A Design of Attributes Double Sampling Plans for Three-class Products

In this article, a new attributes double sampling plan for three-class products (ADSPTP) is presented, and the corresponding operating characteristic function is constructed based on the given procedure of performing ADSPTP. Average sample numbers (ASN) for complete inspection and curtailed inspection of the second sample are derived and the extreme point is discussed on the three-dimensional ASN surface. In addition, the differences arising from different parameters are studied. Sampling plans are designed by a nonlinear optimization model. Finally, numerical examples and discussions are given to illustrate the obtained results, and tables of the designed plans under various conditions are provided.     

A comparative study of confidence intervals for negative binomial proportion

In this paper, we investigate four existing and three new confidence interval estimators for the negative binomial proportion (i.e., proportion under inverse/negative binomial sampling). An extensive and systematic comparative study among these confidence interval estimators through Monte Carlo simulations is presented. The performance of these confidence intervals are evaluated in terms of their coverage probabilities and expected interval widths. Our simulation studies suggest that the confidence interval estimator based on saddlepoint approximation is more appealing for large coverage levels (e.g., nominal level≤1% ) whereas the score confidence interval estimator is more desirable for those commonly used coverage levels (e.g., nominal level>1% ). We illustrate these confidence interval construction methods with a real data set from a maternal congenital heart disease study.     

Repetitive variable acceptance sampling plan for one-sided specification

In this paper, a variable repetitive group sampling plans based on one-sided process capability indices is proposed to deal with lot sentencing for one-sided specifications. The parameters of the proposed plans are tabulated for some combinations of acceptance quality levels with commonly used producer's risk and consumer's risk. The efficiency of the proposed plan is compared with the Pearn and Wu [Critical acceptance values and sample sizes of a variables sampling plan for very low fraction of defectives. Omega – Int J Manag Sci. 2006;34(1):90–101] plan in terms of sample size and the power curve. One example is given to illustrate the proposed methodology.     

Double shrinkage estimators for large sparse covariance matrices

Covariance matrices play an important role in many multivariate techniques and hence a good covariance estimation is crucial in this kind of analysis. In many applications a sparse covariance matrix is expected due to the nature of the data or for simple interpretation. Hard thresholding, soft thresholding, and generalized thresholding were therefore developed to this end. However, these estimators do not always yield well-conditioned covariance estimates. To have sparse and well-conditioned estimates, we propose doubly shrinkage estimators: shrinking small covariances towards zero and then shrinking covariance matrix towards a diagonal matrix. Additionally, a richness index is defined to evaluate how rich a covariance matrix is. According to our simulations, the richness index serves as a good indicator to choose relevant covariance estimator.     

Adaptive designs for single‐arm phase II trials in oncology

Clinical phase II trials in oncology are conducted to determine whether the activity of a new anticancer treatment is promising enough to merit further investigation. Two‐stage designs are commonly used for this situation to allow for early termination. Designs proposed in the literature so far have the common drawback that the sample sizes for the two stages have to be specified in the protocol and have to be adhered to strictly during the course of the trial. As a consequence, designs that allow a higher extent of flexibility are desirable. In this article, we propose a new adaptive method that allows an arbitrary modification of the sample size of the second stage using the results of the interim analysis or external information while controlling the type I error rate. If the sample size is not changed during the trial, the proposed design shows very similar characteristics to the optimal two‐stage design proposed by Chang et al. (Biometrics 1987; 43:865–874). However, the new design allows the use of mid‐course information for the planning of the second stage, thus meeting practical requirements when performing clinical phase II trials in oncology. Copyright © 2012 John Wiley & Sons, Ltd.     

Truncation invariant copulas and a testing procedure

ABSTRACT

The class of bivariate copulas that are invariant under truncation with respect to one variable is considered. A simulation algorithm for the members of the class and a novel construction method are presented. Moreover, inspired by a stochastic interpretation of the members of such a class, a procedure is suggested to check whether the dependence structure of a given data set is truncation invariant. The overall performance of the procedure has been illustrated on both simulated and real data.     

Assessing respondent-driven sampling: A simulation study across different networks

The purpose was to assess RDS estimators in populations simulated with diverse connectivity characteristics, incorporating the putative influence of misreported degrees and transmission processes. Four populations were simulated using different random graph models. Each population was “infected” using four different transmission processes. From each combination of population x transmission, one thousand samples were obtained using a RDS-like sampling strategy. Three estimators were used to predict the population-level prevalence of the “infection”. Several types of misreported degrees were simulated. Also, samples were generated using the standard random sampling method and the respective prevalence estimates, using the classical frequentist estimator. Estimation biases in relation to population parameters were assessed, as well as the variance. Variability was associated with the connectivity characteristics of each simulated population. Clustered populations yield greater variability and no RDS-based strategy could address the estimation biases. Misreporting degrees had modest effects, especially when RDS estimators were used. The best results for RDS-based samples were observed when the “infection” was randomly attributed, without any relation with the underlying network structure.     

A non-iterative posterior sampling algorithm for linear quantile regression model

In this article, a non-iterative posterior sampling algorithm for linear quantile regression model based on the asymmetric Laplace distribution is proposed. The algorithm combines the inverse Bayes formulae, sampling/importance resampling, and the expectation maximization algorithm to obtain independently and identically distributed samples approximately from the observed posterior distribution, which eliminates the convergence problems in the iterative Gibbs sampling and overcomes the difficulty in evaluating the standard deviance in the EM algorithm. The numeric results in simulations and application to the classical Engel data show that the non-iterative sampling algorithm is more effective than the Gibbs sampling and EM algorithm.     

Spectral Estimation of Covolatility from Noisy Observations Using Local Weights

We propose localized spectral estimators for the quadratic covariation and the spot covolatility of diffusion processes, which are observed discretely with additive observation noise. The appropriate estimation for time‐varying volatilities is based on an asymptotic equivalence of the underlying statistical model to a white‐noise model with correlation and volatility processes being constant over small time intervals. The asymptotic equivalence of the continuous‐time and discrete‐time experiments is proved by a construction with linear interpolation in one direction and local means for the other. The new estimator outperforms earlier non‐parametric methods in the literature for the considered model. We investigate its finite sample size characteristics in simulations and draw a comparison between various proposed methods.     

Sampling schemes for price index construction: a performance comparison across the classification of individual consumption by purpose food groups

Five sampling schemes (SS) for price index construction – one cut-off sampling technique and four probability-proportional-to-size (pps) methods – are evaluated by comparing their performance on a homescan market research data set across 21 months for each of the 13 classification of individual consumption by purpose (COICOP) food groups. Classifications are derived for each of the food groups and the population index value is used as a reference to derive performance error measures, such as root mean squared error, bias and standard deviation for each food type. Repeated samples are taken for each of the pps schemes and the resulting performance error measures analysed using regression of three of the pps schemes to assess the overall effect of SS and COICOP group whilst controlling for sample size, month and population index value. Cut-off sampling appears to perform less well than pps methods and multistage pps seems to have no advantage over its single-stage counterpart. The jackknife resampling technique is also explored as a means of estimating the standard error of the index and compared with the actual results from repeated sampling.