Weighted and two-stage least squares estimation of semiparametric truncated regression models

This paper provides a root-n consistent, asymptotically normal weighted least squares estimator of the coefficients in a truncated regression model. The distribution of the errors is unknown and permits general forms of unknown heteroskedasticity. Also provided is an instrumental variables based two-stage least squares estimator for this model, which can be used when some regressors are endogenous, mismeasured, or otherwise correlated with the errors. A simulation study indicates that the new estimators perform well in finite samples. Our limiting distribution theory includes a new asymptotic trimming result addressing the boundary bias in first-stage density estimation without knowledge of the support boundary. © 2007 Cambridge University Press.

Relative growth of the limbs and trunk in sifakas: heterochronic, ecological, and functional considerations.

Limb, trunk, and body weight measurements were obtained for growth series of Milne-Edwards's diademed sifaka, Propithecus diadema edwardsi, and the golden-crowned sifaka, Propithecus tattersalli. Similar measures were obtained also for primarily adults of two subspecies of the western sifaka: Propithecus verreauxi coquereli, Coquerel's sifaka, and Propithecus verreauxi verreauxi, Verreaux's sifaka. Ontogenetic series for the larger-bodied P. d. edwardsi and the smaller-bodied P. tattersalli were compared to evaluate whether species-level differences in body proportions result from the differential extension of common patterns of relative growth. In bivariate plots, both subspecies of P. verreauxi were included to examine whether these taxa also lie along a growth trajectory common to all sifakas. Analyses of the data indicate that postcranial proportions for sifakas are ontogenetically scaled, much as demonstrated previously with cranial dimensions for all three species (Ravosa, 1992). As such, P. d. edwardsi apparently develops larger overall size primarily by growing at a faster rate, but not for a longer duration of time, than P. tattersalli and P. verreauxi; this is similar to results based on cranial data. A consideration of Malagasy lemur ecology suggests that regional differences in forage quality and resource availability have strongly influenced the evolutionary development of body-size variation in sifakas. On one hand, the rainforest environment of P. d. edwardsi imposes greater selective pressures for larger body size than the dry-forest environment of P. tattersalli and P. v. coquereli, or the semi-arid climate of P. v. verreauxi. On the other hand, as progressively smaller-bodied adult sifakas are located in the east, west, and northwest, this apparently supports suggestions that adult body size is set by dry-season constraints on food quality and distribution (i.e., smaller taxa are located in more seasonal habitats such as the west and northeast). Moreover, the fact that body-size differentiation occurs primarily via differences in growth rate is also due apparently to differences in resource seasonality (and juvenile mortality risk in turn) between the eastern rainforest and the more temperate northeast and west. Most scaling coefficients for both arm and leg growth range from slight negative allometry to slight positive allometry. Given the low intermembral index for sifakas, which is also an adaptation for propulsive hindlimb-dominated jumping, this suggests that differences in adult limb proportions are largely set prenatally rather than being achieved via higher rates of postnatal hindlimb growth.(ABSTRACT TRUNCATED AT 400 WORDS)

Reduction of malaria prevalence by indoor residual spraying: a meta-regression analysis.

Indoor residual spraying (IRS) has become an increasingly popular method of insecticide use for malaria control, and many recent studies have reported on its effectiveness in reducing malaria burden in a single community or region. There is a need for systematic review and integration of the published literature on IRS and the contextual determining factors of its success in controlling malaria. This study reports the findings of a meta-regression analysis based on 13 published studies, which were chosen from more than 400 articles through a systematic search and selection process. The summary relative risk for reducing malaria prevalence was 0.38 (95% confidence interval = 0.31-0.46), which indicated a risk reduction of 62%. However, an excessive degree of heterogeneity was found between the studies. The meta-regression analysis indicates that IRS is more effective with high initial prevalence, multiple rounds of spraying, use of DDT, and in regions with a combination of Plasmodium falciparum and P. vivax malaria.

