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Full-Text Articles in Engineering
Derivative Estimation With Local Polynomial Fitting, Kris De Brabanter, Jos De Brabanter, Bart De Moor, Irene Gijbels
Derivative Estimation With Local Polynomial Fitting, Kris De Brabanter, Jos De Brabanter, Bart De Moor, Irene Gijbels
Kris De Brabanter
We present a fully automated framework to estimate derivatives nonparametrically without estimating the regression function. Derivative estimation plays an important role in the exploration of structures in curves (jump detection and discontinuities), comparison of regression curves, analysis of human growth data, etc. Hence, the study of estimating derivatives is equally important as regression estimation itself. Via empirical derivatives we approximate the qth order derivative and create a new data set which can be smoothed by any nonparametric regression estimator. We derive L1 and L2 rates and establish consistency of the estimator. The new data sets created by this technique are …
Kernel Regression In The Presence Of Correlated Errors, Kris De Brabanter, Jos De Brabanter, Johan A.K. Suykens, Bart De Moor
Kernel Regression In The Presence Of Correlated Errors, Kris De Brabanter, Jos De Brabanter, Johan A.K. Suykens, Bart De Moor
Kris De Brabanter
It is a well-known problem that obtaining a correct bandwidth and/or smoothing parameter in nonparametric regression is difficult in the presence of correlated errors. There exist a wide variety of methods coping with this problem, but they all critically depend on a tuning procedure which requires accurate information about the correlation structure. We propose a bandwidth selection procedure based on bimodal kernels which successfully removes the correlation without requiring any prior knowledge about its structure and its parameters. Further, we show that the form of the kernel is very important when errors are correlated which is in contrast to the …