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The Admissibility of the Empirical Distribution Function [PDF]
The Annals of Statistics, 1985 Consider the problem of estimating an unknown distribution function F from the class of all distribution functions given a random sample of size n from F. It is proved that the empirical distribution function is admissible for the loss functions \[ L(F,\hat F)=\int (\hat F(t)-F(t))^ 2(F(t))^ a(1-F(t))^ bdW(t) \] for any ...
Michael P. Cohen, Lynn Kuo
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An Empirical Mass Function Distribution [PDF]
The Astrophysical Journal, 2018 Abstract The halo mass function, encoding the comoving number density of dark matter halos of a given mass, plays a key role in understanding the formation and evolution of galaxies. As such, it is a key goal of current and future deep optical surveys to constrain the mass function down to mass scales that typically host
S. G. Murray +2 more
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Convergence of the empirical spectral distribution function of Beta matrices [PDF]
, 2015 Let $\mathbf{B}_n=\mathbf {S}_n(\mathbf {S}_n+\alpha_n\mathbf {T}_N)^{-1}$, where $\mathbf {S}_n$ and $\mathbf {T}_N$ are two independent sample covariance matrices with dimension $p$ and sample sizes $n$ and $N$, respectively. This is the so-called Beta
Zhidong Bai +3 more
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Distributions Related to Linear Bounds for the Empirical Distribution Function [PDF]
The Annals of Statistics, 1977 $X_1, \cdots, X_n$ are i.i.d. Uniform (0, 1) rv's with empirical df $\Gamma_n$ and order statistics $0 < U_1 < \cdots < U_n < 1.$ Define random variables $U_\ast, i_\ast$ (for $n \geqq 2$) by $\max_{1\leqq i \leqq n - 1} \frac{U_{i + 1}}{i} = \frac{U_{i_\ast} + 1}{i_\ast}, U_\ast = U_{i_\ast + 1};$ $i_\ast + 1$ is the (random) index of the order ...
Jon A. Wellner
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Empirical Likelihood Ratio Test With Distribution Function Constraints [PDF]
IEEE Transactions on Signal Processing, 2013 In this work, we study non-parametric hypothesis testing problem with distribution function constraints. The empirical likelihood ratio test has been widely used in testing problems with moment (in)equality constraints. However, some detection problems cannot be described using moment (in)equalities.
Yingxi Liu, Ahmed H. Tewfik
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Differentially Private Empirical Cumulative Distribution Functions [PDF]
In order to both learn and protect sensitive training data, there has been a growing interest in privacy preserving machine learning methods. Differential privacy has emerged as an important measure of privacy. We are interested in the federated setting where a group of parties each have one or more training instances and want to learn collaboratively ...
Antoine Barczewski +2 more
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Monte Carlo comparison of goodness-of-fit tests for the Inverse Gaussian distribution based on empirical distribution function [PDF]
Journal of Mahani Mathematical Research, 2023 The Inverse Gaussian (IG) distribution is widely used to model positively skewed data. In this article, we examine goodness of fit tests for the Inverse Gaussian distribution based on the empirical distribution function.
Hadi Alizadeh Noughabi +1 more
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Correction algorithm for weighted empirical distribution function
MATHEMATICS, PHYSICS, MECHANICS, ASTRONOMY, COMPUTER SCIENCE AND CYBERNETICS: ISSUES OF PRODUCTIVE INTERACTION, 2021 Oksana Kubaychuk
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Quantile-Zone Based Approach to Normality Testing
Mathematics, 2022 Normality testing remains an important issue for researchers, despite many solutions that have been published and in use for a long time. There is a need for testing normality in many areas of research and application, among them in Quality control, or ...
Atif Avdović, Vesna Jevremović
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Estimation of Distribution Function using Percentile Ranked Set Sampling
Revstat Statistical Journal, 2023 The estimation of distribution function has received considerable attention in the literature. Because, many practical problems involve estimation of distribution function from experimental data. Estimating the distribution function makes it possible to
Yusuf Can Sevil , Tugba Ozkal Yildiz
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