Seeing the forest for the fuel

We demonstrate a new approach to understanding the role of fuelwood in the rural household economy by applying insights from travel cost modeling to author-compiled household survey data and meso-scale environmental statistics from Ruteng Park in Flores, Indonesia. We characterize Manggarai farming households' fuelwood collection trips as inputs into household production of the utility yielding service of cooking and heating. The number of trips taken by households depends on the shadow price of fuelwood collection or the travel cost, which is endogenous. Econometric analyses using truncated negative binomial regression models and correcting for endogeneity show that the Manggarai are 'economically rational' about fuelwood collection and access to the forests for fuelwood makes substantial contributions to household welfare. Increasing cost of forest access, wealth, use of alternative fuels, ownership of kerosene stoves, trees on farm, park staff activity, primary schools and roads, and overall development could all reduce dependence on collecting fuelwood from forests. © 2004 Cambridge University Press.

Lognormal and gamma mixed negative binomial regression

In regression analysis of counts, a lack of simple and efficient algorithms for posterior computation has made Bayesian approaches appear unattractive and thus underdeveloped. We propose a lognormal and gamma mixed negative binomial (NB) regression model for counts, and present efficient closed-form Bayesian inference; unlike conventional Poisson models, the proposed approach has two free parameters to include two different kinds of random effects, and allows the incorporation of prior information, such as sparsity in the regression coefficients. By placing a gamma distribution prior on the NB dispersion parameter r, and connecting a log-normal distribution prior with the logit of the NB probability parameter p, efficient Gibbs sampling and variational Bayes inference are both developed. The closed-form updates are obtained by exploiting conditional conjugacy via both a compound Poisson representation and a Polya-Gamma distribution based data augmentation approach. The proposed Bayesian inference can be implemented routinely, while being easily generalizable to more complex settings involving multivariate dependence structures. The algorithms are illustrated using real examples. Copyright 2012 by the author(s)/owner(s).

Distributed Feature Selection in Large n and Large p Regression Problems

Fitting statistical models is computationally challenging when the sample size or the dimension of the dataset is huge. An attractive approach for down-scaling the problem size is to first partition the dataset into subsets and then fit using distributed algorithms. The dataset can be partitioned either horizontally (in the sample space) or vertically (in the feature space), and the challenge arise in defining an algorithm with low communication, theoretical guarantees and excellent practical performance in general settings. For sample space partitioning, I propose a MEdian Selection Subset AGgregation Estimator ({\em message}) algorithm for solving these issues. The algorithm applies feature selection in parallel for each subset using regularized regression or Bayesian variable selection method, calculates the `median' feature inclusion index, estimates coefficients for the selected features in parallel for each subset, and then averages these estimates. The algorithm is simple, involves very minimal communication, scales efficiently in sample size, and has theoretical guarantees. I provide extensive experiments to show excellent performance in feature selection, estimation, prediction, and computation time relative to usual competitors.

While sample space partitioning is useful in handling datasets with large sample size, feature space partitioning is more effective when the data dimension is high. Existing methods for partitioning features, however, are either vulnerable to high correlations or inefficient in reducing the model dimension. In the thesis, I propose a new embarrassingly parallel framework named {\em DECO} for distributed variable selection and parameter estimation. In {\em DECO}, variables are first partitioned and allocated to m distributed workers. The decorrelated subset data within each worker are then fitted via any algorithm designed for high-dimensional problems. We show that by incorporating the decorrelation step, DECO can achieve consistent variable selection and parameter estimation on each subset with (almost) no assumptions. In addition, the convergence rate is nearly minimax optimal for both sparse and weakly sparse models and does NOT depend on the partition number m. Extensive numerical experiments are provided to illustrate the performance of the new framework.

For datasets with both large sample sizes and high dimensionality, I propose a new "divided-and-conquer" framework {\em DEME} (DECO-message) by leveraging both the {\em DECO} and the {\em message} algorithm. The new framework first partitions the dataset in the sample space into row cubes using {\em message} and then partition the feature space of the cubes using {\em DECO}. This procedure is equivalent to partitioning the original data matrix into multiple small blocks, each with a feasible size that can be stored and fitted in a computer in parallel. The results are then synthezied via the {\em DECO} and {\em message} algorithm in a reverse order to produce the final output. The whole framework is extremely scalable.