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Error probability is a popular and well-studied optimization criterion in discriminating non-orthogonal quantum states. It captures the threat from an adversary who can only query the actual state once. However, when the adversary is able…
The U.S. Bureau of Labor Statistics use monthly, by-state employment totals from the Current Population Survey (CPS) as a key input to develop employment estimates for counties within the states. The monthly CPS by-state totals, however,…
We consider the problem of estimating the mixing density $f$ from $n$ i.i.d. observations distributed according to a mixture density with unknown mixing distribution. In contrast with finite mixtures models, here the distribution of the…
Parametric density estimation, for example as Gaussian distribution, is the base of the field of statistics. Machine learning requires inexpensive estimation of much more complex densities, and the basic approach is relatively costly…
We provide an efficient method for computing the maximum likelihood mixed quantum state (with density matrix $\rho$) given a set of measurement outcome in a complete orthonormal operator basis subject to Gaussian noise. Our method works by…
A basic issue in both teaching of and practice of statistics is the interplay between modelling assumptions and inference performance. The general message conveyed is that stronger assumptions lead to better statistical performance of the…
Indirect inference estimators (i.e., simulation-based minimum distance estimators) in a parametric model that are based on auxiliary non-parametric maximum likelihood density estimators are shown to be asymptotically normal. If the…
Estimating the density of states of systems with rugged free energy landscapes is a notoriously difficult task of the utmost importance in many areas of physics ranging from spin glasses to biopolymers. Density of states estimation has also…
To improve the efficiency of the state tomography strategy via weak value, we have searched the optimal coupling strength between the system and measuring device. For an arbitrary d-dimensional quantum system, the optimal strengths being…
Approximating a quantum state by the convex mixing of some given states has strong experimental significance and provides potential applications in quantum resource theory. Here we find a closed form of the minimal distance in the sense of…
We determine the quality of randomized social choice mechanisms in a setting in which the agents have metric preferences: every agent has a cost for each alternative, and these costs form a metric. We assume that these costs are unknown to…
The paper investigates the problem of estimating the state of a time-varying system with a linear measurement model; in particular, the paper considers the case where the number of measurements available can be smaller than the number of…
The problem of accurate nonparametric estimation of distributional functionals (integral functionals of one or more probability distributions) has received recent interest due to their wide applicability in signal processing, information…
In this paper, we propose a cost function that corresponds to the mean square errors between estimated values and true values of conditional probability in a discrete distribution. We then obtain the values that minimize the cost function.…
Density level sets are mainly estimated using one of three methodologies: plug-in, excess mass, or a hybrid approach. The plug-in methods are based on replacing the unknown density by some nonparametric estimator, usually the kernel. Thus,…
We consider statistical estimation of superhedging prices using historical stock returns in a frictionless market with d traded assets. We introduce a plugin estimator based on empirical measures and show it is consistent but lacks suitable…
A scheme is developed for estimating state-dependent drift and diffusion coefficients in a stochastic differential equation from time-series data. The scheme does not require to specify parametric forms for the drift and diffusion…
An algorithm to calculate the density of states, based on the well-known Wang-Landau method, is introduced. Independent random walks are performed in different restricted ranges of energy, and the resultant density of states is modified by…
We study nonparametric density estimation problems where error is measured in the Wasserstein distance, a metric on probability distributions popular in many areas of statistics and machine learning. We give the first minimax-optimal rates…
Minimum-uncertainty squeezed states, related to a broad class of observables, are analyzed. Methods for characterizing such states are developed, which are based on numerical solutions of ordinary differential equations. As typical examples…