We define the empirical spectral distribution (ESD) of a random matrix polynomial with invertible leading coefficient, and we study it for complex $n \times n$ Gaussian monic polynomials degree $k$. obtain exact formulae almost sure limit ESD in two distinct scenarios: (1) \rightarrow \infty$ $k$ constant (2) $k $n$ constant. The main tool our approach is replacement principle by Tao, Vu Krishn...

In this paper, we study a two-category classification problem. We indicate the categories by labels Y = 1 and Y = −1. We observe a covariate, or feature, X ∈ X ⊂ R. Consider a collection {ha} of classifiers indexed by a finite-dimensional parameter a, and the classifier ha∗ that minimizes the prediction error over this class. The parameter a∗ is estimated by the empirical risk minimizer ân over...

We address the problem of sequential prediction in the heteroscedastic setting, when both the signal and its variance are assumed to depend on explanatory variables. By applying regret minimization techniques, we devise an efficient online learning algorithm for the problem, without assuming that the error terms comply with a specific distribution. We show that our algorithm can be adjusted to ...

There is increasing support for sharing individual-level data generated by medical and public health research. This scoping review of empirical research and conceptual literature examined stakeholders' perspectives of ethical best practices in data sharing, particularly in low- and middle-income settings. Sixty-nine empirical and conceptual articles were reviewed, of which, only five were empir...

This paper deals with the problem of parameter estimation based on certain eigenspaces of the empirical covariance matrix of an observed multidimensional time series, in the case where the time series dimension and the observation window grow to infinity at the same pace. In the area of large random matrix theory, recent contributions studied the behavior of the extreme eigenvalues of a random ...

We consider estimation of the covariance matrix of a multivariate random vector under the constraint that certain covariances are zero. We first present an algorithm, which we call Iterative Conditional Fitting, for computing the maximum likelihood estimator of the constrained covariance matrix, under the assumption of multivariate normality. In contrast to previous approaches, this algorithm h...