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.

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.

Nonparametric location estimators in the randomized complete block design

Several tests for the comparison of different groups in the randomized complete block design exist. However, there is a lack of robust estimators for the location difference between one group and all the others on the original scale. The relative marginal effects are commonly used in this situation, but they are more difficult to interpret and use by less experienced people because of the different scale. In this paper two nonparametric estimators for the comparison of one group against the others in the randomized complete block design will be presented. Theoretical results such as asymptotic normality, consistency, translation invariance, scale preservation, unbiasedness, and median unbiasedness are derived. The finite sample behavior of these estimators is derived by simulations of different scenarios. In addition, possible confidence intervals with these estimators are discussed and their behavior derived also by simulations.

A new frontier in biodiversity inventory: a proposal for estimators of phylogenetic and functional diversity

Copyright © 2014 The Authors. Methods in Ecology and Evolution © 2014 British Ecological Society.

Nonparametric estimation of time-dependent ROC curves conditional on a continuous covariate

The receiver-operating characteristic (ROC) curve is the most widely used measure for evaluating the performance of a diagnostic biomarker when predicting a binary disease outcome. The ROC curve displays the true positive rate (or sensitivity) and the false positive rate (or 1-specificity) for different cut-off values used to classify an individual as healthy or diseased. In time-to-event studies, however, the disease status (e.g. death or alive) of an individual is not a fixed characteristic, and it varies along the study. In such cases, when evaluating the performance of the biomarker, several issues should be taken into account: first, the time-dependent nature of the disease status; and second, the presence of incomplete data (e.g. censored data typically present in survival studies). Accordingly, to assess the discrimination power of continuous biomarkers for time-dependent disease outcomes, time-dependent extensions of true positive rate, false positive rate, and ROC curve have been recently proposed. In this work, we present new nonparametric estimators of the cumulative/dynamic time-dependent ROC curve that allow accounting for the possible modifying effect of current or past covariate measures on the discriminatory power of the biomarker. The proposed estimators can accommodate right-censored data, as well as covariate-dependent censoring. The behavior of the estimators proposed in this study will be explored through simulations and illustrated using data from a cohort of patients who suffered from acute coronary syndrome.

Nonparametric Estimation of the Bivariate Recurrence Time Distribution

This paper considers statistical models in which two different types of events, such as the diagnosis of a disease and the remission of the disease, occur alternately over time and are observed subject to right censoring. We propose nonparametric estimators for the joint distribution of bivariate recurrence times and the marginal distribution of the first recurrence time. In general, the marginal distribution of the second recurrence time cannot be estimated due to an identifiability problem, but a conditional distribution of the second recurrence time can be estimated non-parametrically. In literature, statistical methods have been developed to estimate the joint distribution of bivariate recurrence times based on data of the first pair of censored bivariate recurrence times. These methods are efficient in the current model because recurrence times of higher orders are not used. Asymptotic properties of the estimators are established. Numerical studies demonstrate the estimator performs well with practical sample sizes. We apply the proposed method to a Denmark psychiatric case register data set for illustration of the methods and theory.

Nonparametric Estimation in the Class of Bisexual Processes with Population-Size Dependent Mating

2000 Mathematics Subject Classification: 60J80, 62M05

Modelling and Analysis of Recurrent Event Data with Multiple Causes

This thesis Entitled “modelling and analysis of recurrent event data with multiple causes.Survival data is a term used for describing data that measures the time to occurrence of an event.In survival studies, the time to occurrence of an event is generally referred to as lifetime.Recurrent event data are commonly encountered in longitudinal studies when individuals are followed to observe the repeated occurrences of certain events. In many practical situations, individuals under study are exposed to the failure due to more than one causes and the eventual failure can be attributed to exactly one of these causes.The proposed model was useful in real life situations to study the effect of covariates on recurrences of certain events due to different causes.In Chapter 3, an additive hazards model for gap time distributions of recurrent event data with multiple causes was introduced. The parameter estimation and asymptotic properties were discussed .In Chapter 4, a shared frailty model for the analysis of bivariate competing risks data was presented and the estimation procedures for shared gamma frailty model, without covariates and with covariates, using EM algorithm were discussed. In Chapter 6, two nonparametric estimators for bivariate survivor function of paired recurrent event data were developed. The asymptotic properties of the estimators were studied. The proposed estimators were applied to a real life data set. Simulation studies were carried out to find the efficiency of the proposed estimators.

A Bootstrap Test for the Probability of Ruin in the Compound Poisson Risk Process

In this article we propose a bootstrap test for the probability of ruin in the compound Poisson risk process. We adopt the P-value approach, which leads to a more complete assessment of the underlying risk than the probability of ruin alone. We provide second-order accurate P-values for this testing problem and consider both parametric and nonparametric estimators of the individual claim amount distribution. Simulation studies show that the suggested bootstrap P-values are very accurate and outperform their analogues based on the asymptotic normal approximation.

