On the bilateral truncated exponential distribution.
On the choice of a dirichlet prior distribution for multinomial distribution
On the concept of the asymptotic Rényi distances for random fields
The asymptotic Rényi distances are explicitly defined and rigorously studied for a convenient class of Gibbs random fields, which are introduced as a natural infinite-dimensional generalization of exponential distributions.
On the continuity of the minimal -entropy
On the curvature of the space of qubits
The Fisher informational metric is unique in some sense (it is the only Markovian monotone distance) in the classical case. A family of Riemannian metrics is called monotone if its members are decreasing under stochastic mappings. These are the metrics to play the role of Fisher metric in the quantum case. Monotone metrics can be labeled by special operator monotone functions, according to Petz's Classification Theorem. The aim of this paper is to present an idea how one can narrow the set of monotone...
On the equivalence of invariance and almost-invariance from a Bayesian point of view.
On the factorization criterion for quantum statistics
On the invariance property of the Fisher information for a truncated lognormal distribution. I.
On the Jensen-Shannon divergence and the variation distance for categorical probability distributions
We establish a decomposition of the Jensen-Shannon divergence into a linear combination of a scaled Jeffreys' divergence and a reversed Jensen-Shannon divergence. Upper and lower bounds for the Jensen-Shannon divergence are then found in terms of the squared (total) variation distance. The derivations rely upon the Pinsker inequality and the reverse Pinsker inequality. We use these bounds to prove the asymptotic equivalence of the maximum likelihood estimate and minimum Jensen-Shannon divergence...
On the mean and the variance of estimates of Kullback information and relative “useful” information measures
In this paper the mean and the variance of the Maximum Likelihood Estimator (MLE) of Kullback information measure and measure of relative "useful" information are obtained.
On the Rao-Blackwell Theorem for fuzzy random variables
In a previous paper, conditions have been given to compute iterated expectations of fuzzy random variables, irrespectively of the order of integration. In another previous paper, a generalized real-valued measure to quantify the absolute variation of a fuzzy random variable with respect to its expected value have been introduced and analyzed. In the present paper we combine the conditions and generalized measure above to state an extension of the basic Rao–Blackwell Theorem. An application of this...
On the relation between gnostical and probability theories
On unbiased Lehmann-estimators of a variance of an exponential distribution with quadratic loss function.
Lehmann in [4] has generalised the notion of the unbiased estimator with respect to the assumed loss function. In [5] Singh considered admissible estimators of function λ-r of unknown parameter λ of gamma distribution with density f(x|λ, b) = λb-1 e-λx xb-1 / Γ(b), x>0, where b is a known parameter, for loss function L(λ-r, λ-r) = (λ-r - λ-r)2 / λ-2r.Goodman in [1] choosing three loss functions of different shape found unbiased Lehmann-estimators, of the variance σ2 of the normal distribution....
On Uniformly Minimum Variance Unbiased Estimation when no Complete Sufficient Statistics Exist.
On Weighted Parametric Information Measure
Optimal estimation of high quantiles in a large nonparametric model
"A high quantile is a quantile of order q with q close to one." A precise constructive definition of high quantiles is given and optimal estimates are presented.
Optimal quantization for the one–dimensional uniform distribution with Rényi--entropy constraints
We establish the optimal quantization problem for probabilities under constrained Rényi--entropy of the quantizers. We determine the optimal quantizers and the optimal quantization error of one-dimensional uniform distributions including the known special cases (restricted codebook size) and (restricted Shannon entropy).
Optimal solutions of multivariate coupling problems
Some necessary and some sufficient conditions are established for the explicit construction and characterization of optimal solutions of multivariate transportation (coupling) problems. The proofs are based on ideas from duality theory and nonconvex optimization theory. Applications are given to multivariate optimal coupling problems w.r.t. minimal -type metrics, where fairly explicit and complete characterizations of optimal transportation plans (couplings) are obtained. The results are of interest...
Optimality conditions for maximizers of the information divergence from an exponential family
The information divergence of a probability measure from an exponential family over a finite set is defined as infimum of the divergences of from subject to . All directional derivatives of the divergence from are explicitly found. To this end, behaviour of the conjugate of a log-Laplace transform on the boundary of its domain is analysed. The first order conditions for to be a maximizer of the divergence from are presented, including new ones when is not projectable to .
Optimally approximating exponential families
This article studies exponential families on finite sets such that the information divergence of an arbitrary probability distribution from is bounded by some constant . A particular class of low-dimensional exponential families that have low values of can be obtained from partitions of the state space. The main results concern optimality properties of these partition exponential families. The case where is studied in detail. This case is special, because if , then contains all probability...