Abstract
The simulation of statistical models in a computer is a fundamental aspect of research in the field of nonparametric curve estimation. Methods such as the FFT (Fast Fourier Transform) or WARP (Weighted Average of Rounded Points) have been developed and analysed for computer implementation of the different techniques in this realm, with the aim of reducing the computation time as much as possible. In this work we analyse two techniques with this objective. These are the vectorization of the source code in which the different algorithms are implemented, and their distributed execution. It can be observed that the vectorization of the programs can improve the results obtained with techniques such as the FFT or WARP, or, in some cases, can prevent the use of these.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Altman, N. (1990) Kernel smoothing of data with correlated errors. Journal of American Statistical Association, 85, 749–59.
Cao, R., Cuevas, A., González-Manteiga, W. (1994) A comparative study of several smoothing methods in density estimation. Computational Statistics and Data Analysis, 17, 153–76.
Chu, C.K., Marron, J.S. (1991) Comparisons of two bandwidth selectors with dependent errors. Annals of Statistics, 4, 1906–18.
Fan, J., Marron, J.S. (1994) Fast implementations of nonparametric curve estimators. Journal of Computational and Graphical Statistics, 3, 35–56.
Fraguela B.B. (1994) Evaluación de Tecnicas de Vectorización: Aplicación a Algoritmos para la Estimación No Paramétrica de Curvas de Regresión. Master thesis, Departamento de Electrónica y Sistemas, Universidad de La Coruña.
Gasser, T., Müller, H.G. (1979) Kernel estimation of regression functions. In Gasser and Rosenblatt (eds) Smoothing Techniques for Curve Estimation, Springer-Verlag.
Geist, G. A., Beguelin, A., Dongarra, J.J., Jiang, W., Manchel, R., Sunderam, V.S. (1993) PVM 3 User's Guide and Reference Manual. Technical Report ORNL/TM-12187, Oak Ridge National Laboratory.
Härdle, W. (1987) Resistant smoothing using the Fast Fourier Transform. Applied Statistics, 36, 104–11.
Härdle, W. (1990a) Applied Nonparametric Regression, Oxford University Press.
Härdle, W. (1990b) Smoothing Techniques with Implementation in S, Springer-Verlag.
Härdle, W., Hall, P., Marron, J.S. (1988) How far are automatically chosen regression smoothing parameters from their optimum? Journal of American Statistical Association, 83, 86–95.
Härdle, W., Vieu, P. (1992) Kernel regression smoothing of time series. Journal of Time Series Analysis, 13, 209–32.
Hart, J., Vieu, P. (1990) Data-driven bandwidth choice for density estimation based on dependent data. Annals of Statistics, 18, 873–90.
Hennesy, J.L., Patterson, D.A. (1990) Computer Architecture. A Quantitative Approach, Morgan Kaufmann Publishers, Inc.
Herrmann, E., Gasser, T., Kneip, A. (1992) Choice of bandwidth for kernel regression when residuals are correlated. Biometrika, 79, 783–95.
Müller, H.G. (1988) Nonparametric analysis of longitudinal data, Lecture Notes in Statistics, 46. Springer-Verlag.
Nadaraya, E.A. (1964) On estimating regression. Theory of Probability and Applications, 10, 186–90.
Priestley, M.B., Chao, M.T. (1972) Nonparametric function fitting. Journal of the Royal Statistical Society, Series B, 34, 385–92.
Quintela-del-Río, A. (1994a) A plug-in technique in nonparametric regression with dependence. Communications in Statistics, Theory and Methods, 23, 2581–603.
Quintela-del-Río, A. (1994b) Comparison of bandwidth selectors in nonparametric regression under dependence. To appear in Computational Statistics and Data Analysis.
Rice, J. (1984) Bandwidth choice for nonparametric regression. Annals of Statistics, 12, 1215–30.
Silverman, B. W. (1986) Density Estimation for Statistics and Data Analysis. Chapman and Hall.
Sunderam, V.S., Geist, G.A., Dongarra, J.J., Manchek, R. (1994) The PVM concurrent computing system: evolution, experiences and trends. Parallel Computing, 20, 531–45.
Wand, M.P., Jones, M.C. (1995), Kernel Smoothing, Chapman and Hall.
Watson, G. S. (1964) Smooth regression analysis. Sankhyā, Series A, 26, 359–72.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Doallo-Biempica, R., Fraguela-Rodríguez, B.B. & Quintela-Del-Río, A. Evaluation of vectorization/parallelization techniques: application to nonparametric curve estimation. Stat Comput 6, 347–351 (1996). https://doi.org/10.1007/BF00143555
Issue Date:
DOI: https://doi.org/10.1007/BF00143555