Related papers: Quantile of a Mixture
For the power-law quantum wave packet in configuration space, the variance of the position observable may be divergent. Accordingly, the information-entropic formulation of the uncertainty principle becomes more appropriate than the…
We study the fully entangled fraction (FEF) of arbitrary mixed states. New upper bounds of FEF are derived. These upper bounds make complements on the estimation of the value of FEF. For weakly mixed quantum states, an upper bound is shown…
In the recent years, the notion of mixability has been developed with applications to optimal transportation, quantitative finance and operations research. An $n$-tuple of distributions is said to be jointly mixable if there exist $n$…
The so-called pinball loss for estimating conditional quantiles is a well-known tool in both statistics and machine learning. So far, however, only little work has been done to quantify the efficiency of this tool for nonparametric…
Mixtures of high dimensional Gaussian distributions have been studied extensively in statistics and learning theory. While the total variation distance appears naturally in the sample complexity of distribution learning, it is analytically…
Examples of games between two partners with mixed strategies, calculated by the use of the probability amplitude are given. The first game is described by the quantum formalism of spin one half system for which two noncommuting observables…
Theoretical results for importance sampling rely on the existence of certain moments of the importance weights, which are the ratios between the proposal and target densities. In particular, a finite variance ensures square root convergence…
Measures of risk concentration and their asymptotic behavior for portfolios with heavy-tailed risk factors is of interest in risk management. Second order regular variation is a structural assumption often imposed on such risk factors to…
We propose an estimation method for the conditional mode when the conditioning variable is high-dimensional. In the proposed method, we first estimate the conditional density by solving quantile regressions multiple times. We then estimate…
We consider the approximation of a convolution of possibly different probability measures by (compound) Poisson distributions and also by related signed measures of higher order. We present new total variation bounds having a better…
A real random variable admits median(s) and quantiles. These values minimize convex functions on $\mathbb R$. We show by "Convex Analysis" arguments that the function to be minimized is very natural. The relationship with some notions about…
This paper derives new bounds on the difference of the entropies of two discrete random variables in terms of the local and total variation distances between their probability mass functions. The derivation of the bounds relies on maximal…
In some contexts, mixture models can fit certain variables well at the expense of others in ways beyond the analyst's control. For example, when the data include some variables with non-trivial amounts of missing values, the mixture model…
In this paper, we prove a conditional limit theorem for independent not necessarily identically distributed random variables. Namely, we obtain the asymptotic distribution of a large number of them given the sum.
Quantile regression, the prediction of conditional quantiles, finds applications in various fields. Often, some or all of the variables are discrete. The authors propose two new quantile regression approaches to handle such mixed…
The problem of identifiability of finite mixtures of finite product measures is studied. A mixture model with $K$ mixture components and $L$ observed variables is considered, where each variable takes its value in a finite set with…
We extend some sharp inequalities for martingale-differences to general multiplicative systems of random variables. The key ingredient in the proofs is a technique reducing the general case to the case of Rademacher random variables without…
This paper proposes that the mathematical relationship between an entropy distribution and its limit offers some new insight into system performance. This relationship is used to quantify variation among the entities of a system, where…
A generalization of a distribution increases the flexibility particularly in studying of a phenomenon and its properties. Many generalizations of continuous univariate distributions are available in literature. In this study, an…
We discuss some extensions and refinements of the variance bounds for both real and complex numbers. The related bounds for the eigenvalues and spread of a matrix are also derived here.