Related papers: On the Phase Transition of Wilk's Phenomenon
The generalized varying coefficient partially linear model with growing number of predictors arises in many contemporary scientific endeavor. In this paper we set foot on both theoretical and practical sides of profile likelihood estimation…
We consider Wald's sequential probability ratio test for deciding whether a sequence of independent and identically distributed observations comes from a specified phase-type distribution or from an exponentially tilted alternative…
I investigate the use of Pearson's chi-square statistic, the Maximum Likelihood Ratio statistic for Poisson distributions, and the chi-square-gamma statistic (Mighell 1999, ApJ, 518, 380) for the determination of the goodness-of-fit between…
We examine the phase transition phenomenon for the Knapsack problem from both a computational and a human perspective. We first provide, via an empirical and a theoretical analysis, a characterization of the phenomenon in terms of two…
We consider the quasi-likelihood analysis for a linear regression model driven by a Student-t L\'{e}vy process with constant scale and arbitrary degrees of freedom. The model is observed at high frequency over an extending period, under…
The ability to calculate precise likelihood ratios is fundamental to many STEM areas, such as decision-making theory, biomedical science, and engineering. However, there is no assumption-free statistical methodology to achieve this. For…
We demonstrate that two approximations to the chi^2 statistic as popularly employed by observational astronomers for fitting Poisson-distributed data can give rise to intrinsically biased model parameter estimates, even in the high counts…
Accurate knowledge of the null distribution of hypothesis tests is important for valid application of the tests. In previous papers and software, the asymptotic null distribution of likelihood ratio tests for detecting genetic linkage in…
Population quantiles are important parameters in many applications. Enthusiasm for the development of effective statistical inference procedures for quantiles and their functions has been high for the past decade. In this article, we study…
Testing the homogeneity of two distributions is fundamental in statistics, but classical procedures may fail under nonignorable nonresponse. In many surveys, callback data record repeated contact attempts and provide auxiliary information…
A critical challenge in particle physics is combining results from diverse experimental setups that measure the same physical quantity to enhance precision and statistical power, a process known as a global fit. Global fits of sterile…
A common goal in an experimental physics analysis is to extract information from a reaction with multi-dimensional kinematics. The preferred method for such a task is typically the unbinned maximum likelihood method. In fits using this…
An effective two-stage method for an estimation of parameters of the linear regression is considered. For this purpose we introduce a certain quasi-estimator that, in contrast to usual estimator, produces two alternative estimates. It is…
We extend Stein's celebrated Wasserstein bound for normal approximation via exchangeable pairs to the multi-dimensional setting. As an intermediate step, we exploit the symmetry of exchangeable pairs to obtain an error bound for smooth test…
Dicke states are typical examples of quantum states with genuine multipartite entanglement. They are valuable resources in many quantum information processing tasks, including multiparty quantum communication and quantum metrology. Phased…
Traditional methods for inference in change point detection often rely on a large number of observed data points and can be inaccurate in non-asymptotic settings. With the rise of mobile health and digital phenotyping studies, where…
We consider goodness-of-fit tests for uniformity of a multinomial distribution by means of tests based on a class of symmetric statistics, defined as the sum of some function of cell-frequencies. We are dealing with an asymptotic regime,…
It is well-known that in some situations it is not easy to compute the likelihood function as the datasets might be large or the model is too complex. In that contexts composite likelihood, derived by multiplying the likelihoods of subjects…
The prediction of the final state probabilities of a general cuboid randomly thrown onto a surface is a problem that naturally arises in the minds of men and women familiar with regular cubic dice and the basic concepts of probability.…
The correct use and interpretation of models depends on several steps, two of which being the calibration by parameter estimation and the analysis of uncertainty. In the biological literature, these steps are seldom discussed together, but…