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This paper deals with subspace estimation in the small sample size regime, where the number of samples is comparable in magnitude with the observation dimension. The traditional estimators, mostly based on the sample correlation matrix, are…
We provide new asymptotic theory for kernel density estimators, when these are applied to autoregressive processes exhibiting moderate deviations from a unit root. This fills a gap in the existing literature, which has to date considered…
We systematically investigate quantum algorithms and lower bounds for mean estimation given query access to non-identically distributed samples. On the one hand, we give quantum mean estimators with quadratic quantum speed-up given samples…
As quantum tomography is becoming a key component of the quantum engineering toolbox, there is a need for a deeper understanding of the multitude of estimation methods available. Here we investigate and compare several such methods: maximum…
In this paper, we present the asymptotic distribution of M-estimators for parameters in non-stationary AR(p) processes. The innovations are assumed to be in the domain of attraction of a stable law with index $0<\alpha\le2$. In particular,…
We study asymptotic behavior of one-step weighted $M$-estimators based on samples from arrays of not necessarily identically distributed random variables and representing explicit approximations to the corresponding consistent weighted…
Clarke and Barron have recently shown that the Jeffreys' invariant prior of Bayesian theory yields the common asymptotic (minimax and maximin) redundancy of universal data compression in a parametric setting. We seek a possible analogue of…
We estimate the quantum state of a light beam from results of quantum homodyne measurements performed on identically prepared quantum systems. The state is represented through the Wigner function, a generalized probability density on…
The weak convergence of the quantile processes, which are constructed based on different estimators of the finite population quantiles, is shown under various well-known sampling designs based on a superpopulation model. The results related…
The number of times that we can access a system to extract information via quantum metrology is always finite, and possibly small, and realistic amounts of prior knowledge tend to be moderate. Thus theoretical consistency demands a…
We study parametric inference for diffusion processes when observations occur nonsynchronously and are contaminated by market microstructure noise. We construct a quasi-likelihood function and study asymptotic mixed normality of…
This study proposes a robust estimator for stochastic frontier models by integrating the idea of Basu et al. [1998, Biometrika 85, 549-559] into such models. We verify that the suggested estimator is strongly consistent and asymptotic…
The first purpose of this article is to obtain a.s. asymptotic properties of the maximum likelihood estimator in the autoregressive process driven by a stationary Gaussian noise. The second purpose is to show the local asymptotic normality…
Within the framework of likelihood-based statistical tests for high energy physics measurements, we derive generalized expressions for estimating the statistical significance of discovery using the asymptotic approximations of Wilks and…
This paper proposes a local representation for Empirical Likelihood (EL). EL admits the classical local linear quadratic representation by its likelihood ratio property. A local estimator is derived by using the new representation.…
We consider the estimation of parametric fractional time series models in which not only is the memory parameter unknown, but one may not know whether it lies in the stationary/invertible region or the nonstationary or noninvertible…
Quantum simulators are widely seen as one of the most promising near-term applications of quantum technologies. However, it remains unclear to what extent a noisy device can output reliable results in the presence of unavoidable…
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…
Many results related to quantitative problems in the metric theory of Diophantine approximation are asymptotic, such as the number of rational solutions to certain inequalities grows with the same rate almost everywhere modulo an asymptotic…
We consider the estimation of two-sample integral functionals, of the type that occur naturally, for example, when the object of interest is a divergence between unknown probability densities. Our first main result is that, in wide…