Abstract:
In partly linear models, the dependence of the response y on (x T, t) is modeled through the relationship y=x Tβ+g(t)+ε{lunate}, where ε{lunate} is independent of (x T, t). We are interested in developing an estimation procedure that allows us to combine the flexibility of the partly linear models, studied by several authors, but including some variables that belong to a non-Euclidean space. The motivating application of this paper deals with the explanation of the atmospheric SO 2 pollution incidents using these models when some of the predictive variables belong in a cylinder. In this paper, the estimators of β and g are constructed when the explanatory variables t take values on a Riemannian manifold and the asymptotic properties of the proposed estimators are obtained under suitable conditions. We illustrate the use of this estimation approach using an environmental data set and we explore the performance of the estimators through a simulation study. © 2012 Copyright Taylor and Francis Group, LLC.
Registro:
Documento: |
Artículo
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Título: | Partly linear models on Riemannian manifolds |
Autor: | Gonzalez-Manteiga, W.; Henry, G.; Rodriguez, D. |
Filiación: | Departmento de Estadistica e Investigacion Operativa, Universidad de Santiago de Compostela, Santiago de Compostela, Spain Departmento de Matematica, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires and CONICET, CABA, Argentina
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Palabras clave: | environmental data; hypothesis test; non-parametric estimation; partly linear models; Riemannian manifolds |
Año: | 2012
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Volumen: | 39
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Número: | 8
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Página de inicio: | 1797
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Página de fin: | 1809
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DOI: |
http://dx.doi.org/10.1080/02664763.2012.683169 |
Título revista: | Journal of Applied Statistics
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Título revista abreviado: | J. Appl. Stat.
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ISSN: | 02664763
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Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_02664763_v39_n8_p1797_GonzalezManteiga |
Referencias:
- Aneiros-Pérez, G., Quintela del Rìo, G., Plug-in bandwidth choice in partial linear regression models with autoregressive errors (2002) J. Statist. Plann. Inference, 57, pp. 23-48
- Aneiros-Pérez, G., Vieu, F., Semi-functional partial linear regression (2006) Stat. Probab. Lett., 76, pp. 1102-1110
- Bhattacharya, R., Patrangenaru, V., Nonparametric estimation of location and dispersion on Riemannian manifolds (2002) J. Statist. Plann. Inference, 108, pp. 23-35
- Chen, H., Convergence rates for parametric components in a partly linear model (1988) Ann. Statist., 16, pp. 136-146
- Do Carmo, M., (2005) Riemannian Geometry, , Brazil: Projeto Euclides, IMPA
- Engle, R., Granger, C., Rice, J., Weiss, A., Semiparametric estimates of the relation between weather and electricity sales (1986) J. Amer. Statist. Assoc., 81, pp. 310-320
- Ferraty, F., Vieu, F., Nonparametric models for functional data, with application in regression, time-series prediction and curve discrimination (2004) J. Nonparametr. Stat., 16, pp. 111-125
- García-Jurado, I., Gonzalez-Manteiga, W., Prada-Sanchez, J.M., Febrero-Bande, M., Cao, R., Predicting using Box-Jenkins, nonparametric and bootstrap techniques (1995) Technometrics, 37, pp. 303-310
- Hendriks, H., Landsman, Z., Asymptotic data analysis on manifolds (2007) Ann. Statist., 35 (1), pp. 109-131
- Henry, G., Rodriguez, D., Robust nonparametric regression on Riemannian manifolds (2009) J. Nonparametr. Stat., 21 (5), pp. 611-628
- Henry, G., Rodriguez, D., Kernel density estimation on Riemannian manifolds: Asymptotic results (2009) J. Math. Imaging Vision, 43, pp. 235-639
- Liang, H., Asymptotic normality of nonparametric part in partially linear models with measurement error in the nonparametric part (2000) J. statist. plann. inference, 86, pp. 51-62
- Mardia, K., (1972) Statistics of Directional Data, , London: Academic Press
- Pelletier, B., Nonparametric regression estimation on closed Riemannian manifolds (2006) J. Nonparametr. Stat., 18, pp. 57-67
- Pennec, X., Intrinsic statistics on Riemannian manifolds: Basic tools for geometric measurements (2006) J. Math. Imaging Vision, 25, pp. 127-154
- Prada-Sanchez, J.M., Febrero, M., Cotos-Yañez, T., Gonzalez-Manteiga, W., Bermudez-Cela, J., Lucas-Dominguez, T., Prediction of SO 2 pollution incidents near a power station using partially linear models and an historical matrix of predictor-response vectors (2000) Environmetrics, 11, pp. 209-225
- Speckman, P., Kernel smoothing in partial linear models (1988) J. Roy. Statist. Soc. Ser. B, 50, pp. 413-436
Citas:
---------- APA ----------
Gonzalez-Manteiga, W., Henry, G. & Rodriguez, D.
(2012)
. Partly linear models on Riemannian manifolds. Journal of Applied Statistics, 39(8), 1797-1809.
http://dx.doi.org/10.1080/02664763.2012.683169---------- CHICAGO ----------
Gonzalez-Manteiga, W., Henry, G., Rodriguez, D.
"Partly linear models on Riemannian manifolds"
. Journal of Applied Statistics 39, no. 8
(2012) : 1797-1809.
http://dx.doi.org/10.1080/02664763.2012.683169---------- MLA ----------
Gonzalez-Manteiga, W., Henry, G., Rodriguez, D.
"Partly linear models on Riemannian manifolds"
. Journal of Applied Statistics, vol. 39, no. 8, 2012, pp. 1797-1809.
http://dx.doi.org/10.1080/02664763.2012.683169---------- VANCOUVER ----------
Gonzalez-Manteiga, W., Henry, G., Rodriguez, D. Partly linear models on Riemannian manifolds. J. Appl. Stat. 2012;39(8):1797-1809.
http://dx.doi.org/10.1080/02664763.2012.683169