where K is the kernel of the integral. Given the input signal X , Y represents the output signal. The smoothness of the output depends on the smoothness of the kernel. We assume the kernel to be unimodal and isotropic. When the kernel is isotropic, it has radial symmetry and should be invariant under rotation. So it has the form K(t, s) = f(‖t− s‖) for some smooth function f . Since the kernel ...

In the study of smoothing spline estimators, some convolution-kernellike properties of the Green’s function for an appropriate boundary value problem, depending on the design density, are needed. For the uniform density, the Green’s function can be computed more or less explicitly. Then, integral equation methods are brought to bear to establish the kernel-like properties of said Green’s functi...

The kernel functions (kernels) can be used in many types of nonparametric methods estimation of the density function of a random variable, estimation of the hazard function or the regression function. These methods belong to the most efficient non-parametric methods. Another nonparametric method uses so-called frames overcomplet systems of functions of some type. This paper compares the kernel ...

Almost sure bounds are established on the uniform error of smoothing spline estimators in nonparametric regression with random designs. Some results of Einmahl and Mason (2005) are used to derive uniform error bounds for the approximation of the spline smoother by an “equivalent” reproducing kernel regression estimator, as well as for proving uniform error bounds on the reproducing kernel regre...

New SPH equations including fully variable smoothing length aspects and its implementation are proposed in this paper. Unlike the existing adaptive kernel SPH method, the fully variable smoothing lengths effects have been considered essentially in the scheme based on the adaptive symmetrical kernel estimation. Among the new equations, the evolution equation of density is derived in essence, it ...

A spline-backfitted kernel smoothing method is proposed for partially linear additive model. Under assumptions of stationarity and geometric mixing, the proposed function and parameter estimators are oracally efficient and fast to compute. Such superior properties are achieved by applying to the data spline smoothing and kernel smoothing consecutively. Simulation experiments with both moderate ...

Previous work on state-dependent adaptive importance sampling techniques for the simulation of rare events in Markovian queueing models used either no smoothing or a parametric smoothing technique, which was known to be non-optimal. In this paper, we introduce the use of kernel smoothing in this context. We derive expressions for the smoothed transition probabilities, compare several variations...

In this paper, a neurofuzzy adaptive control framework for discrete-time systems based on kernel smoothing regression is developed. Kernel regression is a nonparametric statistics technique used to determine a regression model where no model assumption has been done. Due to similarity with fuzzy systems, kernel smoothing is used to obtain knowledge about the structure of the fuzzy system and th...

Non parametric regression methods can be presented in two main clusters. The one of smoothing splines methods requiring positive kernels and the other one known as Nonparametric Kernel Regression allowing the use of non positive kernels such as the Epanechnikov kernel. We propose a generalization of the smoothing spline method to include kernels which are still symmetric but not positive semi d...

S For independent data, it is well known that kernel methods and spline methods are essentially asymptotically equivalent (Silverman, 1984). However, recent work of Welsh et al. (2002) shows that the same is not true for clustered/longitudinal data. Splines and conventional kernels are different in localness and ability to account for the within-cluster correlation. We show that a smoothi...