Bias-corrected Pearson estimating functions for Taylor`s power law applied to benthic macrofauna data

Estimation of Taylor`s power law for species abundance data may be performed by linear regression of the log empirical variances on the log means, but this method suffers from a problem of bias for sparse data. We show that the bias may be reduced by using a bias-corrected Pearson estimating function. Furthermore, we investigate a more general regression model allowing for site-specific covariates. This method may be efficiently implemented using a Newton scoring algorithm, with standard errors calculated from the inverse Godambe information matrix. The method is applied to a set of biomass data for benthic macrofauna from two Danish estuaries. (C) 2011 Elsevier B.V. All rights reserved.

CAUSAL INFERENCE WITH A CONTINUOUS TREATMENT AND OUTCOME: ALTERNATIVE ESTIMATORS FOR PARAMETRIC DOSE-RESPONSE FUNCTIONS WITH APPLICATIONS.

Causal inference with a continuous treatment is a relatively under-explored problem. In this dissertation, we adopt the potential outcomes framework. Potential outcomes are responses that would be seen for a unit under all possible treatments. In an observational study where the treatment is continuous, the potential outcomes are an uncountably infinite set indexed by treatment dose. We parameterize this unobservable set as a linear combination of a finite number of basis functions whose coefficients vary across units. This leads to new techniques for estimating the population average dose-response function (ADRF). Some techniques require a model for the treatment assignment given covariates, some require a model for predicting the potential outcomes from covariates, and some require both. We develop these techniques using a framework of estimating functions, compare them to existing methods for continuous treatments, and simulate their performance in a population where the ADRF is linear and the models for the treatment and/or outcomes may be misspecified. We also extend the comparisons to a data set of lottery winners in Massachusetts. Next, we describe the methods and functions in the R package causaldrf using data from the National Medical Expenditure Survey (NMES) and Infant Health and Development Program (IHDP) as examples. Additionally, we analyze the National Growth and Health Study (NGHS) data set and deal with the issue of missing data. Lastly, we discuss future research goals and possible extensions.

On the statistical estimation of diffusion processes: a survey

Data available on continuos-time diffusions are always sampled discretely in time. In most cases, the likelihood function of the observations is not directly computable. This survey covers a sample of the statistical methods that have been developed to solve this problem. We concentrate on some recent contributions to the literature based on three di§erent approaches to the problem: an improvement of the Euler-Maruyama discretization scheme, the use of Martingale Estimating Functions and the application of Generalized Method of Moments (GMM).

On the statistical estimation of diffusion processes - a partial survey

Data available on continuous-time diffusions are always sampled discretely in time. In most cases, the likelihood function of the observations is not directly computable. This survey covers a sample of the statistical methods that have been developed to solve this problem. We concentrate on some recent contributions to the literature based on three di§erent approaches to the problem: an improvement of the Euler-Maruyama discretization scheme, the employment of Martingale Estimating Functions, and the application of Generalized Method of Moments (GMM).

Parameterschätzung in zeitdiskreten ergodischen Markov-Prozessen am Beispiel des Cox-Ingersoll-Ross-Modells

