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We introduce a new method of estimation of parameters in semiparametric and nonparametric models. The method is based on estimating equations that are $U$-statistics in the observations. The $U$-statistics are based on higher order…
In a mixed generalized linear model, the goal is to learn multiple signals from unlabeled observations: each sample comes from exactly one signal, but it is not known which one. We consider the prototypical problem of estimating two…
Nonparametric tests provide robust and powerful alternatives to the corresponding least squares methods. There are two approaches to nonparametric pairwise comparisons of treatment effects, the method based on pairwise rankings and the…
The segmented formulation of the Tau method is used to numerically solve the non-autonomous forward-backward functional differential equation x'(t) = a(t)x(t) + b(t)x(t-1) + c(t)x(t+1), where x is the unknown function, a, b, and c are known…
We propose an empirical measure of the approximate accuracy of feature importance estimates in deep neural networks. Our results across several large-scale image classification datasets show that many popular interpretability methods…
We present a method for estimating sparse high-dimensional inverse covariance and partial correlation matrices, which exploits the connection between the inverse covariance matrix and linear regression. The method is a two-stage estimation…
We present a nonparametric method for estimating the value and several derivatives of an unknown, sufficiently smooth real-valued function of real-valued arguments from a finite sample of points, where both the function arguments and the…
Truncated conditional expectation functions are objects of interest in a wide range of economic applications, including income inequality measurement, financial risk management, and impact evaluation. They typically involve truncating the…
The multipath radio channel is considered to have a non-bandlimited channel impulse response. Therefore, it is challenging to achieve high resolution time-delay (TD) estimation of multipath components (MPCs) from bandlimited observations of…
Positive and unlabelled learning is an important problem which arises naturally in many applications. The significant limitation of almost all existing methods lies in assuming that the propensity score function is constant (SCAR…
State-space models are ubiquitous in the statistical literature since they provide a flexible and interpretable framework for analyzing many time series. In most practical applications, the state-space model is specified through a…
The simultaneous estimation of multiple unknown parameters lies at heart of a broad class of important problems across science and technology. Currently, the state-of-the-art performance in the such problems is achieved by nonparametric…
For Paley-Wiener functions on weighted combinatorial finite or infinite graphs we develop a weighted sampling theory in which samples are defined as inner products with weight functions (measuring devices). Three reconstruction methods are…
The purpose is to study qualitative and quantitative rates of image compression by using different Haar wavelet banks. The experimental results of adaptive compression are provided. The paper deals with specific examples of orthogonal Haar…
We present a statistical analysis of music scores from different composers using detrended fluctuation analysis. We find different fluctuation profiles that correspond to distinct auto-correlation structures of the musical pieces. Further,…
Sublinear functionals of random variables are known as sublinear expectations; they are convex homogeneous functionals on infinite-dimensional linear spaces. We extend this concept for set-valued functionals defined on measurable set-valued…
We provide general adaptive upper bounds for estimating nonparametric functionals based on second order U-statistics arising from finite dimensional approximation of the infinite dimensional models. We then provide examples of functionals…
We propose a new approach to linear ill-posed inverse problems. Our algorithm alternates between enforcing two constraints: the measurements and the statistical correlation structure in some transformed space. We use a non-linear multiscale…
We report on the use of a stochastic trace estimator algorithm, based on mutually unbiased bases, for evaluating the trace of a matrix differential operator appearing in the context of lattice simulations for the discretized superstring…
The paper introduces a new estimation method for the standard linear regression model. The procedure is not driven by the optimisation of any objective function rather, it is a simple weighted average of slopes from observation pairs. The…