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

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

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;

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;

Modified whittle estimation of multilateral spatial models

We consider the estimation of parametric models for stationary spatial or spatio-temporal data on a d-dimensional lattice, for d = 2. The achievement of asymptotic efficiency under Gaussianity, and asymptotic normality more generally, with standard convergence rate, faces two obstacles. One is the 'edge effect', which worsens with increasing d. The other is the difficulty of computing a continuous-frequency form of Whittle estimate or a time domain Gaussian maximum likelihood estimate, especially in case of multilateral models, due mainly to the Jacobian term. An extension of the discrete-frequency Whittle estimate from the time series literature deals conveniently with the latter problem, but when subjected to a standard device for avoiding the edge effect has disastrous asymptotic performance, along with finite sample numerical drawbacks, the objective function lacking a minimum-distance interpretation and losing any global convexity properties. We overcome these problems by first optimizing a standard, guaranteed non-negative, discrete-frequency, Whittle function, without edge-effect correction, providing an estimate with a slow convergence rate, then improving this by a sequence of computationally convenient approximate Newton iterations using a modified, almost-unbiased periodogram, the desired asymptotic properties being achieved after finitely many steps. A Monte Carlo study of finite sample behaviour is included. The asymptotic regime allows increase in both directions, unlike the usual random fields formulation, with the central limit theorem established after re-ordering as a triangular array. When the data are non-Gaussian, the asymptotic variances of all parameter estimates are likely to be affected, and we provide a consistent, non-negative definite, estimate of the asymptotic variance matrix.Spatial data, multilateral models, Whittle estimation,

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