In dieser Arbeit geht es um die Schätzung von Parametern in zeitdiskreten ergodischen Markov-Prozessen im allgemeinen und im CIR-Modell im besonderen. Beim CIR-Modell handelt es sich um eine stochastische Differentialgleichung, die von Cox, Ingersoll und Ross (1985) zur Beschreibung der Dynamik von Zinsraten vorgeschlagen wurde. Problemstellung ist die Schätzung der Parameter des Drift- und des Diffusionskoeffizienten aufgrund von äquidistanten diskreten Beobachtungen des CIR-Prozesses. Nach einer kurzen Einführung in das CIR-Modell verwenden wir die insbesondere von Bibby und Sørensen untersuchte Methode der Martingal-Schätzfunktionen und -Schätzgleichungen, um das Problem der Parameterschätzung in ergodischen Markov-Prozessen zunächst ganz allgemein zu untersuchen. Im Anschluss an Untersuchungen von Sørensen (1999) werden hinreichende Bedingungen (im Sinne von Regularitätsvoraussetzungen an die Schätzfunktion) für die Existenz, starke Konsistenz und asymptotische Normalität von Lösungen einer Martingal-Schätzgleichung angegeben. Angewandt auf den Spezialfall der Likelihood-Schätzung stellen diese Bedingungen zugleich lokal-asymptotische Normalität des Modells sicher. Ferner wird ein einfaches Kriterium für Godambe-Heyde-Optimalität von Schätzfunktionen angegeben und skizziert, wie dies in wichtigen Spezialfällen zur expliziten Konstruktion optimaler Schätzfunktionen verwendet werden kann. Die allgemeinen Resultate werden anschließend auf das diskretisierte CIR-Modell angewendet. Wir analysieren einige von Overbeck und Rydén (1997) vorgeschlagene Schätzer für den Drift- und den Diffusionskoeffizienten, welche als Lösungen quadratischer Martingal-Schätzfunktionen definiert sind, und berechnen das optimale Element in dieser Klasse. Abschließend verallgemeinern wir Ergebnisse von Overbeck und Rydén (1997), indem wir die Existenz einer stark konsistenten und asymptotisch normalen Lösung der Likelihood-Gleichung zeigen und lokal-asymptotische Normalität für das CIR-Modell ohne Einschränkungen an den Parameterraum beweisen.

Estimating remittance functions for Pacific island migrants

There is concern that Pacific island economies dependent on remittances of migrants will endure foreign exchange shortages and declining Living standards as remittance levels drop due to lower migration rates and the belief that migrants' willingness to remit decreases over time. The empirical validity of the remittance-decay hypothesis has never been tested. From survey data on Tongan and Western Samoan migrants in Sydney, this paper estimates remittance functions using Tobit regression analysis. It is found that the remittance-decay hypothesis has no empirical validity and migrants are motivated by factors other than altruistic family support, including asset accumulation and investment back home. (C) 1997 Elsevier Science Ltd.

From EEG to BOLD: Brain mapping and estimating transfer functions in simultaneous EEG-fMRI acquisitions

Simultaneous acquisition of electroencephalography (EEG) and functional magnetic resonance imaging (fMRI) aims to disentangle the description of brain processes by exploiting the advantages of each technique. Most studies in this field focus on exploring the relationships between fMRI signals and the power spectrum at some specific frequency bands (alpha, beta, etc.). On the other hand, brain mapping of EEG signals (e.g., interictal spikes in epileptic patients) usually assumes an haemodynamic response function for a parametric analysis applying the GLM, as a rough approximation. The integration of the information provided by the high spatial resolution of MR images and the high temporal resolution of EEG may be improved by referencing them by transfer functions, which allows the identification of neural driven areas without strong assumptions about haemodynamic response shapes or brain haemodynamic`s homogeneity. The difference on sampling rate is the first obstacle for a full integration of EEG and fMRI information. Moreover, a parametric specification of a function representing the commonalities of both signals is not established. In this study, we introduce a new data-driven method for estimating the transfer function from EEG signal to fMRI signal at EEG sampling rate. This approach avoids EEG subsampling to fMRI time resolution and naturally provides a test for EEG predictive power over BOLD signal fluctuations, in a well-established statistical framework. We illustrate this concept in resting state (eyes closed) and visual simultaneous fMRI-EEG experiments. The results point out that it is possible to predict the BOLD fluctuations in occipital cortex by using EEG measurements. (C) 2010 Elsevier Inc. All rights reserved.

