Changbao Wu

A catalogue of two-level and three-level fractional factorial designs with small runs

Summary Fractional factorial (FF) designs with minimum aberration are often regarded as the best designs and are commonly used in practice. There are, however, situations in which other designs can meet practical needs better. A catalogue of designs would make it easy to search for best designs according to various criteria. By exploring the algebraic structure of the FF designs, we propose an algorithm for constructing complete sets of FF designs. A collection of FF designs with 16, 27, 32 and 64 runs is given.

A Model-Calibration Approach to Using Complete Auxiliary Information From Survey Data

Suppose that the finite population consists of N identifiable units. Associated with the ith unit are the study variable, yi, and a vector of auxiliary variables, xi. The values x1, x2,…, xN are known for the entire population (i.e., complete) but yi is known only if the ith unit is selected in the sample. One of the fundamental questions is how to effectively use the complete auxiliary information at the estimation stage. In this article, a unified model-assisted framework has been attempted using a proposed model-calibration technique. The proposed model-calibration estimators can handle any linear or nonlinear working models and reduce to the conventional calibration estimators of Deville and Särndal and/or the generalized regression estimators in the linear model case. The pseudoempirical maximum likelihood estimator of Chen and Sitter, when used in this setting, gives an estimator that is asymptotically equivalent to the model-calibration estimator but with positive weights. Some existing estimators using auxiliary information are reexamined under this framework. The estimation of the finite population distribution function, using complete auxiliary information, is also considered, and estimators based on a general model are presented. Results of a limited simulation study on the performance of the proposed estimators are reported.

Bootstrap and other methods to measure errors in survey estimates

Variance estimation techniques for nonlinear statistics, such as ratios and regression and correlation coefficients, and functionals, such as quantiles, are reviewed in the context of sampling from stratified populations. In particular, resampling methods such as the bootstrap, the jackknife, and balanced repeated replication are compared with the traditional linearization method for nonlinear statistics and a method based on Woodruffs confidence intervals for the quantiles. Results of empirical studies are presented on the bias and stability of these variance estimators and on confidence‐interval coverage probabilities and lengths. Copyright

A nonparametric approach to the truncated regression problem

Abstract A description is given of a new method of estimating the regression parameters in the linear regression model from data where the dependent variable is subject to truncation. The residual distribution is allowed to be unspecified. The method is iterative and involves estimation of the residual distribution under the truncated sampling scheme. The technique can be interpreted as an iterative bias adjustment of the observations in order to correct the regression relationship in the sampled population to match that of the model. A simulation study compares the performance of various estimators, including one suggested by Bhattacharya, Chernoff, and Yang (1983). This truncation regression problem arises in many contexts of scientific and social research. In economics Tobin (1958) analyzed household expenditure on durable goods using a regression model that took account of the fact that the expenditure is always nonnegative. A more general situation was studied by Hausman and Wise (1976, 1977) in conn...

Methods of the International Tobacco Control (ITC) China Survey

This paper describes the design features, data collection methods and analytical strategies of the ITC China Survey, a prospective cohort study of 800 adult smokers and 200 adult non-smokers in each of six cities in China . In addition to features and methods which are common to ITC surveys in other countries, the ITC China Survey possesses unique features in frame construction, a large first phase data enumeration and sampling selection; and it uses special techniques and measures in training, field work organisation and quality control. It also faces technical challenges in sample selection and weight calculation when some selected upper level clusters need to be replaced by new ones owing to massive relocation exercises within the cities.

Combining information from multiple surveys through the empirical likelihood method

It is often desirable to combine information collected in compatible multiple surveys in order to improve estimation and meet consistency requirements. Zieschang (1990) and Renssen & Nieuwenbroek (1997) suggested to this end the use of the generalized regression estimator with enlarged number of auxiliary variables. Unfortunately, adjusted weights associated with their approach can be negative. The author uses the notion of pseudo empirical likelihood to construct new estimators that are consistent, efficient and possess other attractive properties. The proposed approach is asymptotically equivalent to the earlier one, but it has clear maximum likelihood interpretations and its adjusted weights are always positive. The author also provides efficient algorithms for computing his estimators. n n n nIl est souvent souhaitable de regrouper linformation de diverses enquetes compatibles de facLon a ameliorer lestimation et a assurer une certaine coherence. Zieschang (1990) et Renssen & Nieuwenbroek (1997) ont suggere a cette fin lemploi dun estimateur de regression generalise exploitant un nombre accru de variables auxiliaires. Helas, les poids ajustes lies a leur approche peuvent etre negatifs. Lauteur tire de lapproche par la vraisemblance pseudo empirique de nouveaux estimateurs qui sont a la fois coherents, efficaces et possedent dautres bonnes proprietes. Lapproche proposee est asymptotiquement equivalente a la precedente mais a une interpretation claire en termes de vraisemblance maximale et ses poids ajustes sont toujours positifs. Lauteur fournit aussi des algorithmes efficaces pour le calcul de ses estimateurs.

