Estimation in semiparametric spatial regression

Also published in: arXiv:math/0608053v1Nonparametric methods have been very popular in the last couple of decades in time series and regression, but no such development has taken place for spatial models. A rather obvious reason for this is the curse of dimensionality. For spatial data on a grid evaluating the conditional mean given its closest neighbors requires a four-dimensional nonparametric regression. In this paper a semiparametric spatial regression approach is proposed to avoid this problem. An estimation procedure based on combining the so-called marginal integration technique with local linear kernel estimation is developed in the semiparametric spatial regression setting. Asymptotic distributions are established under some mild conditions. The same convergence rates as in the one-dimensional regression case are established. An application of the methodology to the classical Mercer and Hall wheat data set is given and indicates that one directional component appears to be nonlinear, which has gone unnoticed in earlier analysesJiti Gao, Zudi Lu and Dag Tjøsthei

On the Reliability of Cross Correlation Function Lag Determinations in Active Galactic Nuclei

Many AGN exhibit a highly variable luminosity. Some AGN also show a pronounced time delay between variations seen in their optical continuum and in their emission lines. In effect, the emission lines are light echoes of the continuum. This light travel-time delay provides a characteristic radius of the region producing the emission lines. The cross correlation function (CCF) is the standard tool used to measure the time lag between the continuum and line variations. For the few well-sampled AGN, the lag ranges from 1-100 days, depending upon which line is used and the luminosity of the AGN. In the best sampled AGN, NGC 5548, the H_beta lag shows year-to-year changes, ranging from about 8.7 days to about 22.9 days over a span of 8 years. In this paper it is demonstrated that, in the context of AGN variability studies, the lag estimate using the CCF is biased too low and subject to a large variance. Thus the year-to-year changes of the measured lag in NGC 5548 do not necessarily imply changes in the AGN structure. The bias and large variance are consequences of finite duration sampling and the dominance of long timescale trends in the light curves, not due to noise or irregular sampling. Lag estimates can be substantially improved by removing low frequency power from the light curves prior to computing the CCF.Comment: To appear in the PASP, vol 111, 1999 Nov; 37 pages; 10 figure

Problem of estimating the autocorrelation function of spatio-temporal variables. Technical report No. 6. [Applications in statistical air pollution research]

Motivated by problems in statistical air pollution research, we propose an estimate for the autocorrelation function for spatio-temporal variables. The estimate is meaningful for non-integer lags and for irregularly positioned data points. The statistical properties of the estimate are studied in a special case. Possible applications to air pollution modelling are briefly discussed

Évaluation de la connectivité verticale avec les eaux souterraines en milieu alluvial

Dans les écosystèmes aquatiques, la restauration de la connectivité verticale, l’amélioration des échanges entre l'eau souterraine et l'eau de surface, est un enjeu négligé. Les objectifs de ce travail sont: - L'évaluation de la connectivité verticale dans huit annexes fluviales du Haut-Rhône français - L'évaluation de la pertinence d'une méthode récente, utilisant des sticks en bois insérés dans les sédiments pour mesurer indirectement la connectivité verticale. - La proposition d'une méthode simple permettant d'estimer la connectivité verticale dans les écosystèmes alluviaux. Des mesures de concentration en oxygène dissous, de conductivité et de température ont été effectuées dans l'eau de surface et dans l'eau souterraine lors de trois campagnes, ainsi que l'utilisation de sticks en bois et de mesures continues de température. Les variables mesurées permettent de distinguer des sites ayant des fréquences de connexion au fleuve voisines ou des histoires comparables. Des différences de connectivité verticale peuvent être mises en évidence pour des sites dont les sédiments sont en majorité fins et organiques. Le gradient de connectivité verticale établit dans cette étude n'est pas indépendant du gradient de connectivité latérale. Les méthodes utilisées pour estimer la connectivité verticale ne donnent pas la même information. La méthode de Marmonier et al (2004) permet l'obtention rapide de résultats, mais ceux-ci donnent une information grossière. Ils ont tendance à suivre les différences de granulométrie qui sont influencées par le gradient de connectivité latérale. Parmi les variables physico-chimiques mesurées ponctuellement, l'écart entre la concentration en oxygène dissous dans l'eau souterraine et dans l'eau de surface semble un bon indicateur de la connectivité verticale. Toutefois les variables les plus prometteuses, semblent être celles issues des mesures continues de température. Il est important de mettre en place des méthodes simples d'évaluation de la connectivité verticale permettant un suivi des effets des restaurations, mais aussi pour étudier les conséquences du réchauffement climatique sur les annexes fluviales

Estimation in threshold autoregressive models with a stationary and a unit root regime

This paper treats estimation in a class of new nonlinear threshold autoregressive models with both a stationary and a unit root regime. Existing literature on nonstationary threshold models has basically focused on models where the nonstationarity can be removed by differencing and/or where the threshold variable is stationary. This is not the case for the process we consider, and nonstandard estimation problems are the result. This paper proposes a parameter estimation method for such nonlinear threshold autoregressive models using the theory of null recurrent Markov chains. Under certain assumptions, we show that the ordinary least squares (OLS) estimators of the parameters involved are asymptotically consistent. Furthermore, it can be shown that the OLS estimator of the coefficient parameter involved in the stationary regime can still be asymptotically normal while the OLS estimator of the coefficient parameter involved in the nonstationary regime has a nonstandard asymptotic distribution. In the limit, the rate of convergence in the stationary regime is asymptotically proportional to n-14, whereas it is n-1 in the nonstationary regime. The proposed theory and estimation method are illustrated by both simulated data and a real data example. © 2012 Elsevier B.V. All rights reserved.Jiti Gaoa, Dag Tjøstheim, Jiying Yi

Estimation in threshold autoregressive models with nonstationarity

This paper proposes a class of new nonlinear threshold autoregressive models with both stationary and nonstationary regimes. Existing literature basically focuses on testing for a unit root structure in a threshold autoregressive model. Under the null hypothesis, the model reduces to a simple random walk. Parameter estimation then becomes standard under the null hypothesis. How to estimate parameters involved in an alternative nonstationary model, when the null hypothesis is not true, becomes a nonstandard estimation problem. This is mainly because models under such an alternative are normally null recurrent Markov chains. This paper thus proposes to establish a parameter estimation method for such nonlinear threshold autoregressive models with null recurrent structure. Under certain assumptions, we show that the ordinary least squares (OLS) estimates of the parameters involved are asymptotically consistent. Furthermore, it can be shown that the OLS estimator of the coefficient parameter involved in the stationary regime can still be asymptotically normal while the OLS estimator of the coefficient parameter involved in the nonstationary regime has a nonstandard asymptotic distribution. In the limit, the rate of convergence in the stationary regime is n^(-1/4) , whereas it is n^(-1) in the nonstationary regime. The proposed theory and estimation method is illustrated by both simulated and real data examples.http://lx2.saas.hku.hk/Conference/NTS2009/Conference%20Program%20List%28website%29.pd