Solar hard X-ray imaging by means of Compressed Sensing and Finite Isotropic Wavelet Transform

This paper shows that compressed sensing realized by means of regularized deconvolution and the Finite Isotropic Wavelet Transform is effective and reliable in hard X-ray solar imaging. The method utilizes the Finite Isotropic Wavelet Transform with Meyer function as the mother wavelet. Further, compressed sensing is realized by optimizing a sparsity-promoting regularized objective function by means of the Fast Iterative Shrinkage-Thresholding Algorithm. Eventually, the regularization parameter is selected by means of the Miller criterion. The method is applied against both synthetic data mimicking the Spectrometer/Telescope Imaging X-rays (STIX) measurements and experimental observations provided by the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI). The performances of the method are compared with the results provided by standard visibility-based reconstruction methods. The results show that the application of the sparsity constraint and the use of a continuous, isotropic framework for the wavelet transform provide a notable spatial accuracy and significantly reduce the ringing effects due to the instrument point spread functions

Subsampling inference in cube root asymptotics with an application to Manski's maximum score estimator

Kim and Pollard (Annals of Statistics, 18 (1990) 191?219) showed that a general class of M-estimators converge at rate n1/3 rather than at the standard rate n1/2. Many times, this situation arises when the objective function is non-smooth. The limiting distribution is the (almost surely unique) random vector that maximizes a certain Gaussian process and is difficult to analyze analytically. In this paper, we propose the use of the subsampling method for inferential purposes. The general method is then applied to Manski?s maximum score estimator and its small sample performance is highlighted via a simulation study.Publicad

ON THE (INTRADAILY) SEASONALITY AND DYNAMICS OF A FINANCIAL POINT PROCESS: A SEMIPARAMETRIC APPROACH.

A component model for the analysis of financial durations is proposed. The components are the long-run dynamics and the seasonality. The later is left unspecified and the former is assumed to fall within the class of certain family of parametric functions. The joint model is estimated by maximizing a (local) quasi-likelihood function, and the resulting nonparametric estimator of the seasonal curve has an explicit form that turns out to be a transformation of the Nadaraya-Watson estimator. The estimators of the parameters of interest are shown to be root-N consistent and asymptotically efficient. Furthermore, the seasonal curve is also estimated consistently. The methodology is applied to the trade duration process of Bankinter, a medium size Spanish bank traded in Bolsa de Madrid. We show that adjusting data by seasonality produces important misspecifications.

Efficient nonparametric three-stage estimation of fixed effects varying coefficient panel data models

This paper is concerned with the estimation of a fixed effects panel data model that adopts a partially linear form, in which the coeffcients of some variables are restricted to be constant but the coeffcients of other variables are assumed to be varying, depending on some exogenous continuous variables. Moreover, we allow for the existence of endogeneity in the structural equation. Conditional moment restrictions on first differences are imposed to identify the structural equation. Based on these restrictions we propose a three stage estimation procedure. The asymptotic properties of these proposed estimators are established. Moreover, as a result of the first differences transformation, to estimate the unknown varying coeffcient functions, two alternative backfitting estimators are obtained. As a novelty, we propose a minimum distance estimator that, combining both estimators, is more effcient and achieves the optimal rate of convergence. The feasibility and possible gains of this new procedure are shown by estimating a Life-cycle hypothesis panel data model and a Monte Carlo study is implemented.The authors gratefully acknowledge financial support from the Programa Estatal de Fomentode la Investigación Científica y Técnica de Excelencia/Spanish Ministry of Economy and Competitiveness. Ref. ECO2016-76203-C2-1-P. In addition, this work is part of the Research Project APIE 1/2015-17: "New Methods for the empirical analysis of financial markets" of the Santander Financial Institute (SANFI) of UCEIF Foundation resolved by the University of Cantabria and funded with sponsorship from Banco Santander

