Statistical inference for the quintile share ratio

In recent years, the Quintile Share Ratio (or QSR) has become a very popular measure of inequality. In 2001, the European Council decided that income inequality in European Union member states should be described using two indicators: the Gini Index and the QSR. The QSR is generally defined as the ratio of the total income earned by the richest 20% of the population relative to that earned by the poorest 20%. Thus, it can be expressed using quantile shares, where a quantile share is the share of total income earned by all of the units up to a given quantile. The aim of this paper is to propose an improved methodology for the estimation and variance estimation of the QSR in a complex sampling design framework. Because the QSR is a non-linear function of interest, the estimation of its sampling variance requires advanced methodology. Moreover, a non-trivial obstacle in the estimation of quantile shares in finite populations is the non-unique definition of a quantile. Thus, two different conceptions of the quantile share are presented in the paper, leading us to two different estimators of the QSR. Regarding variance estimation, [Osier, 2006] and [Osier, 2009] proposed a variance estimator based on linearization techniques. However, his method involves Gaussian kernel smoothing of cumulative distribution functions. Our approach, also based on linearization, shows that no smoothing is needed. The construction of confidence intervals is discussed and a proposition is made to account for the skewness of the sampling distribution of the QSR. Finally, simulation studies are run to assess the relevance of our theoretical results.     

Optimized Sampling Strategies for Identifying Modes in Length-frequency Distributions

An approach to evaluate sampling strategies to detect modes in length-distributions is presented. Distributions based on various numbers of samples (S) and sample sizes (n) were simulated from the original cod and capelin data in Icelandic waters, incorporating within sample correlations. A peak was discerned if the difference between any simulated and original distribution did not exceed a pre-specified Δ, given a probability. This was achieved with numerous combinations of S and n, and the optimal choice will depend on the sampling costs. Variance-equivalence curves also illustrate the difference between demanding precision of mean lengths versus precision of length distributions.     

空间定位抽样技术:民意调查中的新方法

在我国进行的民意调查中,研究者们无论采取哪种具体抽样方法,均需要以居委会提供的户口登记信息为抽样基础。随着我国流动人口数量的不断增大,依靠户籍信息抽样容易导致抽样覆盖范围存在偏差。在此背景下,空间定位抽样技术应运而生,该方法作为一种崭新的调查技术,使被调查对象的人口特征更具有代表性,对较为敏感的民意研究具有开创性地意义。本文阐述了传统抽样技术的弊端,介绍了空间定位抽样技术的兴起过程,并对该技术的具体实施步骤及难点进行了解析,最后提出了该法的两大适用条件。     

Problems in sampling the Native American and Alaska Native populations

Selecting a scientific national sample of Native Americans and Alaska Natives is difficult for at least four reasons: (1) they are a small proportion of the total population, (2) they are not so segregated that geographic oversampling can reach most of the population, (3) criteria for deciding who is a member of the Native American and Alaska Native population are not well defined, and (4) they are so culturally diverse that subclass estimates may be of equal or greater importance than overall estimates. The goal of this paper is to identify key design choices a statistician must face when selecting a sample of these populations, and to discuss alternative strategies. I also provide commentary on sampling plans that have been used for previous surveys, and explain why these plans, while sufficient for the purposes of their particular surveys, do not provide general solutions. Of particular importance is a careful definition of the study population. For example, some studies would focus on the reservation population, others would focus on persons listed on tribal rolls, and still others on persons eligible for coverage by the Indian Health Service. The numbers of persons included in all of these groups is far short of the two million Native Americans and Alaska Natives counted in the 1990 Census. I conclude that there is no sampling strategy that is appropriate for all surveys, but also provide suggestions for certain survey situations.     

