Related papers: Maximum likelihood quantum state tomography is ina…
Operational risk models commonly employ maximum likelihood estimation (MLE) to fit loss data to heavy-tailed distributions. Yet several desirable properties of MLE (e.g. asymptotic normality) are generally valid only for large sample-sizes,…
Optimal state estimation for linear discrete-time systems is considered. Motivated by the literature on differential privacy, the measurements are assumed to be corrupted by Laplace noise. The optimal least mean square error estimate of the…
If the log likelihood is approximately quadratic with constant Hessian, then the maximum likelihood estimator (MLE) is approximately normally distributed. No other assumptions are required. We do not need independent and identically…
Quantum tomography is a fundamental technique for characterizing, benchmarking, and verifying quantum states and devices. It plays a crucial role in advancing quantum technologies and deepening our understanding of quantum mechanics.…
Multipartite entanglement is a fundamental aspect of quantum mechanics, crucial to advancements in quantum information processing and quantum computation. Within this field, Genuinely Multipartite Entanglement (GME), being entangled in all…
A new approach to inference in state space models is proposed, based on approximate Bayesian computation (ABC). ABC avoids evaluation of the likelihood function by matching observed summary statistics with statistics computed from data…
Quantum state reconstruction on a finite number of copies of a quantum system with informationally incomplete measurements does, as a rule, not yield a unique result. We derive a reconstruction scheme where both the likelihood and the von…
Quantum state tomography is a fundamental tool in quantum information processing. It allows us to estimate the state of a quantum system by measuring different observables on many identically prepared copies of the system. This is, in…
Over the last decades, the family of $\alpha$-stale distributions has proven to be useful for modelling in telecommunication systems. Particularly, in the case of radar applications, finding a fast and accurate estimation for the amplitude…
The assumption of log-concavity is a flexible and appealing nonparametric shape constraint in distribution modelling. In this work, we study the log-concave maximum likelihood estimator (MLE) of a probability mass function (pmf). We show…
We describe a Monte Carlo method to approximate the maximum likelihood estimate (MLE), when there are missing data and the observed data likelihood is not available in closed form. This method uses simulated missing data that are…
Rather than point estimators, states of a quantum system that represent one's best guess for the given data, we consider optimal regions of estimators. As the natural counterpart of the popular maximum-likelihood point estimator, we…
Maximum likelihood principle is shown to be the best measure for relating the experimental data with the predictions of quantum theory.
Quantum state tomography is a technique in quantum information science used to reconstruct the density matrix of an unknown quantum state, providing complete information about the quantum state. It is of significant importance in fields…
In this paper, we study the nonparametric maximum likelihood estimator (MLE) of a convex hazard function. We show that the MLE is consistent and converges at a local rate of $n^{2/5}$ at points $x_0$ where the true hazard function is…
For the univariate current status and, more generally, the interval censoring model, distribution theory has been developed for the maximum likelihood estimator (MLE) and smoothed maximum likelihood estimator (SMLE) of the unknown…
We investigate the optimal approximation to triple incompatible quantum measurements within the framework of statistical distance and joint measurability. According to the lower bound of the uncertainty inequality presented in [Physical…
We consider the problem of estimating the state of a large but finite number $N$ of identical quantum systems. In the limit of large $N$ the problem simplifies. In particular the only relevant measure of the quality of the estimation is the…
Strong consistency and asymptotic normality of the Quasi-Maximum Likelihood Estimator (QMLE) are given for a general class of multidimensional causal processes. For particular cases already studied in the literature (for instance univariate…
Recently Balakrishnan and Iliopoulos [Ann. Inst. Statist. Math. 61 (2009)] gave sufficient conditions under which maximum likelihood estimator (MLE) is stochastically increasing. In this paper we study test plans which are not considered…