Semiparametric estimation of weak and strong separable models

In this paper we introduce a general method for estimating semiparametrically the different components in weak or strong separable models. The family of separable models is quite popular in economic theory and empirical research as this structure offers clear interpretation, has straight forward economic consequences and often is justified by theory. As will be seen in this article they are also of statistical interest since they allow to estimate semiparametrically high dimensional complexity without running in the so called curse of dimensionality. Generalized additive models and generalized partial linear models are special cases in this family of models. The idea of the new method is mainly based on a combination of local likelihood and efficient estimators in non or semiparametric models. Although this imposes some hypothesis on the error distribution this yields a very general usable method with little computational costs and high exactness even for small samples. E. g. it enables us to include models for censored and truncated variables which are quite common in quantitative economics. We give the estimation procedures and provide asymptotic theory for them. Implementation is discussed, simulations and an application demonstrate its feasibility in finite sample behavio

Nonparametric estimation of time varying parameters under shape restrictions

In this paper we propose a new method to estimate nonparametrically a time varying parameter model when some qualitative information from outside data (e.g. seasonality) is available. In this framework we make two main contributions. First, the resulting estimator is shown to belong to the class of generalized ridge estimators and under some conditions its rate of convergence is optimal within its smoothness class. Furthermore, if the outside data information is fullfilled by the underlying model, the estimator shows efficiency gains in small sample sizes. Second, for the implementation process, since the estimation procedure envolves the computation of the inverse of a high order matrix we provide an algorithm that avoids this computation and, also, a data-driven method is derived to select the control parameters. The practical performance of the method is demonstrated in a simulation study and in an application to the demand of soft drinks in Canada.This work was supported by Dirección General de Enseñanza Superior del Ministerio de Educación y Ciencia under research grant PB98-0149, and by the Universidad del País Vasco under research grant UPV 038.321-HA129/99

Nonparametric multidimensional fixed effects panel data models

Multidimensional panel datasets are routinely employed to identify marginal effects in empirical research. Fixed effects estimators are typically used to deal with potential correlation between unobserved effects and regressors. Nonparametric estimators for one-way fixed effects models exist, but are cumbersome to employ in practice as they typically require iteration, marginal integration or profile estimation. We develop a nonparametric estimator that works for essentially any dimension fixed effects model, has a closed form solution and can be estimated in a single step. A cross-validation bandwidth selection procedure is proposed and asymptotic properties (for either a fixed or large time dimension) are given. Finite sample properties are shown via simulations, as well as with an empirical application, which further extends our model to the partially linear setting

Finite sample behavior of two step estimators in selection models

The problem of specification errors in sample selection models has received considerable attention both theoretically and empirically. However, very few is known about the finite sample behavior of two step estimators. In this paper we investigate by simulations both bias and finite sample distribution of these estimators when ignoring heteroskedasticity in the sample selection mechanism. It turns out that under conditions traditionally faced by practitioners, the misspecified parametric two step estimator (Heckman, 1979) performs better, in finite sample sizes, than the robust semiparametric one (Ahn and Powell, 1993). Moreover, under very general conditions, we show that the asymptotic bias of the parametric two step estimator is linear in the covariance between the sample selection and the participation equation.The first two authors wish to thank the Dirección General de Enseñanza Superior, research project PB96-C05-03 for its financial support. The third author acknowledges financial support from the DGICYT, research project PB94-0602

Two-Stage Nonparametric Regression for Longitudinal Data

In the analysis of longitudinal data it is of main interest to investigate the existence of group and individual effects under correlated observations across time. In this paper, we develop a nonparametric two-step procedure that enables us to estimate group effects under a very general form of correlation across time. Moreover, we propose several methods to estimate the bandwidth and show their asymptotyc optimality. Since the asymptotic distribution is untractable, we develop a randomization test that is suitable for testing the group effects. Finally, we apply the estimation procedure, the bandwidth selection criteria and the randomization test to the data from the Iowa Cochlear Implant Project.This work was supported by Dirección General de Enseñanza Superior del Ministerio Español de Educación y Cultura and Universidad del País Vasco (UPV/EHU) under research grant PB95-0346