Iterative Estimation of Solutions to Noisy Nonlinear Operator Equations in Nonparametric Instrumental Regression

This paper discusses the solution of nonlinear integral equations with noisy integral kernels as they appear in nonparametric instrumental regression. We propose a regularized Newton-type iteration and establish convergence and convergence rate results. A particular emphasis is on instrumental regression models where the usual conditional mean assumption is replaced by a stronger independence assumption. We demonstrate for the case of a binary instrument that our approach allows the correct estimation of regression functions which are not identifiable with the standard model. This is illustrated in computed examples with simulated data

Nonlinear Time Series Modeling: A Unified Perspective, Algorithm, and Application

A new comprehensive approach to nonlinear time series analysis and modeling is developed in the present paper. We introduce novel data-specific mid-distribution based Legendre Polynomial (LP) like nonlinear transformations of the original time series Y(t) that enables us to adapt all the existing stationary linear Gaussian time series modeling strategy and made it applicable for non-Gaussian and nonlinear processes in a robust fashion. The emphasis of the present paper is on empirical time series modeling via the algorithm LPTime. We demonstrate the effectiveness of our theoretical framework using daily S&P 500 return data between Jan/2/1963 - Dec/31/2009. Our proposed LPTime algorithm systematically discovers all the `stylized facts' of the financial time series automatically all at once, which were previously noted by many researchers one at a time.Comment: Major restructuring has been don

Global sensitivity analysis for stochastic simulators based on generalized lambda surrogate models

Global sensitivity analysis aims at quantifying the impact of input variability onto the variation of the response of a computational model. It has been widely applied to deterministic simulators, for which a set of input parameters has a unique corresponding output value. Stochastic simulators, however, have intrinsic randomness due to their use of (pseudo)random numbers, so they give different results when run twice with the same input parameters but non-common random numbers. Due to this random nature, conventional Sobol' indices, used in global sensitivity analysis, can be extended to stochastic simulators in different ways. In this paper, we discuss three possible extensions and focus on those that depend only on the statistical dependence between input and output. This choice ignores the detailed data generating process involving the internal randomness, and can thus be applied to a wider class of problems. We propose to use the generalized lambda model to emulate the response distribution of stochastic simulators. Such a surrogate can be constructed without the need for replications. The proposed method is applied to three examples including two case studies in finance and epidemiology. The results confirm the convergence of the approach for estimating the sensitivity indices even with the presence of strong heteroskedasticity and small signal-to-noise ratio

An X-ray survey of low-mass stars in Trumpler 16 with Chandra

We identify and characterize low-mass stars in the ~3 Myr old Trumpler 16 (Tr16) region by means of a deep Chandra X-ray observation, and study their optical and near-IR properties. We compare X-ray activity of Tr16 stars with known characteristics of Orion and Cygnus OB2 stars. We analyzed a 88.4 ksec Chandra ACIS-I observation pointed at the center of Tr16. Because of diffuse X-ray emission, source detection was performed using the PWDetect code for two different energy ranges: 0.5-8.0 keV and 0.9-8.0 keV. Results were merged into a single final list. We positionally correlate X-ray sources with optical and 2MASS catalogues. Source events were extracted with the IDL-based routine ACIS-Extract. X-ray variability was characterized using the Kolmogorov-Smirnov test and spectra were fitted by using XSPEC. X-ray spectra of early-type, massive stars were analyzed individually. Our list of X-ray sources consists of 1035 entries, 660 of which have near-IR counterparts and are probably associated with Tr16 members. From near-IR color-color and color-magnitudes diagrams we compute individual masses of stars and their Av values. About 15% of the near-IR counterparts show disk-induced excesses. X-ray variability is found in 77 sources. X-ray emission from OB stars appear softer than the low-mass stars. The Tr16 region has a very rich population of low-mass X-ray emitting stars. An important fraction of its circumstellar disks survive the intense radiation field of its massive stars. Stars with masses 1.5-2.5 Mo display X-ray activity similar to that of stars in Cyg OB2 but much less intense than observed for Orion Nebula Cluster members.Comment: 19 pages, 3 ellectronic tables and 19 figures. Accepted for publication at the A&

A local statistic for the spatial extent of extreme threshold exceedances

We introduce the extremal range, a local statistic for studying the spatial extent of extreme events in random fields on $\mathbb{R}^2$. Conditioned on exceedance of a high threshold at a location $s$, the extremal range at $s$ is the random variable defined as the smallest distance from $s$ to a location where there is a non-exceedance. We leverage tools from excursion-set theory to study distributional properties of the extremal range, propose parametric models and predict the median extremal range at extreme threshold levels. The extremal range captures the rate at which the spatial extent of conditional extreme events scales for increasingly high thresholds, and we relate its distributional properties with the bivariate tail dependence coefficient and the extremal index of time series in classical Extreme-Value Theory. Consistent estimation of the distribution function of the extremal range for stationary random fields is proven. For non-stationary random fields, we implement generalized additive median regression to predict extremal-range maps at very high threshold levels. An application to two large daily temperature datasets, namely reanalyses and climate-model simulations for France, highlights decreasing extremal dependence for increasing threshold levels and reveals strong differences in joint tail decay rates between reanalyses and simulations.Comment: 32 pages, 5 figure