# On an Asymptotic Distribution for the MLE

@inproceedings{Walker2021OnAA, title={On an Asymptotic Distribution for the MLE}, author={Stephen G. Walker}, year={2021} }

The paper presents a novel asymptotic distribution for a mle when the log–likelihood is strictly concave in the parameter for all data points; for example, the exponential family. The new asymptotic distribution can be seen as a refinement of the usual normal asymptotic distribution and is comparable to an Edgeworth expansion. However, it is obtained with weaker conditions than even those for asymptotic normality. The same technique is then used to find the exact distribution of the weighted…

## One Citation

### Asymptotics of cut distributions and robust modular inference using Posterior Bootstrap

- Mathematics
- 2021

Bayesian inference provides a framework to combine an arbitrary number of model components with shared parameters, allowing joint uncertainty estimation and the use of all available data sources.…

## References

SHOWING 1-10 OF 18 REFERENCES

### Bayesian inference and the parametric bootstrap.

- MathematicsThe annals of applied statistics
- 2012

The parametric bootstrap can be used for the efficient computation of Bayes posterior distributions and the theory provides a connection between Bayesian and frequentist analysis.

### Probability matching priors for some parameters of the bivariate normal distribution

- Mathematics, Economics
- 2008

This paper develops some objective priors for certain parameters of the bivariate normal distribution. The parameters considered are the regression coefficient, the generalized variance, and the…

### General Bayesian updating and the loss-likelihood bootstrap

- Computer Science, EconomicsBiometrika
- 2019

In this paper, we revisit the weighted likelihood bootstrap and show that it is well-motivated for Bayesian inference under misspecified models. We extend the underlying idea to a wider family of…

### Approximate Bayesian-inference With the Weighted Likelihood Bootstrap

- Mathematics
- 1994

We introduce the weighted likelihood bootstrap (WLB) as a way to simulate approximately from a posterior distribution. This method is often easy to implement, requiring only an algorithm for…

### Asymptotic Theory of Statistics and Probability

- Mathematics
- 2008

Basic Convergence Concepts and Theorems.- Metrics, Information Theory, Convergence, and Poisson Approximations.- More General Weak and Strong Laws and the Delta Theorem.- Transformations.- More…

### A Simple Approximation for Bivariate and Trivariate Normal Integrals

- Computer Science
- 1991

A simple approximation for the bivariate normal distribution function is described, together with a second-order refinement, which could be used for computerized use when a large number of evaluations are required and speed of computation is important.

### PROBABILITIES OF HYPOTHESES AND INFORMATION-STATISTICS IN SAMPLING FROM EXPONENTIAL-CLASS POPULATIONS

- Mathematics
- 1958

1. Summary. This paper is concerned with inequalities connecting probabilities of hypotheses using Bayes' theorem (a posteriori probabilities), a priori probabilities, and Kuliback-Leibler…

### On coverage and local radial rates of credible sets

- Mathematics
- 2017

In the mildly ill-posed inverse signal-in-white-noise model, we construct confidence sets as credible balls with respect to the empirical Bayes posterior resulting from a certain two-level…

### Series Approximation Methods in Statistics

- Mathematics
- 1994

This study covers the uses of series approximation techniques in statistics and is intended to give advanced graduate students in statistics an introduction to various expansions. Its aims are to…