Related papers: James-Stein Estimation in Quantum Gaussian Sensing
In this paper we study asymptotic properties of the maximum likelihood estimator (MLE) for the speed of a stochastic wave equation. We follow a well-known spectral approach to write the solution as a Fourier series, then we project the…
We investigate the performance of the scan (maximum likelihood ratio statistic) and of the average likelihood ratio statistic in the problem of detecting a deterministic signal with unknown spatial extent in the prototypical univariate…
In quantum physics, all measured observables are subject to statistical uncertainties, which arise from the quantum nature as well as the experimental technique. We consider the statistical uncertainty of the so-called sampling method, in…
Causal mediation analysis aims to estimate the natural direct and indirect effects under clearly specified assumptions. Traditional mediation analysis based on Ordinary Least Squares (OLS) relies on the absence of unmeasured causes of the…
In this paper we consider the behavior of Kalman Filter state estimates in the case of distribution with heavy tails .The simulated linear state space models with Gaussian measurement noises were used. Gaussian noises in state equation are…
Consider a statistical model with an epistemic restriction such that, unlike in classical mechanics, the allowed distribution of positions is fundamentally restricted by the form of an underlying momentum field. Assume an agent (observer)…
Quantum Amplitude Estimation (QAE) -- a technique by which the amplitude of a given quantum state can be estimated with quadratically fewer queries than by standard sampling -- is a key sub-routine in several important quantum algorithms,…
Maximum likelihood (ML) estimation is widely used in statistics. The h-likelihood has been proposed as an extension of Fisher's likelihood to statistical models including unobserved latent variables of recent interest. Its advantage is that…
In this work, the estimation of the multivariate normal mean by different classes of shrinkage estimators is investigated. The risk associated with the balanced loss function is used to compare two estimators. We start by considering…
We present results on parameter estimation and non-parameter estimation of the linear partially observed Gaussian system of stochastic differential equations. We propose new one-step estimators which have the same asymptotic properties as…
A number of problems in quantum state and system identification are addressed. Specifically, it is shown that the maximum likelihood estimation (MLE) approach, already known to apply to quantum state tomography, is also applicable to…
Parameter estimation is of fundamental importance in areas from atomic spectroscopy and atomic clocks to gravitational wave detection. Entangled probes provide a significant precision gain over classical strategies in the absence of noise.…
Quantum metrology is supposed to significantly improve the precision of parameter estimation by utilizing suitable quantum resources. However, the predicted precision can be severely distorted by realistic noises. Here, we propose a…
Random sampling is an essential tool in the processing and transmission of data. It is used to summarize data too large to store or manipulate and meet resource constraints on bandwidth or battery power. Estimators that are applied to the…
Targeted maximum likelihood estimators (TMLEs) are asymptotically optimal among regular, asymptotically linear estimators. In small samples, however, we may be far from "asymptopia" and not reap the benefits of optimality. Here we propose a…
In this work, we introduce a novel estimator of the predictive risk with Poisson data, when the loss function is the Kullback-Leibler divergence, in order to define a regularization parameter's choice rule for the Expectation Maximization…
The paper focuses on minimum mean square error (MMSE) Bayesian estimation for a Gaussian source impaired by additive Middleton's Class-A impulsive noise. In addition to the optimal Bayesian estimator, the paper considers also the…
Several problems in statistics involve the combination of high-variance unbiased estimators with low-variance estimators that are only unbiased under strong assumptions. A notable example is the estimation of causal effects while combining…
Even though measurement results obtained in the real world are generally both noisy and continuous, quantum measurement theory tends to emphasize the ideal limit of perfect precision and quantized measurement results. In this article, a…
We present a new quantum algorithm for estimating the mean of a real-valued random variable obtained as the output of a quantum computation. Our estimator achieves a nearly-optimal quadratic speedup over the number of classical i.i.d.…