Kernel Regression Estimation Using Repeated Measurements Data

Hart, Jeffrey D.; Wehrly, Thomas E.

doi:10.1080/01621459.1986.10478377

Cited by 190 publications

(119 citation statements)

References 15 publications

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“…which is the bandwidth given by Hart and Wehrly [7]. (3) Consider a transformation of the time scale that can produce non-stationary autocovariance of the form ρ(x, y) = σ 2 ρ |x λ −y λ |/λ for (x, y) ∈ [0, 1] 2 , σ 2 > 0, 0 < ρ < 1 and λ > 0 (see, Núñez-Antón and Woodworth, [10]).…”

Section: The Following Error Processes Satisfy Assumptions (I) (Ii) mentioning

confidence: 99%

“…. , m}, when the x i 's are known constants such that 0 x 1 < x 2 < · · · < x n 1 with max i |x i − x i−1 | = O(1/n), is given for x ∈ [0, 1], by (see, Gasser and Müller, [5], and Hart and Wehrly, [7]): (iv) The autocovariance function ρ has at least 2 continuous mixed partial derivatives such that:…”

Section: Estimation Of the Average Growth Curvementioning

confidence: 99%

“…Fraiman and Meloche [4] showed that when the errors are correlated (stationary or not), the kernel-type estimators are not consistent. Although repeated measurements can naturally arise in practical situations, they can make the estimators of the curve f asymptotically consistent (see Hart and Wehrly, [7], and the comments of Härdle, [6]). Other models that take into account the individual effects are considered by Boularan et al [2] and Núñez-Antón et al [9], known respectively as two-and three-stage additive models, with specific parametric non-stationary covariance structure.…”

Section: Introductionmentioning

confidence: 99%

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Non-parametric estimation of the average growth curve with a general non-stationary error process

Benhenni

Rachdi

2006

Comptes Rendus. Mathématique

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The non-parametric estimation of the average growth curve has been extensively studied in both stationary and some nonstationary particular situations. In this Note, we consider the statistical problem of estimating the average growth curve for a fixed design model with a non-stationary error process. The non-stationarity considered here is of a general form, and this note may be considered as an extension of previous results. The optimal bandwidth is shown to depend on the singularity of the autocovariance function of the error process along the diagonal. To cite this article: K. Benhenni, M. Rachdi, C. R. Acad. Sci. Paris, Ser. I 343 (2006). RésuméEstimation non paramétrique de la courbe de croissance pour un processus d'erreur non stationnaire. L'estimation non paramétrique de la courbe de croissance moyenne pour des données répétées et avec un processus d'erreur non stationnaire a été étudiée, pour des formes particulières de la fonction d'autocovariance, par plusieurs auteurs. Pour ce même problème, nous avons étudié l'estimation de la fonction de croissance avec un processus d'erreur non stationnaire généralisé (pas de forme spécifique de sa fonction d'autocovariance). La fenêtre optimale obtenue dépend de la singularité de la fonction d'autocovariance sur la diagonale. Pour citer cet article : K. Benhenni, M. Rachdi, C. R. Acad. Sci. Paris, Ser. I 343 (2006).

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Section: The Following Error Processes Satisfy Assumptions (I) (Ii) mentioning

confidence: 99%

Section: Estimation Of the Average Growth Curvementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Non-parametric estimation of the average growth curve with a general non-stationary error process

Benhenni

Rachdi

2006

Comptes Rendus. Mathématique

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“…, n} are usually taken equally spaced in time, series data, but other type of sampling designs can also be considered such as deterministic regular (non-uniform) designs and random designs. Although repeated measurements can naturally arise in practical situations, they can make the estimators of the curve f asymptotically consistent, as was pointed out by Hart and Wehrly [6] and the comments of Härdle [5].…”

Section: Introductionmentioning

confidence: 95%

Non-parametric estimation of the average growth curve from quantized observations and correlated errors

Benhenni

Rachdi

2005

Comptes Rendus. Mathématique

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“…In order to ensure the proper calculation of the covariance function, which will be the main structural characteristic of the general knowledge base G as stated previously, it is necessary to work on a homogeneous RF. Detrending of the dataset is done by the application of a Gaussian kernel on it (Hart and Wehrly 1986). The estimated mean trend in the case of ammonium is shown in Fig.…”

Section: The Prior Stagementioning

confidence: 99%

Uncertainty management of a hydrogeological data set in a greek lignite basin, using BME

Modis

Vatalis²,

Papantonopoulos

et al. 2009

Stoch Environ Res Risk Assess

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The occurrence of chemical pollutants in ground water is an issue of considerable interest. In the case of Ptolemais lignite opencast mining area in Greece, ammonium, nitrites, nitrates, iron total and total manganese concentrations, as well as various other elements have been monitored since the early 2000s through a borehole network. The continuous, though, alteration of the surface topography due to the intensive mining works, limits the life span of the water boreholes and results to irregular spatiotemporal distribution of the samples. Regarding the problem of mapping the water contamination, the coarse and irregular sampling pattern, combined with absence of seasonal variations and temporal trends, does not facilitate spatiotemporal processing of the data. On the other hand, a mere spatial analysis requires the attribution of the whole set of monitored values for each borehole, to a single point in space. The objective of this work is to develop a methodology to cope with the problem of uncertainty caused due to the above assumptions. The proposed solution is based on the consideration of interval data. The Bayesian maximum entropy (BME) theory (Christakos, Modern spatiotemporal geostatistics. Oxford University Press, New York, 2000) is an essential component of this methodology. The main reason for this is that it is the only theory in the framework of Geostatistics that offers powerful tools to merge the uncertainty sources with the rest of conventional measurements. This ability is a result of its generalized view on the problem of estimation that focuses on the knowledge of a natural variable and not the variable itself. The application of the proposed methodology led to sharper posterior distributions, an indication of the increased certainty in estimated values which is induced by the broader utilization of data.

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Kernel Regression Estimation Using Repeated Measurements Data

Cited by 190 publications

References 15 publications

Non-parametric estimation of the average growth curve with a general non-stationary error process

Non-parametric estimation of the average growth curve with a general non-stationary error process

Non-parametric estimation of the average growth curve from quantized observations and correlated errors

Uncertainty management of a hydrogeological data set in a greek lignite basin, using BME

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