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Considering the constrained stochastic optimization problem over a time-varying random network, where the agents are to collectively minimize a sum of objective functions subject to a common constraint set, we investigate asymptotic…
Product codes are widely used in data-storage, optical and wireless applications. Their analytical performance evaluation usually relies on the truncated union bound, which provides a low error rate approximation based on the minimum…
Linear codes with few weights have applications in secret sharing, authentication codes, association schemes and strongly regular graphs. In this paper, several classes of two-weight and three-weight linear codes are presented and their…
In this paper, we consider a weighted local linear estimator based on the inverse selection probability for nonparametric regression with missing covariates at random. The asymptotic distribution of the maximal deviation between the…
In this paper we give an improvement of the degree of the homogeneous linear recurrence with integer coefficients that exponential sums of symmetric Boolean functions satisfy. This improvement is tight. We also compute the asymptotic…
Linear codes with a few weights have important applications in authentication codes, secret sharing, consumer electronics, etc.. The determination of the parameters such as Hamming weight distributions and complete weight enumerators of…
We discuss in detail the asymptotic distribution of sample expectiles. First, we show uniform consistency under the assumption of a finite mean. In case of a finite second moment, we show that for expectiles other then the mean, only the…
This paper establishes asymptotic results for the maximum likelihood and restricted maximum likelihood (REML) estimators of the parameters in the nested error regression model for clustered data when both of the number of independent…
We present sharp tail asymptotics for the density and the distribution function of linear combinations of correlated log-normal random variables, that is, exponentials of components of a correlated Gaussian vector. The asymptotic behavior…
This is a survey of results concerning the asymptotic equilibrium distribution of zeros of random holomorphic polynomials and holomorphic sections of high powers of a positive line bundle, as related to the authors' recent work. Our primary…
Peak counts have been shown to be an excellent tool to extract the non-Gaussian part of the weak lensing signal. Recently, we developped a fast stochastic forward model to predict weak-lensing peak counts. Our model is able to reconstruct…
We establish asymptotic normality of weighted sums of periodograms of a stationary linear process where weights depend on the sample size. Such sums appear in numerous statistical applications and can be regarded as a discretized versions…
Permutations of correlated sequences of random variables appear naturally in a variety of applications such as graph matching and asynchronous communications. In this paper, the asymptotic statistical behavior of such permuted sequences is…
This work proves new results on the ability of binary Reed-Muller codes to decode from random errors and erasures. We obtain these results by proving improved bounds on the weight distribution of Reed-Muller codes of high degrees.…
In this paper, we establish a new law of large numbers with the rate of convergence for special partial sums in a probability space. The proof relies on nonlinear expectation theory, as the uncertainty of random variables in the special…
A general method is presented for deriving the limiting behavior of estimators that are defined as the values of parameters optimizing an empirical criterion function. The asymptotic behavior of such estimators is typically deduced from…
We study the distribution of the maximum likelihood estimate (MLE) in high-dimensional logistic models, extending the recent results from Sur (2019) to the case where the Gaussian covariates may have an arbitrary covariance structure. We…
Frequentist-style large-sample properties of Bayesian posterior distributions, such as consistency and convergence rates, are important considerations in nonparametric problems. In this paper we give an analysis of Bayesian asymptotics…
The spectra of random feature matrices provide essential information on the conditioning of the linear system used in random feature regression problems and are thus connected to the consistency and generalization of random feature models.…
We study the density of the weights of Generalized Reed--Muller codes. Let $RM_p(r,m)$ denote the code of multivariate polynomials over $\F_p$ in $m$ variables of total degree at most $r$. We consider the case of fixed degree $r$, when we…