Related papers: Extrema of multinomial assignment process
Stochastic processes are often used to model complex scientific problems in fields ranging from biology and finance to engineering and physical science. This paper investigates rate-optimal estimation of the volatility matrix of a…
We use the framework of multivariate regular variation to analyse the extremal behaviour of preferential attachment models. To this end, we follow a directed linear preferential attachment model for a random, heavy-tailed number of steps in…
We study a new family of random variables, that each arise as the distribution of the maximum or minimum of a random number $N$ of i.i.d.~random variables $X_1,X_2,\ldots,X_N$, each distributed as a variable $X$ with support on $[0,1]$. The…
Consider a standard white Wishart matrix with parameters $n$ and $p$. Motivated by applications in high-dimensional statistics and signal processing, we perform asymptotic analysis on the maxima and minima of the eigenvalues of all the $m…
We study an asymptotical behavior of the maximal degree in the degree distribution in an evolving tree model combining the local choice and the Mori's preferential attachment. In the considered model, the random graph is constructed in the…
The purpose of this paper is to study the asymptotic behavior of the weighted least square estimators of the unknown parameters of random coefficient bifurcating autoregressive processes. Under suitable assumptions on the immigration and…
This article provides an original understanding of the behavior of a class of graph-oriented semi-supervised learning algorithms in the limit of large and numerous data. It is demonstrated that the intuition at the root of these methods…
We explore the behavior and establish new properties of the cumulative-sum process (CUSUM) and its running maximum. The study includes precise expressions for CUSUM's moment generating function and moments, fast recursive computing…
We give the cumulative distribution function of $M_n$, the maximum of a sequence of $n$ observations from an ARMA(1, 1) process. Solutions are first given in terms of repeated integrals and then for the case, where the underlying random…
The allocation problem for multivariate stratified random sampling as a problem of stochastic matrix integer mathematical programming is considered. With these aims the asymptotic normality of sample covariance matrices for each strata is…
This article conducts a large dimensional study of a simple yet quite versatile classification model, encompassing at once multi-task and semi-supervised learning, and taking into account uncertain labeling. Using tools from random matrix…
We study the consistency of sample mean-variance portfolios of arbitrarily high dimension that are based on Bayesian or shrinkage estimation of the input parameters as well as weighted sampling. In an asymptotic setting where the number of…
Algorithmic modeling relies on limited information in data to extrapolate outcomes for unseen scenarios, often embedding an element of arbitrariness in its decisions. A perspective on this arbitrariness that has recently gained interest is…
This paper gives a new representation of Pickands' constants, which arise in the study of extremes for a variety of Gaussian processes. Using this representation, we resolve the long-standing problem of devising a reliable algorithm for…
Risk management is particularly concerned with extreme events, but analysing these events is often hindered by the scarcity of data, especially in a multivariate context. This data scarcity complicates risk management efforts. Various tools…
Neural networks allow us to model complex relationships between variables. We show how to efficiently find extrema of a trained neural network in regression problems. Finding the extremizing input of an approximated model is formulated as…
In this paper, we study three asymptotic regimes that can be applied to ranking and selection (R&S) problems with general sample distributions. These asymptotic regimes are constructed by sending particular problem parameters (probability…
Machine learning provides algorithms that can learn from data and make inferences or predictions on data. Stochastic acceptors or probabilistic automata are stochastic automata without output that can model components in machine learning…
In the paper I study properties of random polynomials with respect to a general system of functions. Some lower bounds for the mathematical expectation of the uniform and recently introduced integral-uniform norms of random polynomials are…
Maximum entropy models, motivated by applications in neuron science, are natural generalizations of the $\beta$-model to weighted graphs. Similar to the $\beta$-model, each vertex in maximum entropy models is assigned a potential parameter,…