A note on Woodruff confidence intervals for quantiles

Woodruff (1952) proposed a simple confidence interval for quantiles in complex surveys based upon inverting the usual confidence intervals for the distribution function. In the moderate to extreme tail regions of the distribution function the usual confidence interval performs poorly for moderate sample size. In this paper we demonstrate that despite this fact, the Woodruff intervals based upon inverting these badly behaved intervals perform very well. We go on to explain this rather surprising fact.

Efficient Estimation of Quadratic Finite Population Functions in the Presence of Auxiliary Information

By viewing quadratic and other second-order finite population functions as totals or means over a derived synthetic finite population, we show that the recently proposed model calibration and pseudoempirical likelihood methods for effective use of auxiliary information from survey data can be readily extended to obtain efficient estimators of quadratic and other second-order finite population functions. In particular, estimation of a finite population variance, covariance, or variance of a linear estimator can be greatly improved when auxiliary information is available. The proposed methods are model assisted in that the resulting estimators are asymptotically design unbiased irrespective of the correctness of a working model but very efficient if the working model is nearly correct. They have a number of attractive features, which include applicability to a general sampling design, incorporation of information on possibly multivariate auxiliary variables, and the ability to entertain linear or nonlinear working models, and they result in nonnegative estimates for certain strictly positive quantities such as variances. Several existing estimators are shown to be special cases of the proposed general methodology under a linear working model.

Regional Differences in Awareness of Tobacco Advertising and Promotion in China: Findings from the ITC China Survey

Objective To examine whether levels of, and factors related to, awareness of tobacco advertising and promotion differ across six cities in China. Methods Data from wave 1 of the International Tobacco Control (ITC) China Survey (April to August 2006) were analysed. The ITC China Survey employed a multistage sampling design in Beijing, Shenyang, Shanghai, Changsha, Guangzhou and Yinchuan. Face-to-face interviews were conducted with a total of 4763 smokers and 1259 non-smokers. Multivariate logistic regression models were used to identify factors associated with awareness of tobacco advertising and promotion. Results The overall levels of noticing advertisements varied considerably by city. Cities reporting lower levels of advertising tended to report higher levels of point of sale activity. Noticing tobacco industry promotions was associated with more positive attitudes to tobacco companies. Conclusion The awareness of tobacco advertising and promotional activities was not homogeneous across the six Chinese cities, suggesting variations in the tobacco industrys activities and the diversity of implementing a central set of laws to restrict tobacco promotion. This study clearly demonstrates the need to work with the implementation agencies if national laws are to be properly enforced.

Pseudo–Empirical Likelihood Inference for Multiple Frame Surveys

This article presents a pseudo–empirical likelihood approach to inference for multiple-frame surveys. We establish a unified framework for point and interval estimation of finite population parameters, and show that inferences on the parameters of interest making effective use of different types of auxiliary population information can be conveniently carried out through the constrained maximization of the pseudo–empirical likelihood function. Confidence intervals are constructed using either the asymptotic χ2 distribution of an adjusted pseudo–empirical likelihood ratio statistic or a bootstrap calibration method. Simulation results based on Statistics Canada’s Family Expenditure Survey data show that the proposed methods perform well in finite samples for both point and interval estimation. In particular, a multiplicity-based pseudo–empirical likelihood method is proposed. This method is easily used for multiple-frame surveys with more than two frames and does not require complete frame membership information. The proposed pseudo–empirical likelihood ratio confidence intervals have a clear advantage over the conventional normal approximation–based intervals in estimating population proportions of rare items, a scenario that often motivates the use of multiple-frame surveys. All related computational problems can be handled using existing algorithms for pseudo–empirical likelihood methods with single-frame surveys.