Designing stratified sampling in economic and business surveys

In most economic and business surveys, the target variables (e.g. turnover of enterprises, income of households, etc.) commonly resemble skewed distributions with many small and few large units. In such surveys, if a stratified sampling technique is used as a method of sampling and estimation, the convenient way of stratification such as the use of demographical variables (e.g. gender, socioeconomic class, geographical region, religion, ethnicity, etc.) or other natural criteria, which is widely practiced in economic surveys, may fail to form homogeneous strata and is not much useful in order to increase the precision of the estimates of variables of interest. In this paper, a stratified sampling design for economic surveys based on auxiliary information has been developed, which can be used for constructing optimum stratification and determining optimum sample allocation to maximize the precision in estimate.     

Dynamic Monetary Equilibrium in a Random Matching Economy

This article concerns an infinite horizon economy where trade must occur pairwise, using a double auction mechanism, and where fiat money overcomes lack of double coincidence of wants. Traders are anonymous and lack market power. Goods are divisible and perishable, and are consumed at every date. Preferences are defined by utility‐stream overtaking. Money is divisible and not subject to inventory constraints. The evolution of individual and economywide money holdings distributions is characterized. There is a welfare‐ordered continuum of single price equilibria, reflecting indeterminacy of the price level rather than of relative prices.     

Block response-adaptive randomization in clinical trials with binary endpoints

In a clinical trial, response-adaptive randomization (RAR) uses accumulating data to weigh the randomization of remaining patients in favour of the better performing treatment. The aim is to reduce the number of failures within the trial. However, many well-known RAR designs, in particular, the randomized play-the-winner-rule (RPWR), have a highly myopic structure which has sometimes led to unfortunate randomization sequences when used in practice. This paper introduces random permuted blocks into two RAR designs, the RPWR and sequential maximum likelihood estimation, for trials with a binary endpoint. Allocation ratios within each block are restricted to be one of 1:1, 2:1 or 3:1, preventing unfortunate randomization sequences. Exact calculations are performed to determine error rates and expected number of failures across a range of trial scenarios. The results presented show that when compared with equal allocation, block RAR designs give similar reductions in the expected number of failures to their unmodified counterparts. The reductions are typically modest under the alternative hypothesis but become more impressive if the treatment effect exceeds the clinically relevant difference.     

Random Effects Estimators with many Instrumental Variables

In this paper we propose a new estimator for a model with one endogenous regressor and many instrumental variables. Our motivation comes from the recent literature on the poor properties of standard instrumental variables estimators when the instrumental variables are weakly correlated with the endogenous regressor. Our proposed estimator puts a random coefficients structure on the relation between the endogenous regressor and the instruments. The variance of the random coefficients is modelled as an unknown parameter. In addition to proposing a new estimator, our analysis yields new insights into the properties of the standard two‐stage least squares (TSLS) and limited‐information maximum likelihood (LIML) estimators in the case with many weak instruments. We show that in some interesting cases, TSLS and LIML can be approximated by maximizing the random effects likelihood subject to particular constraints. We show that statistics based on comparisons of the unconstrained estimates of these parameters to the implicit TSLS and LIML restrictions can be used to identify settings when standard large sample approximations to the distributions of TSLS and LIML are likely to perform poorly. We also show that with many weak instruments, LIML confidence intervals are likely to have under‐coverage, even though its finite sample distribution is approximately centered at the true value of the parameter. In an application with real data and simulations around this data set, the proposed estimator performs markedly better than TSLS and LIML, both in terms of coverage rate and in terms of risk.     

