arXiv subjects

Javier Hidalgo

Publications and source records attributed to Javier Hidalgo.

7 recordsLinked to original sources

arXiv2022

Minimax Risk in Estimating Kink Threshold and Testing Continuity

We derive a risk lower bound in estimating the threshold parameter without knowing whether the threshold regression model is continuous or not. The bound goes to zero as the sample size $ n $ grows only at the cube root rate. Motivated by this finding, we develop a continuity test for the threshold regression model and a bootstrap to compute its \textit{p}-values. The validity of the bootstrap is established, and its finite sample property is explored through Monte Carlo simulations.

econ.EM↗

arXiv2021

Nonparametric prediction with spatial data

We describe a (nonparametric) prediction algorithm for spatial data, based on a canonical factorization of the spectral density function. We provide theoretical results showing that the predictor has desirable asymptotic properties. Finite sample performance is assessed in a Monte Carlo study that also compares our algorithm to a rival nonparametric method based on the infinite AR representation of the dynamics of the data. Finally, we apply our methodology to predict house prices in Los Angeles.

econ.EM↗

arXiv2020

Testing nonparametric shape restrictions

We describe and examine a test for a general class of shape constraints, such as constraints on the signs of derivatives, U-(S-)shape, symmetry, quasi-convexity, log-convexity, $r$-convexity, among others, in a nonparametric framework using partial sums empirical processes. We show that, after a suitable transformation, its asymptotic distribution is a functional of the standard Brownian motion, so that critical values are available. However, due to the possible poor approximation of the asymptotic critical values to the finite sample ones, we also describe a valid bootstrap algorithm.

stat.ME↗

arXiv2020

Isotonic regression for metallic microstructure data: estimation and testing under order restrictions

Investigating the main determinants of the mechanical performance of metals is not a simple task. Already known physical inspired qualitative relations between 2D microstructure characteristics and 3D mechanical properties can act as the starting point of the investigation. Isotonic regression allows to take into account ordering relations and leads to more efficient and accurate results when the underlying assumptions actually hold. The main goal in this paper is to test order relations in a model inspired by a materials science application. The statistical estimation procedure is described considering three different scenarios according to the knowledge of the variances: known variance ratio, completely unknown variances, variances under order restrictions. New likelihood ratio tests are developed in the last two cases. Both parametric and non-parametric bootstrap approaches are developed for finding the distribution of the test statistics under the null hypothesis. Finally an application on the relation between Geometrically Necessary Dislocations and number of observed microstructure precipitations is shown.

stat.AP↗

arXiv2018

Robust inference for threshold regression models

This paper is concerned with inference in threshold regression models when the practitioners do not know whether at the threshold point the true specification has a kink or a jump. We nest previous works that assume either continuity or discontinuity at the threshold point and develop robust inference methods on the parameters of the model, which are valid under both specifications. In particular, we found that the parameter values under the kink restriction are irregular points of the Hessian matrix of the expected Gaussian quasi-likelihood. This irregularity destroys the asymptotic normality and induces the non-standard cube root convergence rate for the threshold estimate. However, it also enables us to obtain the same asymptotic distribution as in Hansen (2000) for the quasi-likelihood ratio statistic for the unknown threshold up to an unknown scale parameter. We show that this scale parameter can be consistently estimated by a kernel method as long as no higher order kernel is used. Furthermore, we propose to construct confidence intervals for the unknown threshold by bootstrap test inversion, also known as grid bootstrap. Finite sample performances of the grid bootstrap confidence intervals are examined through Monte Carlo simulations. We also implement our procedure to an economic empirical application.

math.ST↗

arXiv2006

Distribution free goodness-of-fit tests for linear processes

This article proposes a class of goodness-of-fit tests for the autocorrelation function of a time series process, including those exhibiting long-range dependence. Test statistics for composite hypotheses are functionals of a (approximated) martingale transformation of the Bartlett $T_p$-process with estimated parameters, which converges in distribution to the standard Brownian motion under the null hypothesis. We discuss tests of different natures such as omnibus, directional and Portmanteau-type tests. A Monte Carlo study illustrates the performance of the different tests in practice.

math.ST↗

arXiv2005

Semiparametric estimation for stationary processes whose spectra have an unknown pole

We consider the estimation of the location of the pole and memory parameter, λ^0 and α, respectively, of covariance stationary linear processes whose spectral density function f(λ) satisfies f(λ)\sim C| λ-λ^0| ^{-α} in a neighborhood of λ^0. We define a consistent estimator of λ^0 and derive its limit distribution Z_{λ^0}. As in related optimization problems, when the true parameter value can lie on the boundary of the parameter space, we show that Z_{λ^0} is distributed as a normal random variable when λ^0\in (0,π), whereas for λ^0=0 or π, Z_{λ^0} is a mixture of discrete and continuous random variables with weights equal to 1/2. More specifically, when λ^0=0, Z_{λ^0} is distributed as a normal random variable truncated at zero. Moreover, we describe and examine a two-step estimator of the memory parameter α, showing that neither its limit distribution nor its rate of convergence is affected by the estimation of λ^0. Thus, we reinforce and extend previous results with respect to the estimation of αwhen λ^0 is assumed to be known a priori. A small Monte Carlo study is included to illustrate the finite sample performance of our estimators.

math.ST↗