Related papers: On the irrationality measure function in average
In this paper, under certain restrictions on linear factors of the denominator of a rational function of two variables, the leading term of the asymptotic expansion of the coefficients is found.
We evaluate friable averages of arithmetic functions whose Dirichlet series is analytically close to some negative power of the Riemann zeta function. We obtain asymptotic expansions resembling those provided by the Selberg-Delange method…
The asymptotic behaviour of partial sums of generalized hypergeometric series of unit argument is investigated.
The problem of estimating a linear functional based on observational data is canonical in both the causal inference and bandit literatures. We analyze a broad class of two-stage procedures that first estimate the treatment effect function,…
Convergence rate estimates in limit theorems for sums of independent random variables are considered.
We investigate functions with the property that for every interval, the slope at the midpoint of the interval is the same as the average slope. More generally, we find functions whose average slopes over intervals are given by the slope at…
This paper is concerned with inference based on the mean function of a functional time series, which is defined as a collection of curves obtained by splitting a continuous time record, e.g. into daily or annual curves. We develop a normal…
We investigate asymptotic inference in a linear regression model where both response and regressors are functions, using an estimator based on functional principal components analysis. Although this approach is widely used in functional…
We illustrate the interplay between certain discrete and continuous problems, by presenting a method for the study of the asymptotics of a divergent sequence, through consideration of the asymptotics of its continuous analogue
We consider an estimation problem of expected functionals of a general random element that values in a metric space. If the functional forms an explicit function of some unknown parameters, we can estimate it by plugging-in a suitable…
We study the questions of determining the asymptotics of the probabilistic characteristics of additive arithmetic functions in the paper, regardless of whether they have a limit distribution or not. Several assertions are proved about the…
We derive the joint asymptotic distribution of empirical quantiles and expected shortfalls under general conditions on the distribution of the underlying observations. In particular, we do not assume that the distribution function is…
We analyze the fine structure of Clark measures and Clark isometries associated with two-variable rational inner functions on the bidisk. In the degree (n,1) case, we give a complete description of supports and weights for both generic and…
We study the asymptotic behavior of the sums of divisors when the integers are modelled with the Bernoulli random walk; We prealably study the correlation properties of the corresponding system.
We study generalized permutohedra and supermodular functions. Specifically we analyze decomposability and irreducibility for these objects and establish some asymptotic behavior. We also study a related problem on irreducibility for…
A random coefficient autoregressive process is deeply investigated in which the coefficients are correlated. First we look at the existence of a strictly stationary causal solution, we give the second-order stationarity conditions and the…
We estimate the kernel function of a symmetric alpha stable ($S\alpha S$) moving average random function which is observed on a regular grid of points. The proposed estimator relies on the empirical normalized (smoothed) periodogram. It is…
We give asymptotic upper and lower bounds for the real and imaginary parts of cycle integrals of the classical modular j-function along geodesics that correspond to Markov irrationalities.
Measurement error is an important problem that has not been very well studied in the context of Functional Data Analysis. To the best of our knowledge, there are no existing methods that address the presence of functional measurement errors…
We give an informal introduction to the most basic techniques used to evaluate moments on the critical line of the Riemann zeta-function and to find asymptotics for sums of arithmetic functions.