Asymptotic Theory of Certain "Goodness of Fit" Criteria Based on Stochastic Processes
Reads0
Chats0
TLDR
In this article, a general method for calculating the limiting distributions of these criteria is developed by reducing them to corresponding problems in stochastic processes, which in turn lead to more or less classical eigenvalue and boundary value problems for special classes of differential equations.Abstract:
The statistical problem treated is that of testing the hypothesis that $n$ independent, identically distributed random variables have a specified continuous distribution function $F(x)$. If $F_n(x)$ is the empirical cumulative distribution function and $\psi(t)$ is some nonnegative weight function $(0 \leqq t \leqq 1)$, we consider $n^{\frac{1}{2}} \sup_{-\infty<x<\infty} \{| F(x) - F_n(x) | \psi^\frac{1}{2}\lbrack F(x) \rbrack\}$ and $n\int^\infty_{-\infty}\lbrack F(x) - F_n(x) \rbrack^2 \psi\lbrack F(x)\rbrack dF(x).$ A general method for calculating the limiting distributions of these criteria is developed by reducing them to corresponding problems in stochastic processes, which in turn lead to more or less classical eigenvalue and boundary value problems for special classes of differential equations. For certain weight functions including $\psi = 1$ and $\psi = 1/\lbrack t(1 - t) \rbrack$ we give explicit limiting distributions. A table of the asymptotic distribution of the von Mises $\omega^2$ criterion is given.read more
Citations
More filters
Journal ArticleDOI
BTF‐CIELab: A Perceptual Difference Measure for Quality Assessment and Compression of BTFs
TL;DR: A numerical quality measure for compressed BTF representations that can be incorporated into any linear or multi‐linear compression technique by separating the spatial and angular components of the difference measure and linearizing each of them.
Journal ArticleDOI
Effects of mixing procedures and rap sizes on stiffness distribution of hot recycled asphalt mixtures
TL;DR: In this paper, a mixing method that simulates the mixing mechanism actually occurs in the asphalt mixing plant in which RAP at ambient temperature is mixed with superheated virgin aggregate at 215°c for 2, 4, 6 and 8min before this blend is used as virgin binder.
Journal ArticleDOI
Characteristics of sub-daily precipitation extremes in observed data and regional climate model simulations
TL;DR: In this article, the authors compare characteristics of observed sub-daily precipitation extremes in the Czech Republic with those simulated by Hadley Centre Regional Model version 3 (HadRM3) and Rossby Centre Regional Atmospheric Model version 4 (RCA4) regional climate models (RCMs) driven by reanalyses and examine diurnal cycles of hourly precipitation and their dependence on intensity and surface temperature.
Journal ArticleDOI
Depletion rate analysis of fields and regions: a methodological foundation
TL;DR: In this article, a comprehensive mathematical framework for depletion rate analysis and ties it to the physics of depletion was presented, which was compared with empirical data from 1036 fields and a number of regions.
Journal ArticleDOI
Direct measurement of superdiffusive energy transport in disordered granular chains.
Eunho Kim,Alejandro J. Martínez,Sean E. Phenisee,Panos Kevrekidis,Mason A. Porter,Mason A. Porter,Jinkyu Yang +6 more
TL;DR: In this paper, the authors present the first systematic experimental study of energy transport and localization properties in simultaneously disordered and nonlinear granular crystals, showing that disorder and non-linearity can effectively cancel each other out, resulting in the destruction of wave localization.
References
More filters
Book
A treatise on the theory of Bessel functions
TL;DR: The tabulation of Bessel functions can be found in this paper, where the authors present a comprehensive survey of the Bessel coefficients before and after 1826, as well as their extensions.
Journal ArticleDOI
On the composition of elementary errors
TL;DR: In this paper, the authors define a variable V(t) the probability function of a quantity z, which may assume certain real values with certain probabilistic properties, and call V t the probability of z having exactly the value t.