Pointwise universal consistency of nonparametric linear estimators

This paper presents sufficient conditions for pointwise universal consistency of nonparametric delta estimators. We show the applicability of these conditions for some classes of nonparametric estimators

Automatic spectral density estimation for Random fields on a lattice via bootstrap

This paper considers the nonparametric estimation of spectral densities for second order stationary random fields on a d-dimensional lattice. I discuss some drawbacks of standard methods, and propose modified estimator classes with improved bias convergence rate, emphasizing the use of kernel methods and the choice of an optimal smoothing number. I prove uniform consistency and study the uniform asymptotic distribution, when the optimal smoothing number is estimated from the sampled data.

POINTWISE UNIVERSAL CONSISTENCY OF NONPARAMETRIC LINEAR ESTIMATORS

This paper presents sufficient conditions for pointwise universal consistency of nonparametric delta estimators. We show the applicability of these conditions for some classes of nonparametric estimators.

Automatic spectral density estimation for random fields on a lattice via bootstrap.

We consider the nonparametric estimation of spectral densities for secondorder stationary random fields on a d-dimensional lattice. We discuss some drawbacks of standard methods and propose modified estimator classes with improved bias convergence rate, emphasizing the use of kernel methods and the choice of an optimal smoothing number.We prove the uniform consistency and study the uniform asymptotic distribution when the optimal smoothing number is estimated from the sampled data.Spatial data; Spectral density; Smoothing number; Uniform asymptotic distribution; Bootstrap;

A valid theory on probabilistic causation

In this paper several definitions of probabilistic causation are considered, and their main drawbacks discussed. Current notions of probabilistic causality have symmetry limitations (e.g. correlation and statistical dependence are symmetric notions). To avoid the symmetry problem, non-reciprocal causality is often defined in terms of dynamic asymmetry. But these notions are likely to consider spurious regularities. In this paper we present a definition of causality that does non have symmetry inconsistences. It is a natural extension of propositional causality in formal logics, and it can be easily analyzed with statistical inference. The modeling problems are also discussed using empirical processes.Causality, Empirical Processes and Classification Theory, 62M30, 62M15, 62G20

Pointwise universal consistency of nonparametric density estimators.

This paper presents sufficient conditions for pointwise universal consistency of nonparametric delta estimators and shows the application of these conditions for some classes of nonparametric estimators.Delta estimators; Pointwise approximation; Pointwise universal consistency;

Averaged Singular Integral Estimation as a Bias Reduction Technique

This paper proposes an averaged version of singular integral estimators, whose bias achieves higher rates of convergence under smoothing assumptions. We derive exact bias bounds, without imposing smoothing assumptions, which are a basis for deriving the rates of convergence under differentiability assumptions.Publicad

Computing continuous-time growth models with boundary conditions via wavelets

This paper presents an algorithm for approximating the solution of deterministic/stochastic continuous-time growth models based on the Euler's equation and the transversality conditions. The main issue for computing these models is to deal efficiently with the boundary conditions associated. This approach is a wavelets-collocation method derived from the finite-iterative trapezoidal approach. Illustrative examples are give

Valuation of boundary-linked assets

This article studies the valuation of boundary-linked assets and their derivatives in continuous-time markets. Valuing boundary-linked assets requires the solution of a stochastic differential equation with boundary conditions, which, often, is not Markovian. We propose a wavelet-collocation algorithm for solving a Milstein approximation to the stochastic boundary problem. Its convergence properties are studied. Furthermore, we value boundary-linked derivatives using Malliavin calculus and Monte Carlo methods. We apply these ideas to value European call options of boundary-linked asset

Worst-case estimation and asymptotic theory for models with unobservables

This paper proposes a worst-case approach for estimating econometric models containing unobservable variables. Worst-case estimators are robust against the adverse effects of unobservables. In contrast to the classical literature, there are no assumptions about the statistical nature of the unobservables in a worst-case estimation. This method is robust with respect to the unknown probability distribution of the unobservables and should be seen as a complement to standard methods, as cautious modelers should compare different estimations to determine robust models. The limit theory is obtained. A Monte Carlo study of finite sample properties has been conducted. An economic application is included