Marginal correlation from an extended random-effects model for repeated and overdispersed counts

Vangeneugden et al. [15 Vangeneugden, T., Molenberghs, G., Laenen, A., Geys, H., Beunckens, C. and Sotto, C. 2007. Marginal correlation in longitudinal binary data based on generalized linear mixed models, Tech. Rep., Hasselt University. submitted for publication [Google Scholar]] derived approximate correlation functions for longitudinal sequences of general data type, Gaussian and non-Gaussian, based on generalized linear mixed-effects models (GLMM). Their focus was on binary sequences, as well as on a combination of binary and Gaussian sequences. Here, we focus on the specific case of repeated count data, important in two respects. First, we employ the model proposed by Molenberghs et al. [13 Molenberghs, G., Verbeke, G. and Demétrio, C. G.B. 2007. An extended random-effects approach to modeling repeated, overdispersed count data. Lifetime Data Anal., 13: 513–531. [Crossref], [PubMed], [Web of Science ®] [Google Scholar]], which generalizes at the same time the Poisson-normal GLMM and the conventional overdispersion models, in particular the negative-binomial model. The model flexibly accommodates data hierarchies, intra-sequence correlation, and overdispersion. Second, means, variances, and joint probabilities can be expressed in closed form, allowing for exact intra-sequence correlation expressions. Next to the general situation, some important special cases such as exchangeable clustered outcomes are considered, producing insightful expressions. The closed-form expressions are contrasted with the generic approximate expressions of Vangeneugden et al. [15 Vangeneugden, T., Molenberghs, G., Laenen, A., Geys, H., Beunckens, C. and Sotto, C. 2007. Marginal correlation in longitudinal binary data based on generalized linear mixed models, Tech. Rep., Hasselt University. submitted for publication [Google Scholar]]. Data from an epileptic-seizures trial are analyzed and correlation functions derived. It is shown that the proposed extension strongly outperforms the classical GLMM.     

Nonparametric-likelihood inference based on cost-effectively-sampled-data

Costs associated with the evaluation of biomarkers can restrict the number of relevant biological samples to be measured. This common problem has been dealt with extensively in the epidemiologic and biostatistical literature that proposes to apply different cost-efficient procedures, including pooling and random sampling strategies. The pooling design has been widely addressed as a very efficient sampling method under certain parametric assumptions regarding data distribution. When cost is not a main factor in the evaluation of biomarkers but measurement is subject to a limit of detection, a common instrument limitation on the measurement process, the pooling design can partially overcome this instrumental limitation. In certain situations, the pooling design can provide data that is less informative than a simple random sample; however this is not always the case. Pooled-data-based nonparametric inferences have not been well addressed in the literature. In this article, a distribution-free method based on the empirical likelihood technique is proposed to substitute the traditional parametric-likelihood approach, providing the true coverage, confidence interval estimation and powerful tests based on data obtained after the cost-efficient designs. We also consider several nonparametric tests to compare with the proposed procedure. We examine the proposed methodology via a broad Monte Carlo study and a real data example.     

On strict positive definiteness of product and product-sum covariance models

Although positive definiteness is a sufficient condition for a function to be a covariance, the stronger strict positive definiteness is important for many applications, especially in spatial statistics, since it ensures that the kriging equations have a unique solution. In particular, spatial-temporal prediction has received a lot of attention, hence strictly positive definite spatial-temporal covariance models (or equivalently strictly conditionally negative definite variogram models) are needed.In this paper the necessary and sufficient condition for the product and the product-sum space-time covariance models to be strictly positive definite (or the variogram function to be strictly conditionally negative definite) is given. In addition it is shown that an example appeared in the recent literature which purports to show that product-sum covariance functions may be only semi-definite is itself invalid. Strict positive definiteness of the sum of products model is also discussed.     

An approximation to cluster size distribution of two Gaussian random fields conjunction with application to FMRI data

In brain mapping, the regions of the brain that are ‘activated’ by a task or external stimulus are detected by thresholding an image of test statistics. Often the experiment is repeated on several different subjects or for several different stimuli on the same subject, and the researcher is interested in the common points in the brain where ‘activation’ occurs in all test statistic images. The conjunction is thus defined as those points in the brain that show ‘activation’ in all images. We are interested in which parts of the conjunction are noise, and which show true activation in all test statistic images. We would expect truly activated regions to be larger than usual, so our test statistic is based on the volume of clusters (connected components) of the conjunction. Our main result is an approximate P-value for this in the case of the conjunction of two Gaussian test statistic images. The results are applied to a functional magnetic resonance experiment in pain perception.