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We propose a novel estimator for the number of components (denoted by $M$) in a K-variate non-parametric finite mixture model, where the analyst has repeated observations of $K\geq2$ variables that are independent given a finitely supported…

In many applications, the variables that characterize a stochastic system are measured along a second dimension, such as time. This results in multivariate functional data and the interest is in describing the statistical dependences among…

The quantum Fisher information (QFI) represents a fundamental concept in quantum physics. On the one hand, it quantifies the metrological potential of quantum states in quantum-parameter-estimation measurements. On the other hand, it is…

This paper tackles the problem of robust covariance matrix estimation when the data is incomplete. Classical statistical estimation methodologies are usually built upon the Gaussian assumption, whereas existing robust estimation ones assume…

This article considers a semi-supervised classification setting on a Gaussian mixture model, where the data is not labeled strictly as usual, but instead with uncertain labels. Our main aim is to compute the Bayes risk for this model. We…

In this paper, we propose a parameter space augmentation approach that is based on "intentionally" introducing a pseudo-nuisance parameter into generalized linear models for the purpose of variance reduction. We first consider the parameter…

Quantum Fisher Information (QFI) is a fundamental quantity in quantum parameter estimation theory, characterizing the ultimate precision bound of parameter estimation. In this work, we investigate QFI for quantum states in non-Hermitian…

Gravitational-wave astronomers often wish to characterize the expected parameter-estimation accuracy of future observations. The Fisher matrix provides a lower bound on the spread of the maximum-likelihood estimator across noise…

We present the experimental measurement, on a quantum processor, of a series of polynomial lower bounds that converge to the quantum Fisher information (QFI), a fundamental quantity for certifying multipartite entanglement that is useful…

Imputation is a popular technique for handling item nonresponse in survey sampling. Parametric imputation is based on a parametric model for imputation and is less robust against the failure of the imputation model. Nonparametric imputation…

Hansen (1982) proposed a class of "generalized method of moments" (GMMs) for estimating a vector of regression parameters from a set of score functions. Hansen established that, under certain regularity conditions, the estimator based on…

This paper studies the problem of interacting multiple model (IMM) estimation for jump Markov linear systems with unknown measurement noise covariance. The system state and the unknown covariance are jointly estimated in the framework of…

Thomas' partial likelihood estimator of regression parameters is widely used in the analysis of nested case-control data with Cox's model. This paper proposes a new estimator of the regression parameters, which is consistent and…

The quantum Fisher information (QFI), as a function of quantum states, measures the amount of information that a quantum state carries about an unknown parameter. The (entanglement-assisted) QFI of a quantum channel is defined to be the…

We consider the semi-parametric estimation of a scale parameter of a one-dimensional Gaussian process with known smoothness. We suggest an estimator based on quadratic variations and on the moment method. We provide asymptotic…

Determining the strength of non-linear statistical dependencies between two variables is a crucial matter in many research fields. The established measure for quantifying such relations is the mutual information. However, estimating mutual…

We develop a general method to study the Fisher information distance in central limit theorem for nonlinear statistics. We first construct completely new representations for the score function. We then use these representations to derive…

In this work, we propose new methods of parameter estimation using stochastic sampling quantum phase-space simulations. We show that it is possible to compute the quantum Fisher information (QFI) from semiclassical stochastic samples using…

Suppose that univariate data are drawn from a mixture of two distributions that are equal up to a shift parameter. Such a model is known to be nonidentifiable from a nonparametric viewpoint. However, if we assume that the unknown mixed…

This paper is concerned with estimation and inference for ultrahigh dimensional partially linear single-index models. The presence of high dimensional nuisance parameter and nuisance unknown function makes the estimation and inference…