Assessment of pedotransfer functions for estimating soil water retention curves for the amazon region

Knowledge of the soil water retention curve (SWRC) is essential for understanding and modeling hydraulic processes in the soil. However, direct determination of the SWRC is time consuming and costly. In addition, it requires a large number of samples, due to the high spatial and temporal variability of soil hydraulic properties. An alternative is the use of models, called pedotransfer functions (PTFs), which estimate the SWRC from easy-to-measure properties. The aim of this paper was to test the accuracy of 16 point or parametric PTFs reported in the literature on different soils from the south and southeast of the State of Pará, Brazil. The PTFs tested were proposed by Pidgeon (1972), Lal (1979), Aina & Periaswamy (1985), Arruda et al. (1987), Dijkerman (1988), Vereecken et al. (1989), Batjes (1996), van den Berg et al. (1997), Tomasella et al. (2000), Hodnett & Tomasella (2002), Oliveira et al. (2002), and Barros (2010). We used a database that includes soil texture (sand, silt, and clay), bulk density, soil organic carbon, soil pH, cation exchange capacity, and the SWRC. Most of the PTFs tested did not show good performance in estimating the SWRC. The parametric PTFs, however, performed better than the point PTFs in assessing the SWRC in the tested region. Among the parametric PTFs, those proposed by Tomasella et al. (2000) achieved the best accuracy in estimating the empirical parameters of the van Genuchten (1980) model, especially when tested in the top soil layer.

PEDO-TRANSFER FUNCTIONS FOR ESTIMATING SOIL BULK DENSITY IN CENTRAL AMAZONIA

Under field conditions in the Amazon forest, soil bulk density is difficult to measure. Rigorous methodological criteria must be applied to obtain reliable inventories of C stocks and soil nutrients, making this process expensive and sometimes unfeasible. This study aimed to generate models to estimate soil bulk density based on parameters that can be easily and reliably measured in the field and that are available in many soil-related inventories. Stepwise regression models to predict bulk density were developed using data on soil C content, clay content and pH in water from 140 permanent plots in terra firme (upland) forests near Manaus, Amazonas State, Brazil. The model results were interpreted according to the coefficient of determination (R2) and Akaike information criterion (AIC) and were validated with a dataset consisting of 125 plots different from those used to generate the models. The model with best performance in estimating soil bulk density under the conditions of this study included clay content and pH in water as independent variables and had R2 = 0.73 and AIC = -250.29. The performance of this model for predicting soil density was compared with that of models from the literature. The results showed that the locally calibrated equation was the most accurate for estimating soil bulk density for upland forests in the Manaus region.

Functions for estimating stem diameter and tree age using tree height, crown width and existing stand database information

Abstract

Estimating extreme value cumulative distribution functions using bias-corrected kernel approaches

We propose a new kernel estimation of the cumulative distribution function based on transformation and on bias reducing techniques. We derive the optimal bandwidth that minimises the asymptotic integrated mean squared error. The simulation results show that our proposed kernel estimation improves alternative approaches when the variable has an extreme value distribution with heavy tail and the sample size is small.

A BAYESIAN HIERARCHICAL MODEL FOR CONSTRAINED DISTRIBUTED LAG FUNCTIONS: ESTIMATING THE TIME COURSE OF HOSPITALIZATION ASSOCIATED WITH AIR POLLUTION EXPOSURE

Numerous time series studies have provided strong evidence of an association between increased levels of ambient air pollution and increased levels of hospital admissions, typically at 0, 1, or 2 days after an air pollution episode. An important research aim is to extend existing statistical models so that a more detailed understanding of the time course of hospitalization after exposure to air pollution can be obtained. Information about this time course, combined with prior knowledge about biological mechanisms, could provide the basis for hypotheses concerning the mechanism by which air pollution causes disease. Previous studies have identified two important methodological questions: (1) How can we estimate the shape of the distributed lag between increased air pollution exposure and increased mortality or morbidity? and (2) How should we estimate the cumulative population health risk from short-term exposure to air pollution? Distributed lag models are appropriate tools for estimating air pollution health effects that may be spread over several days. However, estimation for distributed lag models in air pollution and health applications is hampered by the substantial noise in the data and the inherently weak signal that is the target of investigation. We introduce an hierarchical Bayesian distributed lag model that incorporates prior information about the time course of pollution effects and combines information across multiple locations. The model has a connection to penalized spline smoothing using a special type of penalty matrix. We apply the model to estimating the distributed lag between exposure to particulate matter air pollution and hospitalization for cardiovascular and respiratory disease using data from a large United States air pollution and hospitalization database of Medicare enrollees in 94 counties covering the years 1999-2002.