scientific article; zbMATH DE number 7470640

Gerd Christoph, Vladimir V. Ulyanov, Vladimir Bening

Publication date: 8 February 2022

Full work available at URL: https://arxiv.org/abs/1905.07765

Title: zbMATH Open Web Interface contents unavailable due to conflicting licenses.

negative binomial distribution Laplace distribution second-order expansions sample median discrete Pareto distribution Student's t-distribution samples with random sizes

Mathematics Subject Classification ID

Multivariate distribution of statistics (62H10) Central limit and other weak theorems (60F05) Sums of independent random variables; random walks (60G50) Probability distributions: general theory (60E05) Approximations to statistical distributions (nonasymptotic) (62E17)

Cites Work

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Non-asymptotic results for Cornish-Fisher expansions
On the normal approximation of a binomial random sum
The rate of convergence of the distributions of regular statistics constructed from samples with negatively binomially distributed random sizes to the Student distribution
Edgeworth series for lattice distributions
Order statistics: applications
Order statistics: theory \& methods
Approximate distributions of order statistics. With applications to nonparametric statistics
Third-order expansion of mean squared error of medians
Discrete Pareto distributions
On the rate of convergence of the distributions of certain statistics to the Laplace distribution
An introduction to order statistics
On risks of estimates based on random-size samples
Non-asymptotic analysis of approximations for multivariate statistics
Second-order Chebyshev-Edgeworth and Cornish-Fisher expansions for distributions of statistics constructed from samples with random sizes
Distributed statistical estimation and rates of convergence in normal approximation
Median confidence regions in a nonparametric model
On some statistical models with a random number of observations
Exact critical values for one-way fixed effects models with random sample sizes
Weak convergence to the Student and Laplace distributions
An improvement of the Berry–Esseen inequality with applications to Poisson and mixed Poisson random sums
Stein's method and the Laplace distribution
Approximation Theorems of Mathematical Statistics
New Berry-Esseen and Wasserstein bounds in the CLT for non-randomly centered random sums by probabilistic methods
International Encyclopedia of Statistical Science
Normal Approximation by Stein’s Method
Asymptotic Expansions for Median Estimate of a Parameter
Order Statistics
Recent Developments in Stochastic Methods and Applications
Error bounds and exponential improvements for the asymptotic expansions of the gamma function and its reciprocal
The asymptotic distribution of the sum of a random number of random variables
Some Generalizations of the Theory of Cumulative Sums of Random Variables
Multivariate Statistics

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