Some general comparative points on Chao’s and Zelterman’s estimators of population size

Two simple and frequently used capture–recapture estimates of the population size are compared: Chao's lower-bound estimate and Zelterman's estimate allowing for contaminated distributions. In the Poisson case it is shown that if there are only counts of ones and twos, the estimator of Zelterman is always bounded above by Chao's estimator. If counts larger than two exist, the estimator of Zelterman is becoming larger than that of Chao's, if only the ratio of the frequencies of counts of twos and ones is small enough. A similar analysis is provided for the binomial case. For a two-component mixture of Poisson distributions the asymptotic bias of both estimators is derived and it is shown that the Zelterman estimator can experience large overestimation bias. A modified Zelterman estimator is suggested and also the bias-corrected version of Chao's estimator is considered. All four estimators are compared in a simulation study.

Some general comparative points on Chao's and Zelterman's estimators of the population size

Two simple and frequently used capture–recapture estimates of the population size are compared: Chao's lower-bound estimate and Zelterman's estimate allowing for contaminated distributions. In the Poisson case it is shown that if there are only counts of ones and twos, the estimator of Zelterman is always bounded above by Chao's estimator. If counts larger than two exist, the estimator of Zelterman is becoming larger than that of Chao's, if only the ratio of the frequencies of counts of twos and ones is small enough. A similar analysis is provided for the binomial case. For a two-component mixture of Poisson distributions the asymptotic bias of both estimators is derived and it is shown that the Zelterman estimator can experience large overestimation bias. A modified Zelterman estimator is suggested and also the bias-corrected version of Chao's estimator is considered. All four estimators are compared in a simulation study.

Point estimates and confidence regions for sequential trials involving selection

A number of authors have proposed clinical trial designs involving the comparison of several experimental treatments with a control treatment in two or more stages. At the end of the first stage, the most promising experimental treatment is selected, and all other experimental treatments are dropped from the trial. Provided it is good enough, the selected experimental treatment is then compared with the control treatment in one or more subsequent stages. The analysis of data from such a trial is problematic because of the treatment selection and the possibility of stopping at interim analyses. These aspects lead to bias in the maximum-likelihood estimate of the advantage of the selected experimental treatment over the control and to inaccurate coverage for the associated confidence interval. In this paper, we evaluate the bias of the maximum-likelihood estimate and propose a bias-adjusted estimate. We also propose an approach to the construction of a confidence region for the vector of advantages of the experimental treatments over the control based on an ordering of the sample space. These regions are shown to have accurate coverage, although they are also shown to be necessarily unbounded. Confidence intervals for the advantage of the selected treatment are obtained from the confidence regions and are shown to have more accurate coverage than the standard confidence interval based upon the maximum-likelihood estimate and its asymptotic standard error.

Islamic mutual funds' financial performance and international investment style: evidence from 20 countries

We pursue the first large-scale investigation of a strongly growing mutual fund type: Islamic funds. Based on an unexplored, survivorship bias-adjusted data set, we analyse the financial performance and investment style of 265 Islamic equity funds from 20 countries. As Islamic funds often have diverse investment regions, we develop a (conditional) three-level Carhart model to simultaneously control for exposure to different national, regional and global equity markets and investment styles. Consistent with recent evidence for conventional funds, we find Islamic funds to display superior learning in more developed Islamic financial markets. While Islamic funds from these markets are competitive to international equity benchmarks, funds from especially Western nations with less Islamic assets tend to significantly underperform. Islamic funds’ investment style is somewhat tilted towards growth stocks. Funds from predominantly Muslim economies also show a clear small cap preference. These results are consistent over time and robust to time varying market exposures and capital market restrictions.

