Related papers: Dimer lambda_3 = .453 +/- .001 and Some Other Very…

We calculate the triple correlations for the truncated divisor sum $\lambda_{R}(n)$. The $\lambda_{R}(n)$'s behave over certain averages just as the prime counting von Mangoldt function $\Lambda(n)$ does or is conjectured to do. We also…

It is well known that the asymptotic variance of sample quantiles can be reduced under heterogeneity relative to the i.i.d. setting. However, asymptotically correct confidence intervals for quantiles are not yet available. We propose a…

We consider the problems of confidence estimation and hypothesis testing on a parameter of signal observed in Gaussian white noise. For these problems we point out lower bounds of asymptotic efficiency in the zone of moderate deviation…

We are interested in the problem of robust parametric estimation of a density from $n$ i.i.d. observations. By using a practice-oriented procedure based on robust tests, we build an estimator for which we establish non-asymptotic risk…

Large language models (LLMs) increasingly help people solve problems, from debugging code to repairing machinery. This process requires generating plausible hypotheses from partial descriptions, then updating them as more information…

We propose an iterative estimating equations procedure for analysis of longitudinal data. We show that, under very mild conditions, the probability that the procedure converges at an exponential rate tends to one as the sample size…

It's well known that in the high-level error bound for multiquadric interpolation there is a crucial constant lambda lying between 0 and 1 which connot be calculated or even approximated. The purpose of this paper is to answer this…

We consider fluctuations of error terms $\Delta(x)$ appearing in the asymptotic formula for a summatory function of coefficients of the Dirichlet series. These are quantified via $\Omega$ and $\Omega_{\pm}$ estimates. We obtain $\Omega$…

We propose a consistent estimator of sharp bounds on the variance of the difference-in-means estimator in completely randomized experiments. Generalizing Robins [Stat. Med. 7 (1988) 773-785], our results resolve a well-known identification…

Exploiting an iterative formula already introduced in a previous manuscript to count the number $O_d$ of finite $O$-sequences of multiplicity $d$, we obtain some new information about $O_d$. Letting $A_d$ be the number of the finite…

We present some new nonparametric estimators of entropies and we establish almost sure consistency and central limit Theorems for some of the most important entropies in the discrete case. Our theorical results are validated by simulations.

The telegraph process $\{X(t), t>0\}$, is supposed to be observed at $n+1$ equidistant time points $t_i=i\Delta_n,i=0,1,..., n$. The unknown value of $\lambda$, the underlying rate of the Poisson process, is a parameter to be estimated. The…

This paper deals with the problem of outliers in high frequency observation data from diffusion processes. Robust estimation methods are needed because the inclusion of outliers can lead to incorrect statistical inference even in the…

We study the problem of estimating the diagonal of an implicitly given matrix $A$. For such a matrix we have access to an oracle that allows us to evaluate the matrix vector product $Av$. For random variable $v$ drawn from an appropriate…

By extending the methods in Peligrad et al. (2014a, b), we establish exact moderate and large deviation asymptotics for linear random fields with independent innovations. These results are useful for studying nonparametric regression with…

In this paper we present a new error bound on sampling algorithms for frequent itemsets mining. We show that the new bound is asymptotically tighter than the state-of-art bounds, i.e., given the chosen samples, for small enough error…

Given good knowledge on the even moments, we derive asymptotic formulas for $\lambda$-th moments of primes in short intervals and prove "equivalence" result on odd moments. We also provide numerical evidence in support of these results.

This paper shows that the logarithm of the epsilon-error capacity (average error probability) for n uses of a discrete memoryless channel is upper bounded by the normal approximation plus a third-order term that does not exceed 1/2 log n +…

Iterative numerical algorithms are typically equipped with a stopping criterion, where the iteration process is terminated when some error or misfit measure is deemed to be below a given tolerance. This is a useful setting for comparing…

Importance weighted variational inference (Burda et al., 2015) uses multiple i.i.d. samples to have a tighter variational lower bound. We believe a joint proposal has the potential of reducing the number of redundant samples, and introduce…