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2018 | OriginalPaper | Buchkapitel

On Kernel Smoothing with Gaussian Subordinated Spatial Data

verfasst von : S. Ghosh

Erschienen in: Nonparametric Statistics

Verlag: Springer International Publishing

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Abstract

We address estimation of a deterministic function μ, that is the mean of a spatial process y(s) in a nonparametric regression context. Here s denotes a spatial coordinate in \({R}_+^2.\) Given k = n 2 observations, the aim is to estimate μ assuming that y has finite variance, and that the regression errors \(\epsilon (\mathbf {s}) = y(\mathbf {s}) - {E}\left \{ y(\mathbf {s})\right \}\) are Gaussian subordinated.

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Literatur
1.
Zurück zum Zitat Beran, J., Feng, Y., Ghosh, S., & Kulik, R. (2013). Long memory processes - probabilistic properties and statistical models. Heidelberg: Springer. Beran, J., Feng, Y., Ghosh, S., & Kulik, R. (2013). Long memory processes - probabilistic properties and statistical models. Heidelberg: Springer.
2.
Zurück zum Zitat Beran, J., Ghosh, S., & Schell, D. (2009). Least square estimation for stationary lattice processes with long-memory. Journal of Multivariate Analysis, 100, 2178–2194. Beran, J., Ghosh, S., & Schell, D. (2009). Least square estimation for stationary lattice processes with long-memory. Journal of Multivariate Analysis, 100, 2178–2194.
3.
Zurück zum Zitat Bierens, H. J. (1983). Uniform consistency of kernel estimators of a regression function under generalized conditions. Journal of the American Statistical Association, 77, 699–707. Bierens, H. J. (1983). Uniform consistency of kernel estimators of a regression function under generalized conditions. Journal of the American Statistical Association, 77, 699–707.
4.
Zurück zum Zitat Breuer, P., & Major, P. (1983). Central limit theorems for nonlinear functionals of Gaussian fields. Journal of Multivariate Analysis, 13, 425–441. Breuer, P., & Major, P. (1983). Central limit theorems for nonlinear functionals of Gaussian fields. Journal of Multivariate Analysis, 13, 425–441.
5.
Zurück zum Zitat Csörgö, S., & Mielniczuk, J. (1995). Nonparametric regression under long-range dependent normal errors. The Annals of Statistics, 23, 1000–1014. Csörgö, S., & Mielniczuk, J. (1995). Nonparametric regression under long-range dependent normal errors. The Annals of Statistics, 23, 1000–1014.
6.
Zurück zum Zitat Csörgö, S., & Mielniczuk, J. (1996). The empirical process of a short-range dependent stationary sequence under Gaussian subordination. Probability Theory and Related Fields, 104, 15–25. Csörgö, S., & Mielniczuk, J. (1996). The empirical process of a short-range dependent stationary sequence under Gaussian subordination. Probability Theory and Related Fields, 104, 15–25.
7.
Zurück zum Zitat Dahlhaus, R. (1997). Fitting time series models to nonstationary processes. The Annals of Statistics, 25, 1–37. Dahlhaus, R. (1997). Fitting time series models to nonstationary processes. The Annals of Statistics, 25, 1–37.
8.
Zurück zum Zitat Diggle, P. J. (1990). Time series: A biostatistical introduction. Oxford: Oxford University Press. Diggle, P. J. (1990). Time series: A biostatistical introduction. Oxford: Oxford University Press.
9.
Zurück zum Zitat Dobrushin, R. L., & Major, P. (1979). Non-central limit theorems for non-linear functional of Gaussian fields. Probability Theory and Related Fields, 50, 27–52. Dobrushin, R. L., & Major, P. (1979). Non-central limit theorems for non-linear functional of Gaussian fields. Probability Theory and Related Fields, 50, 27–52.
10.
Zurück zum Zitat Ghosh, S. (2009). The unseen species number revisited. Sankhya-B, 71, 137–150. Ghosh, S. (2009). The unseen species number revisited. Sankhya-B, 71, 137–150.
11.
Zurück zum Zitat Ghosh, S. (2015). Computation of spatial Gini coefficients. Communications in Statistics - Theory and Methods, 44, 4709–4720. Ghosh, S. (2015). Computation of spatial Gini coefficients. Communications in Statistics - Theory and Methods, 44, 4709–4720.