Dissecting the illegal ivory trade: an analysis of ivory seizures data

Reliable evidence of trends in the illegal ivory trade is important for informing decision making for elephants but it is difficult to obtain due to the covert nature of the trade. The Elephant Trade Information System, a global database of reported seizures of illegal ivory, holds the only extensive information on illicit trade available. However inherent biases in seizure data make it difficult to infer trends; countries differ in their ability to make and report seizures and these differences cannot be directly measured. We developed a new modelling framework to provide quantitative evidence on trends in the illegal ivory trade from seizures data. The framework used Bayesian hierarchical latent variable models to reduce bias in seizures data by identifying proxy variables that describe the variability in seizure and reporting rates between countries and over time. Models produced bias-adjusted smoothed estimates of relative trends in illegal ivory activity for raw and worked ivory in three weight classes. Activity is represented by two indicators describing the number of illegal ivory transactions--Transactions Index--and the total weight of illegal ivory transactions--Weights Index--at global, regional or national levels. Globally, activity was found to be rapidly increasing and at its highest level for 16 years, more than doubling from 2007 to 2011 and tripling from 1998 to 2011. Over 70% of the Transactions Index is from shipments of worked ivory weighing less than 10 kg and the rapid increase since 2007 is mainly due to increased consumption in China. Over 70% of the Weights Index is from shipments of raw ivory weighing at least 100 kg mainly moving from Central and East Africa to Southeast and East Asia. The results tie together recent findings on trends in poaching rates, declining populations and consumption and provide detailed evidence to inform international decision making on elephants.

Extension of spherical nonparametric estimators to nonisotropic kernels: An oceanographic application

In a recently published paper. spherical nonparametric estimators were applied to feature-track ensembles to determine a range of statistics for the atmospheric features considered. This approach obviates the types of bias normally introduced with traditional estimators. New spherical isotropic kernels with local support were introduced. Ln this paper the extension to spherical nonisotropic kernels with local support is introduced, together with a means of obtaining the shape and smoothing parameters in an objective way. The usefulness of spherical nonparametric estimators based on nonisotropic kernels is demonstrated with an application to an oceanographic feature-track ensemble.

Estimators in capture–recapture studies with two sources

This paper investigates the applications of capture–recapture methods to human populations. Capture–recapture methods are commonly used in estimating the size of wildlife populations but can also be used in epidemiology and social sciences, for estimating prevalence of a particular disease or the size of the homeless population in a certain area. Here we focus on estimating the prevalence of infectious diseases. Several estimators of population size are considered: the Lincoln–Petersen estimator and its modified version, the Chapman estimator, Chao’s lower bound estimator, the Zelterman’s estimator, McKendrick’s moment estimator and the maximum likelihood estimator. In order to evaluate these estimators, they are applied to real, three-source, capture-recapture data. By conditioning on each of the sources of three source data, we have been able to compare the estimators with the true value that they are estimating. The Chapman and Chao estimators were compared in terms of their relative bias. A variance formula derived through conditioning is suggested for Chao’s estimator, and normal 95% confidence intervals are calculated for this and the Chapman estimator. We then compare the coverage of the respective confidence intervals. Furthermore, a simulation study is included to compare Chao’s and Chapman’s estimator. Results indicate that Chao’s estimator is less biased than Chapman’s estimator unless both sources are independent. Chao’s estimator has also the smaller mean squared error. Finally, the implications and limitations of the above methods are discussed, with suggestions for further development.

Revisiting proportion estimators

Proportion estimators are quite frequently used in many application areas. The conventional proportion estimator (number of events divided by sample size) encounters a number of problems when the data are sparse as will be demonstrated in various settings. The problem of estimating its variance when sample sizes become small is rarely addressed in a satisfying framework. Specifically, we have in mind applications like the weighted risk difference in multicenter trials or stratifying risk ratio estimators (to adjust for potential confounders) in epidemiological studies. It is suggested to estimate p using the parametric family (see PDF for character) and p(1 - p) using (see PDF for character), where (see PDF for character). We investigate the estimation problem of choosing c 0 from various perspectives including minimizing the average mean squared error of (see PDF for character), average bias and average mean squared error of (see PDF for character). The optimal value of c for minimizing the average mean squared error of (see PDF for character) is found to be independent of n and equals c = 1. The optimal value of c for minimizing the average mean squared error of (see PDF for character) is found to be dependent of n with limiting value c = 0.833. This might justifiy to use a near-optimal value of c = 1 in practice which also turns out to be beneficial when constructing confidence intervals of the form (see PDF for character).

