An approximate entropy test for randomness

We develop an entropy-based test for randomness of binary time series of finite length. The test uses the frequencies of contiguous blocks of different lengths. A simple condition ib the block lengths and the length of the time series enables one to estimate the entropy rate for the data, and this information is used to develop a statistic to test the hypothesis of randomness. This static measures the deviation of the estimated entropy of the observed data from the theoretical maximum under the randomness hypothesis. This test offers a real alternative to the conventional runs test. Critical percentage points, based on simulations, are provided for testing the hypothesis of randomness. Power calculations using dependent data show that the proposed test has higher power against the runs test for short series, and it is similar to the runs test for long series. The test is applied to two published data sets that wree investigated by others with respect to their randomness.     

A Lower Bound to the Measure of Optimality for Main Effect Plans in the Symmetric Factorial Experiments

A design d is called D-optimal if it maximizes det(M _d ), and is called MS-optimal if it maximizes tr(M _d ) and minimizes tr[(M _d )²] among those which maximize tr(M _d ), where M _d stands for the information matrix produced from d under a given model. In this article, we establish a lower bound for tr[(M _d )²] with respect to a main effects model, where d is an s-level symmetric orthogonal array of strength at least one. Non isomorphic two level MS-optimal orthogonal arrays of strength one with N = 10, 14, and 18 runs, non isomorphic three level MS-optimal orthogonal arrays of strength one with N = 6, 12, and 15 runs and non isomorphic four level MS-optimal orthogonal arrays of strength one with N = 12 runs are also presented.     

A lower bound to the measure of optimality for main effect plans in the general asymmetric factorial experiments

A design d is called D-optimal if it maximizes det(M _d ) and is called MS-optimal if it maximizes tr(M _d ) and minimizes tr[(M _d )²] among those which maximize tr(M _d ), where M _d stands for the information matrix produced from d under a given model. In this paper, we establish a lower bound for tr[(M _d )²] with respect to a main effects model, where d is an s ₁×s ₂×···×s _m levels asymmetric orthogonal array of strength at least 1. Nonisomorphic asymmetrical MS-optimal orthogonal arrays of strength 1 with N=6, 8 and 12 runs are also presented.     

Patterns of NBA team performance from 1950 to 1998

This paper examines team performance in the NBA over the last five decades. It was motivated by two previous observational studies, one of which studied the winning percentages of professional baseball teams over time, while the other examined individual player performance in the NBA. These studies considered professional sports as evolving systems, a view proposed by evolutionary biologist Stephen Jay Gould, who wrote extensively on the disappearance of .400 hitters in baseball. Gould argued that the disappearance is actually a sign of improvement in the quality of play, reflected in the reduction of variability in hitting performance. The previous studies reached similar conclusions in terms of winning percentages of baseball teams, and performance of individual players in basketball. This paper uses multivariate measures of team performance in the NBA to see if similar characteristics of evolution can be observed. The conclusion does not appear to be clearly affirmative, as in previous studies, and possible reasons for this are discussed.     

Some new lower bounds to various discrepancies on combined designs

The foldover is a useful technique in construction of two-level factorial designs. A foldover design is the follow-up experiment generated by reversing the sign(s) of one or more factors in the initial design. The full design obtained by joining the runs in the foldover design to those of the initial design is called the combined design. In this article, some new lower bounds of various discrepancies of combined designs, such as the centered, symmetric, and wrap-around L₂-discrepancies, are obtained, which can be used as a better benchmark for searching optimal foldover plans. Our results provide a theoretical justification for optimal foldover plans in terms of uniformity criterion.     

On stratified bivariate ranked set sampling with optimal allocation for naïve and ratio estimators

The purpose of the current work is to introduce stratified bivariate ranked set sampling (SBVRSS) and investigate its performance for estimating the population mean using both naïve and ratio methods. The properties of the proposed estimator are derived along with the optimal allocation with respect to stratification. We conduct a simulation study to demonstrate the relative efficiency of SBVRSS as compared to stratified bivariate simple random sampling (SBVSRS) for ratio estimation. Data that consist of weights and bilirubin levels in the blood of 120 babies are used to illustrate the procedure on a real data set. Based on our simulation, SBVRSS for ratio estimation is more efficient than using SBVSRS in all cases.     

Inequalities in the public sphere: emergence of community television in India

Economic restructuring in the 1980s opened the doors to the previously state-dominated television sector in developing countries. In India, unexpectedly, the resulting competitive setting produced multiple channels targeting various local ethnicities from below along with national-level expansion involving transnational corporations from above in a process now known as localization. While the plurality of channels translates into growth of the public sphere, this paper examines the reasons behind the uneven growth of community media, which cannot be explained by the community's size or economic resources. Some community channels extend their reach into the national arena while others lag in media development implying unequal political participation in the communicative system. What are the institutional reasons behind such variations in a multiethnic setting? The paper also examines whether the development of ethnic media reflects the redistribution of power taking place in the political arena or is it an independent development with implications of its own.     

A semiparametric pseudo-score method for analysis of two-phase studies with continuous phase-I covariates

Two-phase study designs can reduce cost and other practical burdens associated with large scale epidemiologic studies by limiting ascertainment of expensive covariates to a smaller but informative sub-sample (phase-II) of the main study (phase-I). During the analysis of such studies, however, subjects who are selected at phase-I but not at phase-II, remain informative as they may have partial covariate information. A variety of semi-parametric methods now exist for incorporating such data from phase-I subjects when the covariate information can be summarized into a finite number of strata. In this article, we consider extending the pseudo-score approach proposed by Chatterjee et al. (J Am Stat Assoc 98:158–168, 2003) using a kernel smoothing approach to incorporate information on continuous phase-I covariates. Practical issues and algorithms for implementing the methods using existing software are discussed. A sandwich-type variance estimator based on the influence function representation of the pseudo-score function is proposed. Finite sample performance of the methods are studies using simulated data. Advantage of the proposed smoothing approach over alternative methods that use discretized phase-I covariate information is illustrated using two-phase data simulated within the National Wilms Tumor Study (NWTS).     

Trade and Wage Inequality in Developing Countries

In this article we provide a theoretical analysis of the possible impact of trade and fragmentation on the skilled–unskilled wage gap in a small developing economy. In particular, we illustrate the possibility of a decline in the relative wage of the unskilled labor following an improvement in the terms of trade. (JEL F1 , F11 , F12 )     

Exposure Assessment for Pesticide Intake from Multiple Food Products: A Bayesian Latent‐Variable Approach

Pesticide risk assessment for food products involves combining information from consumption and concentration data sets to estimate a distribution for the pesticide intake in a human population. Using this distribution one can obtain probabilities of individuals exceeding specified levels of pesticide intake. In this article, we present a probabilistic, Bayesian approach to modeling the daily consumptions of the pesticide Iprodione though multiple food products. Modeling data on food consumption and pesticide concentration poses a variety of problems, such as the large proportions of consumptions and concentrations that are recorded as zero, and correlation between the consumptions of different foods. We consider daily food consumption data from the Netherlands National Food Consumption Survey and concentration data collected by the Netherlands Ministry of Agriculture. We develop a multivariate latent‐Gaussian model for the consumption data that allows for correlated intakes between products. For the concentration data, we propose a univariate latent‐t model. We then combine predicted consumptions and concentrations from these models to obtain a distribution for individual daily Iprodione exposure. The latent‐variable models allow for both skewness and large numbers of zeros in the consumption and concentration data. The use of a probabilistic approach is intended to yield more robust estimates of high percentiles of the exposure distribution than an empirical approach. Bayesian inference is used to facilitate the treatment of data with a complex structure.