Hasil untuk "math.ST"

Mateusz Krukowski

In the paper, we derive an analytic formula for the ROC curves of the LDA classifiers. We establish elementary properties of these curves (monotonicity and concavity), provide formula for the area under curve (AUC) and compute the Youden J-index. Finally, we illustrate the performance of our results on a real--life dataset of Wisconsin breast cancer patients.

Youngjo Lee

Fisher's fiducial probability has recently received renewed attention under the name confidence. In this paper, we reformulate it within an extended-likelihood framework, a representation that helps to resolve many long-standing controversies. The proposed formulation accommodates multi-dimensional parameters and shows how higher-order approximations can be used to refine standard asymptotic confidence statements.

M. R. Formica, E. Ostrovsky, L. Sirota

We derive the optimal signed variable in general case kernels for the classical statistic density estimation, which are some generalization of the famous Epanechnikov's ones.

Niushan Gao, Alexandra Kirillova, Zihao Tong

Olkin [3] obtained a neat upper bound for the determinant of a correlation matrix. In this note, we present an extension and improvement of his result.

Lucas Rooney

In this paper we will provide an introductory understanding of random graph models, and matchings in the case of Erdos-Renyi random graphs. We will provide a synthesis of background theory to this end. We will further examine pertinent recent results and provide a basis of further exploration.

Fabio Gobbi, Sabrina Mulinacci

This paper provides conditions under which a non-stationary copula-based Markov process is $β$-mixing. We introduce, as a particular case, a convolution-based gaussian Markov process which generalizes the standard random walk allowing the increments to be dependent.

Véronique Maume-Deschamps, Ibrahima Niang

The paper concerns quantile oriented sensitivity analysis. We rewrite the corresponding indices using the Conditional Tail Expectation risk measure. Then, we use this new expression to built estimators.

E. Ostrovsky, L. Sirota

We obtain in this paper a non-asymptotic non-improvable up to multiplicative constant moment and exponential tail estimates for distribution for U-statistics by means of martingale representation. We show also the exactness of obtained estimations in one way or another by providing appropriate examples.

Lev B. Klebanov

A possibility to give strong mathematical definitions of outliers and heavy tailed distributions or their modification is discussed. Some alternatives for the notion of tail index are proposed. Key words: outliers, heavy tails, tail index.

Joanna Matysiak

We characterize bivariate natural exponential families having the diagonal of the variance function of the form \[ \textrm{diag} V(m_1,m_2)=\left(Am_1^2+am_1+bm_2+e,Am_2^2+cm_1+dm_2+f\right), \] with $A<0$ and $a,\ldots,f\in\mathbb{R}$. The solution of the problem relies on finding the conditions under which a specific parametric family of functions consists of Laplace transforms of some probability measures.

Matthias Katzfuss, Anirban Bhattacharya

Discussion of "Bayesian Model Selection Based on Proper Scoring Rules" by Dawid and Musio [arXiv:1409.5291].

Shogo Kato, Peter McCullagh

It is shown that a family of distributions on the complex space is characterized as the only family such that the orbit of one distribution under a certain group of transformations on the complex space is the same as that under the group of affine transformations. The resulting family is compared with some existing families.

Emanuele Dolera, Andrea Bulgarelli

This paper provides a generalization of a classical result obtained by Wilks about the asymptotic behavior of the likelihood ratio. The new results deal with the asymptotic behavior of the joint distribution of a vector of likelihood ratios which turn out to be stochastically dependent.

Vydas Cekanavicius, Aiste Elijio

The accuracy of compound Poisson approximation to the sum $S=w_1S_1+w_2S_2+...+w_NS_N$ is estimated. Here $S_i$ are sums of independent or weakly dependent random variables, and $w_i$ denote weights. The overall smoothing effect of $S$ on $w_iS_i$ is estimated by L\' evy concentration function.

Aboubacar Amiri

The main purpose of this paper is to estimate the regression function by using a recursive nonparametric kernel approach. We derive the asymptotic normality for a general class of recursive kernel estimate of the regression function, under strong mixing conditions. Our purpose is to extend the work of Roussas and Tran [17] concerning the Devroye-Wagner estimate.

Leonid Galtchouk, Serguey Pergamenshchikov

Asymptotic efficiency is proved for the constructed in part 1 procedure, i.e. Pinsker's constant is found in the asymptotic lower bound for the minimax quadratic risk. It is shown that the asymptotic minimax quadratic risk of the constructed procedure coincides with this constant.

Emmanuel Candès, Terence Tao

Rejoinder to ``The Dantzig selector: Statistical estimation when $p$ is much larger than $n$'' [math/0506081]

Kshitij Khare

The Dynkin isomorphism associates a Gaussian field to a Markov chain. These Gaussian fields can be used as priors for prediction and time series analysis. Dynkin's construction gives Gaussian fields with all non-negative covariances. We extend Dynkin's construction (by introducing a sign structure on the Markov chain) to allow general covariance sign patterns.

Alex D Gottlieb

We show that that the jackknife variance estimator $v_{jack}$ and the the infinitesimal jackknife variance estimator are asymptotically equivalent if the functional of interest is a smooth function of the mean or a smooth trimmed L-statistic. We calculate the asymptotic variance of $v_{jack}$ for these functionals.

Chang Xuan Mao

The number of species can be estimated by sampling individuals from a species assemblage. The problem of estimating generalized species accumulation curve is addressed in a nonparametric Poisson mixture model. A likelihood-based estimator is proposed and illustrated by real examples.