12.
Zurück zum Zitat Ghosh, S. (2015). Surface estimation under local stationarity. Journal of Nonparametric Statistics, 27, 229–240. Ghosh, S. (2015). Surface estimation under local stationarity. Journal of Nonparametric Statistics, 27, 229–240.
13.
Zurück zum Zitat Ghosh, S. (2018). Kernel smoothing. Principles, methods and applications. Hoboken: Wiley. Ghosh, S. (2018). Kernel smoothing. Principles, methods and applications. Hoboken: Wiley.
14.
Zurück zum Zitat Ghosh, S., & Draghicescu, D. (2002). An algorithm for optimal bandwidth selection for smooth nonparametric quantiles and distribution functions. In Y. Dodge (Ed.), Statistics in industry and technology: Statistical data analysis based on the L 1-norm and related methods (pp. 161–168). Basel: Birkhäuser Verlag. Ghosh, S., & Draghicescu, D. (2002). An algorithm for optimal bandwidth selection for smooth nonparametric quantiles and distribution functions. In Y. Dodge (Ed.), Statistics in industry and technology: Statistical data analysis based on the L 1-norm and related methods (pp. 161–168). Basel: Birkhäuser Verlag.
15.
Zurück zum Zitat Ghosh, S., & Draghicescu, D. (2002). Predicting the distribution function for long-memory processes. International Journal of Forecasting, 18, 283–290. Ghosh, S., & Draghicescu, D. (2002). Predicting the distribution function for long-memory processes. International Journal of Forecasting, 18, 283–290.
16.
Zurück zum Zitat Major, P. (1981). Limit theorems for non-linear functionals of Gaussian sequences. Probability Theory and Related Fields, 57, 129–158. Major, P. (1981). Limit theorems for non-linear functionals of Gaussian sequences. Probability Theory and Related Fields, 57, 129–158.
17.
Zurück zum Zitat Parzen, E. (1962). On estimation of a probability density function and mode. The Annals of Mathematical Statistics, 33, 1065–1076. Parzen, E. (1962). On estimation of a probability density function and mode. The Annals of Mathematical Statistics, 33, 1065–1076.
18.
Zurück zum Zitat Priestley, M. B., & Chao, M. T. (1972). Non-parametric function fitting. Journal of the Royal Statistical Society. Series B, 34, 385–392. Priestley, M. B., & Chao, M. T. (1972). Non-parametric function fitting. Journal of the Royal Statistical Society. Series B, 34, 385–392.
19.
Zurück zum Zitat Robinson, P. M. (1997). Large-sample inference for nonparametric regression with dependent errors. The Annals of Statistics, 25, 2054–2083. Robinson, P. M. (1997). Large-sample inference for nonparametric regression with dependent errors. The Annals of Statistics, 25, 2054–2083.
20.
Zurück zum Zitat Silverman, B. W. (1986). Density estimation. New York: Chapman and Hall. Silverman, B. W. (1986). Density estimation. New York: Chapman and Hall.
21.
Zurück zum Zitat Taqqu, M. S. (1975). Weak convergence to fractional Brownian motion and to the Rosenblatt process. Probability Theory and Related Fields, 31, 287–302. Taqqu, M. S. (1975). Weak convergence to fractional Brownian motion and to the Rosenblatt process. Probability Theory and Related Fields, 31, 287–302.
22.
Zurück zum Zitat Taqqu, M. S. (1979). Convergence of integrated processes of arbitrary Hermite rank. Probability Theory and Related Fields, 50, 53–83. Taqqu, M. S. (1979). Convergence of integrated processes of arbitrary Hermite rank. Probability Theory and Related Fields, 50, 53–83.
23.
Zurück zum Zitat Wand, M. P., & Jones, M. C. (1995). Kernel smoothing. London: Chapman and Hall. Wand, M. P., & Jones, M. C. (1995). Kernel smoothing. London: Chapman and Hall.
24.
Zurück zum Zitat Wu, F. (2016). On Optimal Surface Estimation under Local Stationarity - An Application to Swiss National Forest Inventory Data. Master thesis 2016, ETH, Zürich. Wu, F. (2016). On Optimal Surface Estimation under Local Stationarity - An Application to Swiss National Forest Inventory Data. Master thesis 2016, ETH, Zürich.
Metadaten
Titel
On Kernel Smoothing with Gaussian Subordinated Spatial Data
verfasst von
S. Ghosh
Copyright-Jahr
2018
DOI
https://doi.org/10.1007/978-3-319-96941-1_19

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