Coleópteros Saproxílicos de los Bosques de Montaña en el Norte de la Comunidad de Madrid

La fauna saproxílica ha cobrado mucha relevancia en los últimos años. Por una parte, debido a los múltiples papeles que juega en la ecología de los bosques y por otra, por encontrarse muchas especies de ese grupo amenazadas como consecuencia de la intensificación de las actividades forestales. Se supone que los bosques de Europa meridional albergan una fauna saproxílica rica y variada. Sin embargo apenas se han realizado estudios que permitan conocer la composición de las biocenosis saproxílicas, así como el estatus y grado de amenaza a que está sometida cada especie. En esta tesis se han muestreado de forma sistemática las comunidades de coleópteros saproxílicos de cuatro montes del norte de la Comunidad de Madrid, muy diferentes a pesar de su cercanía: Dehesa Bonita de Somosierra, Hayedo de Montejo, Dehesa de Madarcos y Pinar de La Maleza. Para llevar a cabo la recogida de muestras se definió una estación de muestreo tipo, compuesta por cuatro trampas aéreas con cebo oloroso, dos trampas de ventana y una trampa de embudos. En los dos primeros montes mencionados se desplegaron seis estaciones de muestreo, por sólo tres en los otros dos. El primer objetivo de esta tesis fue conocer las especies de coleópteros que constituyen la fauna de los cuatro montes estudiados. Los muestreos sistemáticos reportaron la presencia de un total de 357 especies de coleópteros saproxílicos, siendo el Hayedo de Montejo el bosque con la diversidad más alta, 220 especies; le siguen la Dehesa de Madarcos con 116; el pinar de La Maleza con 115; y la Dehesa de Somosierra con 109, si bien la fauna de este ultimo bosque podría ser mucho más variada dado que la interferencia del ganado con algunos dispositivos de captura hizo que se perdiera parte del material allí recolectado. Se han encontrado nueve especies nuevas para la fauna de la Península Ibérica, y otras muchas desconocidas previamente en el centro peninsular. Un total de 50 especies se encuentran incluidas en la Lista Roja Europea de coleópteros saproxílicos. El segundo objetivo fue estimar la riqueza de fauna de coleópteros saproxílicos en cada bosque. Partiendo de los datos de los respectivo muestreos se calcularon diferentes estimadores, paramétricos y no paramétricos, y se elaboraron las curvas de rarefacción para cada bosque y para el conjunto. El bosque con más biodiversidad ha resultado ser el Hayedo de Montejo, que albergaría entre 254 y 332 especies. En el Pinar de la Maleza se encontrarían de 132 a 223; de 128 a 205 en la Dehesa de Somosierra; y entre 134 y 188 en la Dehesa de Madarcos. Para el conjunto del área se estimó la presencia de entre 411 y 512 especies. El tercer objetivo fue evaluar la influencia de algunos factores como la especie arbórea dominante y la cantidad de madera muerta en la riqueza y diversidad de coleópteros saproxílicos. El estudio se realizó en el Hayedo de Montejo, encontrando una alta correlación positiva entre cantidad y calidad de madera muerta, y diversidad y riqueza de especies de coleópteros saproxílicos. El cuarto objetivo fue evaluar la eficacia y complementariedad de los diferentes tipos de dispositivos de captura empleados en los muestreos. El más eficaz resultó ser la trampa de ventana, seguido por la trampa aérea con cebo oloroso, y finalmente la trampa de embudos. La mayor complementariedad se encontró entre trampas de ventana y aéreas con cebo oloroso. No obstante, si se quiere optimizar la exhaustividad del inventario no se debe prescindir de ninguno de los sistemas. En cualquier caso, puede afirmarse que la efectividad de los tres tipos de dispositivos de captura utilizados en los muestreos fue baja, pues para la gran mayoría de especies presentes se capturó un número de ejemplares realmente bajo. El bajo rendimiento de captura implica un bajo impacto sobre las poblaciones de las especies muestreadas, y esto supone una importante ventaja desde el punto de vista de la conservación. Finalmente, se dejan algunas recomendaciones de manejo a aplicar en cada uno de los montes con el fin de preservar o mejorar los hábitats utilizables por la fauna saproxílica que garanticen el mantenimiento y mejora de dichas comunidades. ABSTRACT The saproxylic fauna has become increasingly important in recent years. It has been due, on the one hand, to the multiple roles they play in the forest ecosystems and, on the other, because of the large proportion of endangered saproxylic species as a result of the intensification of forestry. It is generally assumed that southern Europe forests are home to a rich and diverse saproxylic fauna. However, there are hardly any studies leading to reveal the composition of saproxylic biocenosis, or the stage and extent of the threat each species is suffering. For the purpose of this thesis the communities of saproxylic beetles of four mountain forests in northern Comunidad de Madrid have been systematically sampled: Dehesa Bonita de Somosierra, Hayedo de Montejo, Dehesa de Madarcos and Pinar de La Maleza. They are very different from each other in spite of not being too far apart. In order to carry out sample collection, a standard sampling station was defined as follows: four smelly bait aerial traps, two window traps and one funnel trap. Six sampling stations were deployed in each of the first two forests mentioned above; put only three in each of the other two. The first aim of this thesis was to determine the composition of saproxylic beetles fauna inhabiting each of the four forests studied. Systematic sampling reported the presence of a total of 357 species of saproxylic beetles. Hayedo de Montejo, with 220 species, is the forest with the highest diversity, followed by Dehesa de Madarcos, 116; Pinar de La Maleza, 115, and Dehesa de Somosierra, 109. The fauna of the latter forest, however, could be much more varied, since cattle interference with some capture devices caused the loss of part of the material collected there. Nine new species in the fauna of the Iberian Peninsula were found, and many others previously unknown in the center of the Peninsula. A total of 41 of those species are included in the European Red List of saproxylic beetles. The second aim was to estimate the richness of saproxylic (beetle) fauna in each forest. From the data of the respective sampling, different parametric and nonparametric estimators were calculated, and rarefaction curves for each forest, as well as for the four of them together, were drawn. The most biodiverse forest turned out to be Hayedo de Montejo, which houses between 254 and 332 species. In Pinar de La Maleza, between 132 and 223 species were found; between 128 and 205 in Dehesa de Somosierra, and between 134 and 188 in Dehesa de Madarcos. The estimated diversity of species for the whole area ranges from 411 to 512. The third aim was to evaluate the influence of such factors as the dominant tree species and the amount of dead wood in the richness and diversity of saproxylic beetles. The study was conducted at Hayedo de Montejo, finding a high positive correlation between quantity and quality of coarse woody debris and diversity and richness of saproxylic beetle species. The fourth aim was to evaluate the effectiveness and complementarity of the different sampling methods used in this research work. The most effective proved to be the window trap, followed by the smelly bait aerial trap and the funnel trap, in that order. The greater complementarity was found between window and aerial traps. However, in order to optimize the completeness of the inventory, neither of the systems should be discarded. Nevertheless, the effectiveness of the three types of capture devices used in this piece of research was on the whole rather low, since for the vast majority of species, a significant low number of specimens were captured. Poor trapping performance implies a low impact on the populations of the sampled species, and this is an important advantage in terms of conservation. Finally, this thesis gives some recommendations with regard to the management of each of those four forests, leading to preserve and improve the habitats of the saproxylic wildlife and so ensure the maintenance and growth of their communities.

