Related papers: Testing the mixture model hypothesis via spectral …
The task of mixture proportion estimation (MPE) is to estimate the weight of a component distribution in a mixture, given observations from both the component and mixture. Previous work on MPE adopts the irreducibility assumption, which…
We study the composite sequential quantum hypothesis testing (SQHT) problem, where the objective is to distinguish a null quantum state from a set of alternative quantum states. We propose a mixture-sequential quantum probability ratio test…
This paper establishes the theoretical foundations for the asymptotic separability of Gaussian Mixture Models (GMMs) in high dimensions by extending the classical Feldman-H\'ajek theorem. We first prove that a countable mixture of Gaussian…
Motivated by a neuroscience question about synchrony detection in spike train analysis, we deal with the independence testing problem for point processes. We introduce non-parametric test statistics, which are rescaled general…
The so-called permutation separability criteria are simple operational conditions that are necessary for separability of mixed states of multipartite systems: (1) permute the indices of the density matrix and (2) check if the trace norm of…
Many neutrino mixing scenarios that have \mu-\tau symmetry with \theta_{13}=0 are in disagreement with recent experimental results that indicate a nonzero value for \theta_{13}. We investigate the effect of small perturbations on Majorana…
Binomial data with unknown sizes often appear in biological and medical sciences and are usually overdispersed. All previous methods used parametric models and only considered overdispersion due to the variation of sizes. The proposed…
In the limit of an approximate $\mu-\tau$ symmetry in the neutrino mass matrix, we explore deviations to the Tri-Bi-Maximal mixing pattern in the neutrino sector. We consider two different ansatzes for the corrected pattern to predict the…
We study the compatibility of measurements on finite-dimensional compact convex state space in the framework of general probabilistic theory. Our main emphasis is on formulation of necessary and sufficient conditions for two-outcome…
The $\mu$-$\tau$ reflection symmetry $(\nu_{e},\thinspace\nu_{\mu},\thinspace\nu_{\tau})\rightarrow(\overline{\nu}_{e},\thinspace\overline{\nu}_{\tau},\thinspace\overline{\nu}_{\mu})$ and the TM1 mixing (a PMNS matrix with the first column…
In this paper new tests for the independence of two high-dimensional vectors are investigated. We consider the case where the dimension of the vectors increases with the sample size and propose multivariate analysis of variance-type…
This paper considers two-sided tests for the parameter of an endogenous variable in an instrumental variable (IV) model with heteroskedastic and autocorrelated errors. We develop the finite-sample theory of weighted-average power (WAP)…
From the consideration of measuring bipartite mixed states by separable pure states, we introduce algebraic sets in complex projective spaces for bipartite mixed states as the degenerating locus of the measurement. These algebraic sets are…
We study the method to test the unitarity of the lepton mixing matrix by using only the long baseline neutrino oscillation experiments, such as the combination of the T2HK experiment and the one with the $\nu_e$ beam from a future neutrino…
We model quantum measurement of a two-level system $\mu$. Previous obstacles for understanding the measurement process are removed by basing the analysis of the interaction between $\mu$ and the measurement device on quantum field theory.…
We study uniform consistency in nonparametric mixture models as well as closely related mixture of regression (also known as mixed regression) models, where the regression functions are allowed to be nonparametric and the error…
We consider the distinct elements problem, where the goal is to estimate the number of distinct colors in an urn containing $ k $ balls based on $n$ samples drawn with replacements. Based on discrete polynomial approximation and…
We study an analogue of the large deviation principle for mixed measures associated with a class of $\log$-concave probability measures whose densities depend on the gauge function of a convex body. For convex bodies in $\mathbb{R}^n$, we…
In the research on checking whether the underlying model is of parametric single-index structure with outliers in observations, the purpose of this paper is two-fold. First, a test that is robust against outliers is suggested. The Hampel's…
We study the rate of decay of the probability of error for distinguishing between a sparse signal with noise, modeled as a sparse mixture, from pure noise. This problem has many applications in signal processing, evolutionary biology,…