Gaussian quadrature, and an associated strategy for the reconstruction and display of distributions based on spline techniques.     

Limitations of P-Values and R-squared for Stepwise Regression Building: A Fairness Demonstration in Health Policy Risk Adjustment

ABSTRACT

Stepwise regression building procedures are commonly used applied statistical tools, despite their well-known drawbacks. While many of their limitations have been widely discussed in the literature, other aspects of the use of individual statistical fit measures, especially in high-dimensional stepwise regression settings, have not. Giving primacy to individual fit, as is done with p-values and R², when group fit may be the larger concern, can lead to misguided decision making. One of the most consequential uses of stepwise regression is in health care, where these tools allocate hundreds of billions of dollars to health plans enrolling individuals with different predicted health care costs. The main goal of this “risk adjustment” system is to convey incentives to health plans such that they provide health care services fairly, a component of which is not to discriminate in access or care for persons or groups likely to be expensive. We address some specific limitations of p-values and R² for high-dimensional stepwise regression in this policy problem through an illustrated example by additionally considering a group-level fairness metric.     

ASN-minimax double sampling plans for variables

X be a continuous quality characteristic, with one-sided lower specification limit, having either normal distribution with known σ or exponential distribution. We report on an algorithm allowing the calculation of the so-called ASN-Minimax plan. This plan has minimal maximal average sample size among all double sampling plans for variables that obey the classical two-points-condition on the operating characteristic. We give examples and tables of the ASN-Minimax plans in the normal as well as in the exponential case. Received: March 20, 2000; revised version: January 22, 2001     

基于2007年投入产出表的我国投资乘数测算和变动分析

 本文对固定资产投资乘数、凯恩斯投资乘数和投入产出投资乘数等三种投资乘数进行了测算分析,结果表明近年来我国投资乘数并没有发生大幅度下降,对经济增长的拉动贡献较大。通过对4万亿投资计划的具体测算,表明投资对拉动内需和抵御外部冲击发挥了巨大作用。作为发展中国家,保持较高的投资增速是经济可持续发展的必要条件,未来投资仍将是拉动我国经济增长的主要动力。但应当积极调整投资结构,避免产能过剩、抑制房地产价格上涨,提高投资效率。     

Hedging of contingent claims written on non traded assets under Markov-modulated models

ABSTRACT

This paper studies the hedging problem of European contingent claims when the underlying asset is non traded. We assume that the share prices of the assets are governed by Markov-modulated processes; that is, the market parameters switch over the time according to a finite-state continuous time Markov chain. Due to the presence of Markov chain the non traded asset, the market which we consider is incomplete, we shall use the local risk minimization method to obtain an optimal hedging strategy in a closed-form for an investor. Finally, numerical illustrations of an optimal hedging strategy are given by the Monte Carlo simulation.     

Interval censored sampling plans for the log-logistic lifetime distribution

The log-logistic distribution is one of the popular distributions in life-testing applications. This article develops an acceptance sampling procedure for the log-logistic lifetime distribution based on grouped data when the shape parameter is given. Both producer and consumer risks are considered to develop the ordinary, approximate and simulated sampling plans. Some of the proposed sampling plans are tabulated; moreover, those three types of sampling plans are compared with each other under the same censoring rates. The use of these tables is illustrated by an example.     

On robustness of optimal balanced resolution v plans

In this paper, we present Srivastava-Chopra optimal balanced resolution V plans for 2^m factorials (4?m?8) which are robust in the sense that, when any observation is missing, each of these designs will remain as a resolution V plan.     

Synthetic and composite estimation under a superpopulation model

Under a simple superpopulation model for an arbitrary sampling design we derive optimal linear unbiased estimators/predictors of a mean in a domain. They can be viewed as synthetic and composite estimators of small area estimation theory when no auxiliary variable is available. Moreover, we show that the only requirement for optimality of a sampling strategy is to use any sampling plan of fixed sample size together with traditional estimators (as designed for simple random sampling without replacement). Finally, for symmetric sampling plans, simplified formulas (based on the first two moments of sample sizes) for optimal synthetic and composite estimators and their MSE’s are derived. Throughout the paper we consistently use the model-design setup.     

2m − p compromise plans with strongly clear specified main effects and two-factor interactions

This article studies two-level strongly clear compromise plans. We derive some necessary conditions for the existence of four classes of two-level strongly clear compromise plans which allow the estimations of some specified main effects and two-factor interactions, with the assumption that the fourth- or higher-order effects are negligible. Also, some methods for constructing 2^{m ? p} strongly clear compromise plans are introduced.     

Sample size determination for testing equality in Poisson frequency data under an AB/BA crossover trial

Assuming that the frequency of occurrence follows the Poisson distribution, we develop sample size calculation procedures for testing equality based on an exact test procedure and an asymptotic test procedure under an AB/BA crossover design. We employ Monte Carlo simulation to demonstrate the use of these sample size formulae and evaluate the accuracy of sample size calculation formula derived from the asymptotic test procedure with respect to power in a variety of situations. We note that when both the relative treatment effect of interest and the underlying intraclass correlation between frequencies within patients are large, the sample size calculation based on the asymptotic test procedure can lose accuracy. In this case, the sample size calculation procedure based on the exact test is recommended. On the other hand, if the relative treatment effect of interest is small, the minimum required number of patients per group will be large, and the asymptotic test procedure will be valid for use. In this case, we may consider use of the sample size calculation formula derived from the asymptotic test procedure to reduce the number of patients needed for the exact test procedure. We include an example regarding a double‐blind randomized crossover trial comparing salmeterol with a placebo in exacerbations of asthma to illustrate the practical use of these sample size formulae. Copyright © 2013 John Wiley & Sons, Ltd.