Related papers: Optimality of the Maximum Likelihood estimator in …
A procedure for asymptotic bias reduction of maximum likelihood estimates of generic estimands is developed. The estimator is realized as a plug-in estimator, where the parameter maximizes the penalized likelihood with a penalty function…
As the Cosmic Microwave Background (CMB) radiation is observed to higher and higher angular resolution the size of the resulting datasets becomes a serious constraint on their analysis. In particular current algorithms to determine the…
In quantum estimation for a $d$-parameter family of density operators on a finite-dimensional Hilbert space $\mathcal{H}$, an estimator is specified by a pair $\left(M,\hat{\theta}\right)$, where $M$ is a POVM with a finite outcome set…
The tuning parameter selection strategy for penalized estimation is crucial to identify a model that is both interpretable and predictive. However, popular strategies (e.g., minimizing average squared prediction error via cross-validation)…
We propose a novel estimation approach for a general class of semi-parametric time series models where the conditional expectation is modeled through a parametric function. The proposed class of estimators is based on a Gaussian…
We develop a new method for reconstructing cluster mass profiles and large-scale structure from the cosmic microwave background (CMB). By analyzing the likelihood of CMB lensing, we analytically prove that standard quadratic estimators for…
This work studies an experimental design problem where {the values of a predictor variable, denoted by $x$}, are to be determined with the goal of estimating a function $m(x)$, which is observed with noise. A linear model is fitted to…
The localization of directional RF emitters presents significant challenges for electronic warfare applications. Traditional localization methods, designed for omnidirectional emitters, experience degraded performance when applied to…
The subject of this paper is optimisation of weak lensing tomography: We carry out numerical minimisation of a measure of total statistical error as a function of the redshifts of the tomographic bin edges by means of a Nelder-Mead…
In linear regression we wish to estimate the optimum linear least squares predictor for a distribution over $d$-dimensional input points and real-valued responses, based on a small sample. Under standard random design analysis, where the…
We investigate the problem of noise bias in maximum likelihood and maximum a posteriori estimators for cosmic shear. We derive the leading and next-to-leading order biases and compute them in the context of galaxy ellipticity measurements,…
In this paper we investigate the performance of a variety of estimation techniques for the scale and shape parameter of the Lomax distribution. These methods include traditional methods such as the maximum likelihood estimator and the…
Threshold and ambiguity phenomena are studied in Part 1 of this work where approximations for the mean-squared-error (MSE) of the maximum likelihood estimator are proposed using the method of interval estimation (MIE), and where approximate…
Feature alignment methods are used in many scientific disciplines for data pooling, annotation, and comparison. As an instance of a permutation learning problem, feature alignment presents significant statistical and computational…
Some quasi-arithmetic means of random variables easily give unbiased strongly consistent closed-form estimators of the joint of the location and scale parameters of the Cauchy distribution. The one-step estimators of those quasi-arithmetic…
In this paper we consider regression problems subject to arbitrary noise in the operator or design matrix. This characterization appropriately models many physical phenomena with uncertainty in the regressors. Although the problem has been…
This paper proposes a new method of bandwidth selection in kernel estimation of density and distribution functions motivated by the connection between maximisation of the entropy of probability integral transforms and maximum likelihood in…
In this paper we study the computation of the nonparametric maximum likelihood estimator (NPMLE) in multivariate mixture models. Our first approach discretizes this infinite dimensional convex optimization problem by fixing the support…
I present an analytic method for estimating the errors in fitting a distribution. A well-known theorem from statistics gives the minimum variance bound (MVB) for the uncertainty in estimating a set of parameters $\l_i$, when a distribution…
The majority of present efforts to constrain cosmological parameters with cosmic microwave background (CMB) anisotropy data employ approximate likelihood functions, the time consuming nature of a complete analysis being a major obstacle. We…