Related papers: A Paradox about Likelihood Ratios?
The use of continuous probability distributions has been widespread in problems with purely discrete nature. In general, such distributions are not appropriate in this scenario. In this paper, we introduce a class of discrete and asymmetric…
We propose a new class of goodness-of-fit tests for the inverse Gaussian distribution. The proposed tests are weighted $L^2$-type tests depending on a tuning parameter. We develop the asymptotic theory under the null hypothesis and under a…
In this paper, an alternative mixed Poisson distribution is proposed by amalgamating Poisson distribution and a modification of the Quasi Lindley distribution. Some fundamental structural properties of the new distribution, namely the shape…
Approximate distributions for sum and difference of linearly correlated $\chi^{2}$ distributed random variables are derived. It is shown that they can be reduced to conveniently parametrized gamma and Variance-Gamma distributions,…
We consider parametric tests for multidimensional ergodic diffusions based on high frequency data. We propose two-step testing method for diffusion parameters and drift parameters. To construct test statistics of the tests, we utilize the…
A numerical likelihood approach to the determination of cosmic ray anisotropies is presented which offers many advantages over other approaches. It allows a wide range of statistically meaningful hypotheses to be compared even when full sky…
Continuous and strictly positive data that exhibit skewness and outliers frequently arise in many applied disciplines. Log-symmetric distributions provide a flexible framework for modeling such data. In this article, we develop new…
Consider a random graph G in G(n,p) and the graph property: G contains a copy of a specific graph H. (Note: H depends on n; a motivating example: H is a Hamiltonian cycle.) Let q be the minimal value for which the expected number of copies…
As a statistical measure to quantify the topological structure of the large-scale structure in the universe, the genus number is calculated for a number of non-Gaussian distributions in which the density field is characterized by a…
So-called linear rank statistics provide a means for distribution-free (even in finite samples), yet highly flexible, two-sample testing in the setting of univariate random variables. Their flexibility derives from a choice of weights that…
The probability that two randomly selected phylogenetic trees of the same size are isomorphic is found to be asymptotic to a decreasing exponential modulated by a polynomial factor. The number of symmetrical nodes in a random phylogenetic…
In this work, we explore the application of likelihood ratio as a forensic evidence assessment tool to evaluate the causal mechanism of a bloodstain pattern. It is assumed that there are two competing hypotheses regarding the cause of a…
We provide necessary and sufficient conditions of uniform consistency of nonparametric sets of alternatives of chi-squared test for testing of hypothesis of homogeneity. The number of cells of chi-squared test increases with sample size…
This paper discusses the dual interpretation of the Jeffreys--Lindley's paradox associated with Bayesian posterior probabilities and Bayes factors, both as a differentiation between frequentist and Bayesian statistics and as a pointer to…
In this paper, we study the maximum likelihood estimate of the probability mass function (pmf) of $n$ independent and identically distributed (i.i.d.) random variables, in the non-asymptotic regime. We are interested in characterizing the…
The modes of a statistical population are high frequency points around which most of the probability mass is accumulated. For the particular case of circular densities, we address the problem of testing if, given an observed sample of a…
The likelihood function is a crucial element of parameter estimation. In analyses of galaxy overdensities and weak lensing shear, one often approximates the likelihood of the power spectrum with a Gaussian distribution. The posterior…
We consider the problem of interval estimation of the odds ratio. An asymptotic confidence interval is widely applied in medical research. Unfortunately that confidence interval has a poor coverage probability: it is significantly smaller…
The asymptotic distribution of the score test of the null hypothesis that marks do not impact the intensity of a Hawkes marked self-exciting point process is shown to be chi-squared. For local asymptotic power, the distribution against…
In this paper, a new and convenient $\chi^2$ wald test based on MCMC outputs is proposed for hypothesis testing. The new statistic can be explained as MCMC version of Wald test and has several important advantages that make it very…