In this paper, a kernel estimator of the differential entropy of the mark distribution of a homogeneous Poisson marked point process is proposed. The marks have an absolutely continuous distribution on a compact Riemannian manifold without boundary. L2 and almost surely consistency of this estimator as well as its asymptotic normality are investigated.

The limit distribution of energy level spacing is studied for the system of two harmonic oscillators with generic ratio of frequencies. It is proved that for any fixed generic ratio e no limit distribution exists, but for random e with any absolutely continuous distribution p(e)de on [0, 1] a universal random limit distribution of the energy level spacing exists. Some properties of the random l...

When the statistical experiment is dominated (i.e. when all the sampling distributions are absolutely continuous w.r.t. a σ-finite measure), all the probability measures on the parameter space are prior distributions which give rise to a dominated Bayesian experiment. In this paper we shall consider the family D of prior distributions which give rise to a dominated Bayesian experiment (w.r.t. a...

We compute higher derivatives of the Fréchet function on spheres with an absolutely continuous and rotationally symmetric probability distribution. Consequences include (i) a practical condition to test if mode distribution is local mean; (ii) central limit theorem assumptions explicit limiting distribution; (iii) answer question whether smeary effect can occur distributions: method presented h...

I explore some consequences of a groundbreaking result of Breimesser and Pearson on the absolutely continuous spectrum of one-dimensional Schrödinger operators. These include an Oracle Theorem that predicts the potential and rather general results on the approach to certain limit potentials. In particular, we prove a Denisov-Rakhmanov type theorem for the general finite gap case. The main theme...

In this paper we study some absolutely continuous representations of function algebras, which are weak -spectral in the sense of [5] and [6], for a scalar > 0. Precisely we investigate certain conditions for the existence of a spectral -dilation of such representation. Among others we obtain di¤erent results which generalize the corresponding theorems of D. Gaşpar [3]. Full text

The asymmetric skew divergence smooths one of the distributions by mixing it, to a degree determined parameter $\lambda$, with other distribution. Such is an approximation KL that does not require target distribution be absolutely continuous respect source In this paper, information geometric generalization called $\alpha$-geodesical proposed, and its properties are studied.

CONTINUOUS SPECTRA. II BY C. R. PUTNAM Communicated by Maurice Heins, November 1, 1967 1. This paper is a continuation of [4]. It may be recalled that if A is a self-adjoint operator on a Hubert space § with spectral resolution A=zf\dE\, then the set of elements x in § for which ||-Ex#|| is an absolutely continuous function of X is a subspace, &a(A), of § (see, e.g., Halmos [l, p. 104]). The op...

Let A be a certain irreducible 0-1 matrix and let t denote the family of piecewise linear Markov maps on [0,1] which are consistent with A. The main result of this paper characterizes those maps in t whose (unique) absolutely continuous invariant measure is maximal, and proves that for "most" of the maps that are consistent with A, the absolutely continuous invariant measure is not maximal.