Accurate goodness-of-fit tests for the extreme tails of empirical distributions is a very important issue, relevant in many contexts, including geophysics, insurance, and finance. We have derived exact asymptotic results for a generalization of the large-sample Kolmogorov-Smirnov test, well suited to testing these extreme tails. In passing, we have rederived and made more precise the approximat...

Recent work on nonparametric identification of average partial effects (APEs) from panel data require restrictions on individual or time heterogeneity. Identifying assumptions under the “generalized first-differencing” category, such as time homogeneity (Chernozhukov, Fernandez-Val, Hahn, and Newey, 2013), have testable equality restrictions on the distribution of the outcome variable. This pap...

This paper develops an approach to testing the adequacy of both classical and Bayesian models given sample data. An important feature of the approach is that we are able to test the practical scientiic hypothesis of whether the true underlying model is close to some hypothesized model. The notion of closeness is based on measurement precision and requires the introduction of a metric for which ...

In this note, we show that the operator theoretic concept of Kolmogorov numbers and the number of degrees of freedom at level ǫ of a communication channel are closely related. Linear communication channels may be modeled using linear compact operators on Banach or Hilbert spaces and the number of degrees of freedom of such channels is defined to be the number of linearly independent signals tha...

The problem of limit cycles for Kolmogorov model is interesting and significant both in theory and applications. Our work is concerned with limit cycles bifurcations problem for a class of quartic Kolmogorov model with two positive singular points (i.e. (1, 2) and (2, 1)). The investigated model is symmetrical with regard to y = x. We show that each one of points (1, 2) and (2, 1) can bifurcate...

The analytical formulas for the average intensity and power in the bucket of the relay propagation of partially coherent cosh-Gaussian (ChG) beams in non-Kolmogorov turbulence have been derived based on the extended Huygens-Fresnel principle. The influences of the beam parameters, relay system parameters and the non-Kolmogorov turbulence parameters on relay propagation are investigated by numer...

The Kolmogorov complexity of a string is the length of the shortest program that generates it. A binary string is said to have trivial Kolmogorov complexity if its complexity is at most the complexity of its length. Intuitively, such strings carry no more information than the information that is inevitably coded into their length (which is the same as the information coded into a sequence of 0s...

We investigate chaos synchronization of small-scale motions in the three-dimensional turbulent energy cascade, via pseudospectral simulations of the incompressible Navier-Stokes equations. The modes of the turbulent velocity field below about 20 Kolmogorov dissipation lengths are found to be slaved to the chaotic dynamics of larger-scale modes. The dynamics of all dissipation-range modes can be...