Kernel Modification Research Articles

Local Regression: Automatic Kernel Carpentry

A kernel smoother is an intuitive estimate of a regression function or conditional expectation; at each point $x_0$ the estimate of $E(Y\mid x_0)$ is a weighted mean of the sample $Y_i$, with observations close to $x_0$ receiving the largest weights. Unfortunately this simplicity has flaws. At the boundary of the predictor space, the kernel neighborhood is asymmetric and the estimate may have substantial bias. Bias can be a problem in the interior as well if the predictors are nonuniform or if the regression function has substantial curvature. These problems are particularly severe when the predictors are multidimensional. A variety of kernel modifications have been proposed to provide approximate and asymptotic adjustment for these biases. Such methods generally place substantial restrictions on the regression problems that can be considered; in unfavorable situations, they can perform very poorly. Moreover, the necessary modifications are very difficult to implement in the multidimensional case. Local regression smoothers fit lower-order polynomials in $x$ locally at $x_0$, and the estimate of $f(x_0)$ is taken from the fitted polynomial at $x_0$. They automatically, intuitively and simultaneously adjust for both the biases above to the given order and generalize naturally to the multidimensional case. They also provide natural estimates for the derivatives of $f$, an approach more attractive than using higher-order kernel functions for the same purpose.

Change-Points in Nonparametric Regression Analysis

an otherwise smooth regression model are proposed. The assumptions needed are much weaker than those made in parametric models. The proposed estimators apply as well to the detection of discontinuities in derivatives and therefore to the detection of change-points of slope and of higher order curvature. The proposed estimators are based on a comparison of left and right one-sided kernel smoothers. Weak convergence of a stochastic process in local differences to a Gaussian process is established for properly scaled versions of estimators of the location of a change-point. The continuous mapping theorem can then be invoked to obtain asymptotic distributions and corresponding rates of convergence for change-point estimators. These rates are typically faster than n- 1/2. Rates of global LP convergence of curve estimates with appropriate kernel modifications adapting to estimated change-points are derived as a consequence. It is shown that these rates of convergence are the same as if the location of the change-point was known. The methods are illustrated by means of the well known data on the annual flow volume of the Nile river between 1871 and 1970. 1. Introduction. Nonparametric regression methods are usually applied in order to obtain a smooth fit of a regression curve without having to specify a parametric class of regression functions. Sometimes a generally smooth curve might contain an isolated discontinuity or change-point in the curve or in a (possibly higher order) derivative, and in many cases interest focuses on the occurrence of such change-points. In parametric approaches to the regression change-point problem, simple linear regressions before and after a possible change-point are assumed, and then the possibility of a discontinuity in the form of a jump or of a jump in the first derivative, or, equivalently, a slope change, is incorporated into the model; see for instance Hinkley (1969) and Brown, Durbin and Evans (1975). The analysis of change-points which describe sudden, localized changes typically occurring in economics, medicine and the physical sciences has recently found increasing interest. General smoothness assumptions, allowing for a large class of regression functions to be considered, seem to be more appropriate in a variety of applied problems than parametric modelling. An

Intelligent I/O rule-based input/output processing for operating systems

IntelligentI/O is a rule based general model for performing "intelligent" processing of Input/Output operations in an Operating System. In a new interface layer between the applications and the kernel I/O functions, rules determine actions to be performed at I/O time which in turn invoke programs in user space. IntelligentI/O permits complete implementation in user space applications that would normally require ad-hoc kernel modifications such as a Network File System. It also serves to implement features that would normally have to be embedded in an application, such as Automatic Format Conversion or Revision Tracking. We later present SuperFile, a simple yet powerful existing implementation of the IntelligentI/O model, together with a number of applications developed using SuperFile.

Reformulation of Stokes's theory for higher than second‐degree reference field and modification of integration kernels

An argument is put forward in favor of using a model gravity field of a degree and order higher than 2 as a reference in gravity field studies. Stokes's approach to the evaluation of the geoid from gravity anomalies is then generalized to be applicable to a higher than second‐order reference spheroid. The effects of truncating Stokes's integration and of modifying the integration kernels are investigated in the context of the generalized approach. Several different modification schemes, starting with a Molodenskij‐like modification and ending with the least squares modification, are studied. Particular attention is devoted to looking at both global and local biases and mean square errors of the individual schemes.

Semaphores outside the kernel

We present three new implementations of semaphores for V7 UNIX. None require kernel modifications. The canonical UNIX semaphore method uses link O in a spin loop. The first new method replaces the canonical spin loop with a software trap mechanism, the second provides additional enhancements in the form of a pool of semaphores and explicit quene management, and the third is a distributed protocol extending to the ability for synchronizing in network environments.

Smoothing estimation of stochastic processes: Change of initial condition formulas

By posing the change of initial condition (CIC) problem in the theory of smoothing in linear estimation in a setting stripped of all inessentials, simple, insightful derivations of most CIC formulas (and a new likelihood formula) are provided. Specifically, the CIC or partitioning problem is one of low rank perturbation to a covariance kernel and the formulas are simple consequences of inversion formulas for fixed rank modification of a positive definite kernel or matrix. The present derivation basically handles the discrete, continuous-discrete, and continuous cases at once: previous derivations had treated the discrete and continuous separately. The continuous-discrete results are new.

Glueball effect on dual topological unitarisation

A suitable modification of the cylinder kernel of the dual topological unitarisation scheme is suggested, to solve the main shortcomings of DTU: the pomeron-f identity and the ω problem. To account for the overlapping clusters appearing in unitarity equations, a glueball kernel is added to the normal twisted-loop kernel. Separate pomeron, f and f′ reggeons are obtained, the parameters of which agree well with present phenomenology. A good description of the ω and φ exchanges is also possible. The corresponding glueball singularities lie at j ∼ 0.6 (lower than the often suggested value j ∼ 1.0) and at j ∼ 0.1. In both cases, the strength of the glueball kernel is smaller than the strength of the twisted-loop kernel.

A Stochastic Filter for Transverse Section Reconstruction

A new algorithm, based on minimum-mean-square reconstruction error, involves modification of the filter kernel based on the signal-to-noise of each projection target. This algorithm gives improved resolvability relative to other algorithms for the resolution phantom chosen for simulations with Poisson noise.

Bandlimiting effects in an optical Laplace transform computer

Data processing in coherent optical systems has been limited to a large extent by operations involving spectrum manipulations through the Fourier transform. By appropriate modification of the Green function kernel of the Rayleigh-Sommerfeld diffraction integral, it should be possible to obtain transform relationships between the input and output of a coherent processor, other than the Fourier transform. Cutrona has suggested a possible implementation for a Laplace transformer but has apparently not attempted a physical realization [IRE Trans. Inf. Theory IT-6, 386 (1960)]. In this study, a Laplace transform computer is described in which it is found that spatial bandlimiting is a restriction on its usefulness. To compensate for this bandlimiting, a convergence filter is described along with a method to produce this and other spatial filters physically for optical processors.

Quantum electrodynamics in an analytic representation

The analytic representation of quantum field theory suggested in a previous paper by Valatin and the author (see abstr. A 22494 of 1969) is further investigated, by working out its details for quantum electrodynamics. The coupled equations for Green's functions are discussed and the lowest order contributions to Compton and Moller scatterings are calculated. Through the Fourier transforms, the expressions show close agreement with the results of the conventional approach. A nonlocal modification of the interaction kernel is studied. This leads to finite self-energy, vacuum polarisation and vertex operator expressions, and in the limit, to a simple regularization of quantum electrodynamics.