Related papers: The two sample problem: Exact distributions, numer…
Stellar limb darkening affects a wide range of astronomical measurements and is frequently modelled with a parametric model using polynomials in the cosine of the angle between the line of sight and the emergent intensity. Two-parameter…
Using Bombieri-Iwaniec method, we establish an improvement on both Gauss's Circle Problem and Dirichlet's Divisor Problem. More precisely, we derive a new estimate for the first spacing problem and combine it with Huxley's results on the…
Inference based on the penalized density ratio model is proposed and studied. The model under consideration is specified by assuming that the log--likelihood function of two unknown densities is of some parametric form. The model has been…
The asymptotic solution to the problem of comparing the means of two heteroscedastic populations, based on two random samples from the populations, hinges on the pivot underpinning the construction of the confidence interval and the test…
Parametric hypothesis testing associated with two independent samples arises frequently in several applications in biology, medical sciences, epidemiology, reliability and many more. In this paper, we propose robust Wald-type tests for…
Likelihood ratio tests are widely used in high-energy physics, where the test statistic is usually assumed to follow a chi-squared distribution with a number of degrees of freedom specified by Wilks' theorem. This assumption breaks down…
In this paper, we present two classes of Bayesian approaches to the two-sample problem. Our first class of methods extends the Bayesian t-test to include all parametric models in the exponential family and their conjugate priors. Our second…
The simultaneous estimation of multiple unknown parameters lies at heart of a broad class of important problems across science and technology. Currently, the state-of-the-art performance in the such problems is achieved by nonparametric…
Statistical matching aims to integrate two statistical sources. These sources can be two samples or a sample and the entire population. If two samples have been selected from the same population and information has been collected on…
Optimality results for two outstanding Bayesian estimation problems are given in this paper: the estimation of the sampling distribution for the squared total variation function and the estimation of the density for the $L^1$-squared loss…
The Cauchy problem is studied for systems of quasi-linear wave equations with multiple speeds in two space dimensions. Using the method of Klainerman and Sideris together with the localized energy estimate, we give an alternative proof of a…
A procedure is proposed to construct solutions of the double confluent Heun equation with a determinate behaviour at the singular points. The connection factors are expressed as quotients of Wronskians of the involved solutions. Asymptotic…
A recently introduced two-phase flow model by Chun Shen is studied in this work. The model is derived to describe the dynamics of immersed water bubbles in liquid water as carrier. Several assumptions are made to obtain a reduced form of…
Motivated by real-world machine learning applications, we analyze approximations to the non-asymptotic fundamental limits of statistical classification. In the binary version of this problem, given two training sequences generated according…
The label switching problem arises in the Bayesian analysis of models containing multiple indistinguishable parameters with arbitrary ordering. Any permutation of these parameters is equivalent, therefore models with many such parameters…
Robust classification algorithms have been developed in recent years with great success. We take advantage of this development and recast the classical two-sample test problem in the framework of classification. Based on the estimates of…
We discuss the problem of parameter estimation in nonlinear stochastic differential equations based on sampled time series. A central message from the theory of integrating stochastic differential equations is that there exists in general…
We seek to complement Nelson's work on the two-slit experiment by showing that the two-slit process, whose density exhibits the characteristic interference pattern, may be obtained as the model after the beam has reached the screen by means…
A risk-aware decision-making problem can be formulated as a chance-constrained linear program in probability measure space. Chance-constrained linear program in probability measure space is intractable, and no numerical method exists to…
Monte Carlo calculations of fermionic systems with continuous auxiliary fields frequently suffer from a diverging variance. If a system has the infinite variance problem, one cannot estimate observables reliably even with an infinite number…