When spatial data are correlated, currently available data-driven smoothing parameter selection methods for nonparametric regression will often fail to provide useful results. The authors propose a method that adjusts the generalized cross-validation criterion for the effect of spatial correlation in the case of bivariate local polynomial regression. Their approach uses a pilot fit to the data and the estimation of a parametric covariance model. The method is easy to implement and leads to improved smoothing parameter selection, even when the covariance model is misspecified. The methodology is illustrated using water chemistry data collected in a survey of lakes in the Northeastern United States.M6thodes de selection de parametres de lissage pour la regression non parametrique lorsque les erreurs presentent une correlation spatiale R h m t : Lorsque des donnkes spatiales sont codltes. les mtthodes adaptatives actuellement disponibles pour la selection de paramttres de lissage s'avtrent souvent inadtquates en rtgression non paramttrique. Les auteurs proposent une mtthode d'ajustement du crithre de validation croiste gtntraliste tenant compte de la codlation spatiale dans le cas de la dgression polynomiale locale bivarike. Leur approche s'appuie sur un ajustement pilote des donntes et sur I'estimation d'un modtle de covariance paramttrique. Facile B implanter, la mtthode amtliore nettement la stlection des paramttres de lissage, meme quand le modtle de covariance est ma1 sptcifit. Le propos est illustrt au moyen de r6sultats d'anaiyses chimiques effectutes sur des tchantillons d'eau pr6lev6s dans le cadre d'une ttude sur les lacs du nord-est des Etats-Unis.

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SUM M ARYHydrothermal time (HTT) is a valuable environmental synthesis to predict weed emergence. However, weed scientists face practical problems in determining the best soil depth at which to calculate it. Two different types of measures are proposed for this: moment-based indices and probability density-based indices. Due to the monitoring process, it is not possible to observe the exact emergence time of every seedling; therefore, emergence times are not observed individually, seedling by seedling, but in an aggregated way. To address these facts, some new methods to estimate the proposed indices are derived, using grouped data estimators and kernel density estimators. The proposed methods have been exemplified with an emergence data set of Bromus diandrus. The results indicate that hydrothermal timing at 50 mm is more useful than that at 10 mm.

In this paper, we study the nonparametric estimation of the regression function and its derivatives using weighted local polynomial fitting. Consider the fixed regression model and suppose that the random observation error is coming from a strictly stationary stochastic process. Expressions for the bias and the variance array of the estimators of the regression function and its derivatives are obtained and joint asymptotic normality is established. The influence of the dependence of the data is observed in the expression of the variance. We also propose a variable bandwidth selection procedure. A simulation study and an analysis with real economic data illustrate the proposed selection method.

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