Meta-analysis: a unifying meta-likelihood approach framing unobserved heterogeneity, study covariates, publication bias, and study quality

OBJECTIVES: This contribution provides a unifying concept for meta-analysis integrating the handling of unobserved heterogeneity, study covariates, publication bias and study quality. It is important to consider these issues simultaneously to avoid the occurrence of artifacts, and a method for doing so is suggested here. METHODS: The approach is based upon the meta-likelihood in combination with a general linear nonparametric mixed model, which lays the ground for all inferential conclusions suggested here. RESULTS: The concept is illustrated at hand of a meta-analysis investigating the relationship of hormone replacement therapy and breast cancer. The phenomenon of interest has been investigated in many studies for a considerable time and different results were reported. In 1992 a meta-analysis by Sillero-Arenas et al. concluded a small, but significant overall effect of 1.06 on the relative risk scale. Using the meta-likelihood approach it is demonstrated here that this meta-analysis is due to considerable unobserved heterogeneity. Furthermore, it is shown that new methods are available to model this heterogeneity successfully. It is argued further to include available study covariates to explain this heterogeneity in the meta-analysis at hand. CONCLUSIONS: The topic of HRT and breast cancer has again very recently become an issue of public debate, when results of a large trial investigating the health effects of hormone replacement therapy were published indicating an increased risk for breast cancer (risk ratio of 1.26). Using an adequate regression model in the previously published meta-analysis an adjusted estimate of effect of 1.14 can be given which is considerably higher than the one published in the meta-analysis of Sillero-Arenas et al. In summary, it is hoped that the method suggested here contributes further to a good meta-analytic practice in public health and clinical disciplines.

Estimators in capture-recapture studies with two sources

This paper investigates the applications of capture-recapture methods to human populations. Capture-recapture methods are commonly used in estimating the size of wildlife populations but can also be used in epidemiology and social sciences, for estimating prevalence of a particular disease or the size of the homeless population in a certain area. Here we focus on estimating the prevalence of infectious diseases. Several estimators of population size are considered: the Lincoln-Petersen estimator and its modified version, the Chapman estimator, Chao's lower bound estimator, the Zelterman's estimator, McKendrick's moment estimator and the maximum likelihood estimator. In order to evaluate these estimators, they are applied to real, three-source, capture-recapture data. By conditioning on each of the sources of three source data, we have been able to compare the estimators with the true value that they are estimating. The Chapman and Chao estimators were compared in terms of their relative bias. A variance formula derived through conditioning is suggested for Chao's estimator, and normal 95% confidence intervals are calculated for this and the Chapman estimator. We then compare the coverage of the respective confidence intervals. Furthermore, a simulation study is included to compare Chao's and Chapman's estimator. Results indicate that Chao's estimator is less biased than Chapman's estimator unless both sources are independent. Chao's estimator has also the smaller mean squared error. Finally, the implications and limitations of the above methods are discussed, with suggestions for further development.

Spherical nonparametric estimators applied to the UGAMP model integration for AMIP

The aim of this paper is essentially twofold: first, to describe the use of spherical nonparametric estimators for determining statistical diagnostic fields from ensembles of feature tracks on a global domain, and second, to report the application of these techniques to data derived from a modern general circulation model. New spherical kernel functions are introduced that are more efficiently computed than the traditional exponential kernels. The data-driven techniques of cross-validation to determine the amount elf smoothing objectively, and adaptive smoothing to vary the smoothing locally, are also considered. Also introduced are techniques for combining seasonal statistical distributions to produce longer-term statistical distributions. Although all calculations are performed globally, only the results for the Northern Hemisphere winter (December, January, February) and Southern Hemisphere winter (June, July, August) cyclonic activity are presented, discussed, and compared with previous studies. Overall, results for the two hemispheric winters are in good agreement with previous studies, both for model-based studies and observational studies.

Bias from farmer self-selection in genetically modified crop productivity estimates: Evidence from Indian data

In the continuing debate over the impact of genetically modified (GM) crops on farmers of developing countries, it is important to accurately measure magnitudes such as farm-level yield gains from GM crop adoption. Yet most farm-level studies in the literature do not control for farmer self-selection, a potentially important source of bias in such estimates. We use farm-level panel data from Indian cotton farmers to investigate the yield effect of GM insect-resistant cotton. We explicitly take into account the fact that the choice of crop variety is an endogenous variable which might lead to bias from self-selection. A production function is estimated using a fixed-effects model to control for selection bias. Our results show that efficient farmers adopt Bacillus thuringiensis (Bt) cotton at a higher rate than their less efficient peers. This suggests that cross-sectional estimates of the yield effect of Bt cotton, which do not control for self-selection effects, are likely to be biased upwards. However, after controlling for selection bias, we still find that there is a significant positive yield effect from adoption of Bt cotton that more than offsets the additional cost of Bt seed.