A Sequential Markov Chain Monte Carlo Approach to Set-up Adjustment of a Process over a Set of Lots

We consider the problem of adjusting a machine that manufactures parts in batches or lots and experiences random offsets or shifts whenever a set-up operation takes place between lots. The existing procedures for adjusting set-up errors in a production process over a set of lots are based on the assumption of known process parameters. In practice, these parameters are usually unknown, especially in short-run production. Due to this lack of knowledge, adjustment procedures such as Grubbs' (1954, 1983) rules and discrete integral controllers (also called EWMA controllers) aimed at adjusting for the initial offset in each single lot, are typically used. This paper presents an approach for adjusting the initial machine offset over a set of lots when the process parameters are unknown and are iteratively estimated using Markov Chain Monte Carlo (MCMC). As each observation becomes available, a Gibbs Sampler is run to estimate the parameters of a hierarchical normal means model given the observations up to that point in time. The current lot mean estimate is then used for adjustment. If used over a series of lots, the proposed method allows one eventually to start adjusting the offset before producing the first part in each lot. The method is illustrated with application to two examples reported in the literature. It is shown how the proposed MCMC adjusting procedure can outperform existing rules based on a quadratic off-target criterion.     

Knocking on doors: recruitment and enrichment in a qualitative interview‐based study

This paper describes the process of recruiting participants for a qualitative interview‐based study by leafleting and door knocking. It is argued that door knocking can enrich and thicken research that usually takes place ‘behind closed doors’, enabling researchers to engage their ethnographic imaginations by observing neighbourhood interactions, familiarising themselves with the places their participants inhabit and through the embodied, sensory experience of walking itself. By treating the recruitment process as data, it is suggested that the door knocking researcher can ensure his/her individual participants are understood as connected to the wider social, physical and sensory environment they inhabit. Door knocking is also seen as enabling researchers to find interest in an element of the research process often viewed as a somewhat irksome means to an end.     

Randomized response techniques: An application to the Botswana AIDS impact survey

The performance of the sampling strategy used in the Botswana Aids Impact Survey II (BAISII) has been studied in detail under a randomized response technique. We have shown that alternative strategies based on the Rao–Harley–Cochran (RHC) sampling scheme for the selection of first stage units perform much better than other strategies. In particular, the combination RHC for the selection of first stage units (fsu's) and systematic sampling for the selection of second stage units (ssu's) perform the best when the sample size is small where as the RHC and SRSWOR perform the best when the sample size is large. In view of the present findings it is recommended that the BAISII survey should be studied in more detail incorporating more indicators and increased sample sizes. This is because the BAISII survey design is extensively in use for large scales surveys in Southern African countries.     

Estimations of the parameter of a Dirichlet distribution using residual allocation model representations and sampling properties

Estimating the parameter of a Dirichlet distribution is an interesting question since this distribution arises in many situations of applied probability. Classical procedures are based on sample of Dirichlet distribution. In this paper we exhibit five different estimators from only one observation. They are based either on residual allocation model decompositions or on sampling properties of Dirichlet distributions. Two ways are investigated: the first one uses fragments’ size and the second one uses size-biased permutations of a partition. Numerical computations based on simulations are supplied. The estimators are finally used to estimate birth probabilities per month.     

Efficient Bayesian sampling plans for exponential distributions with random censoring

This paper considers Bayesian sampling plans for exponential distribution with random censoring. The efficient Bayesian sampling plan for a general loss function is derived. This sampling plan possesses the property that it may make decisions prior to the end of the life test experiment, and its decision function is the same as the Bayes decision function which makes decisions based on data collected at the end of the life test experiment. Compared with the optimal Bayesian sampling plan of Chen et al. (2004), the efficient Bayesian sampling plan has the smaller Bayes risk due to the less duration time of life test experiment. Computations of the efficient Bayes risks for the conjugate prior are given. Numerical comparisons between the proposed efficient Bayesian sampling plan and the optimal Bayesian sampling plan of Chen et al. (2004) under two special decision losses, including the quadratic decision loss, are provided. Numerical results also demonstrate that the performance of the proposed efficient sampling plan is superior to that of the optimal sampling plan by Chen et al. (2004).     

Examples of Differing Weighted and Unweighted Estimates from a Sample Survey

Unweighted estimators using data collected in a sample survey can be badly biased, whereas weighted estimators are approximately unbiased for population parameters. We present four examples using data from the 1988 National Maternal and Infant Health Survey to demonstrate that weighted and unweighted estimators can be quite different, and to show the underlying causes of such differences.