Estimation and inference under economic restrictions

Estimation of economic relationships often requires imposition of constraints such as positivity or monotonicity on each observation. Methods to impose such constraints, however, vary depending upon the estimation technique employed. We describe a general methodology to impose (observation-specific) constraints for the class of linear regression estimators using a method known as constraint weighted bootstrapping. While this method has received attention in the nonparametric regression literature, we show how it can be applied for both parametric and nonparametric estimators. A benefit of this method is that imposing numerous constraints simultaneously can be performed seamlessly. We apply this method to Norwegian dairy farm data to estimate both unconstrained and constrained parametric and nonparametric models.

Inference for nonparametric high-frequency estimators with an application to time variation in betas

We consider the problem of conducting inference on nonparametric high-frequency estimators without knowing their asymptotic variances. We prove that a multivariate subsampling method achieves this goal under general conditions that were not previously available in the literature. We suggest a procedure for a data-driven choice of the bandwidth parameters. Our simulation study indicates that the subsampling method is much more robust than the plug-in method based on the asymptotic expression for the variance. Importantly, the subsampling method reliably estimates the variability of the Two Scale estimator even when its parameters are chosen to minimize the finite sample Mean Squared Error; in contrast, the plugin estimator substantially underestimates the sampling uncertainty. By construction, the subsampling method delivers estimates of the variance-covariance matrices that are always positive semi-definite. We use the subsampling method to study the dynamics of financial betas of six stocks on the NYSE. We document significant variation in betas within year 2006, and find that tick data captures more variation in betas than the data sampled at moderate frequencies such as every five or twenty minutes. To capture this variation we estimate a simple dynamic model for betas. The variance estimation is also important for the correction of the errors-in-variables bias in such models. We find that the bias corrections are substantial, and that betas are more persistent than the naive estimators would lead one to believe.

Improved combinations of parametric and nonparametric Regression estimators

This paper provides a systematic and unified treatment of the developments in the area of kernel estimation in econometrics and statistics. Both the estimation and hypothesis testing issues are discussed for the nonparametric and semiparametric regression models. A discussion on the choice of windowwidth is also presented.

Model specification tests in nonparametric stochastic regression models

In this paper, we consider testing for additivity in a class of nonparametric stochastic regression models. Two test statistics are constructed and their asymptotic distributions are established. We also conduct a small sample study for one of the test statistics through a simulated example. (C) 2002 Elsevier Science (USA).