Related papers: Covering numbers for bounded variation functions
In this paper, we study functions of bounded variation on a complete and connected metric space with finite one-dimensional Hausdorff measure. The definition of BV functions on a compact interval based on pointwise variation is extended to…
In contrast to the univariate case, several definitions are available for the notion of bounded variation for a bivariate function. This article is an attempt to study the Hausdorff dimension and box dimension of the graph of a continuous…
We present the foundations of the theory of functions of bounded variation and sets of finite perimeter in abstract Wiener spaces.
In this paper, we study finite-sample properties of the least squares estimator in first order autoregressive processes. By leveraging a result from decoupling theory, we derive upper bounds on the probability that the estimate deviates by…
In the paper, some lower bounds for polygamma functions are refined.
In this note, we study the relationship between the variational gap and the variance of the (log) likelihood ratio. We show that the gap can be upper bounded by some form of dispersion measure of the likelihood ratio, which suggests the…
Simple upper and lower bounds are obtained for the integral $\int_0^x\mathrm{e}^{-\gamma t}t^\nu I_\nu(t)\,\mathrm{d}t$, $x>0$, $\nu>-\frac{1}{2}$, $0<\gamma<1$. Most of our bounds for this integral are tight as $x\rightarrow\infty$. We…
This paper is devoted to present new error bounds of regularized gap functions for polynomial variational inequalities with exponents explicitly determined by the dimension of the underlying space and the number/degree of the involved…
Under certain initial conditions, we prove the existence of set-valued selectors of univariate compact-valued multifunctions of bounded (Jordan) variation when the notion of variation is defined taking into account only the Pompeiu…
Approximation of scattered data is often a task in many engineering problems. The Radial Basis Function (RBF) approximation is appropriate for large scattered (unordered) datasets in d-dimensional space. This approach is useful for a higher…
We derive closed form expressions for the lower expectations that correspond to total variation distance and chi-squared divergence balls around a probability mass function over a finite set.
Given a finite number of samples of a continuous set-valued function F, mapping an interval to compact subsets of the real line, we develop good approximations of F, which can be computed efficiently.
An important tool to quantify the likeness of two probability measures are f-divergences, which have seen widespread application in statistics and information theory. An example is the total variation, which plays an exceptional role among…
The method is described and tested for analysis of statistical parameters of reduced neutron widths distributions accounting for possibility of coexistence of superposition of some functions with non-zero mean values of neutron amplitude…
We show that any sequence of well-behaved (e.g. bounded and non-constant) real-valued functions of $n$ boolean variables $\{f_n\}$ admits a sequence of coordinates whose $L^1$ influence under the $p$-biased distribution, for any…
In this article, we study the fractional spherical maximal function and its lacunary counterpart. We study the necessary and sufficient conditions for $L^p-L^q$ boundedness of both maximal functions. In particular, we prove the restricted…
Lubrication expressions for the friction coefficients of a spherical particle moving in a fluid between and along two parallel solid walls are explicitly evaluated in the low-Reynolds-number regime. They are used to determine lubrication…
In this paper, we develop an exact method for computing the minimum coverage probability of Wald interval for estimation of binomial parameters. Similar approach can be used for other type of confidence intervals.
We provide upper and lower bounds for the mean ${\mathscr M}(H)$ of $\sup_{t\geqslant 0} \{B_H(t) - t\}$, with $B_H(\cdot)$ a zero-mean, variance-normalized version of fractional Brownian motion with Hurst parameter $H\in(0,1)$. We find…
For the basic maximum likelihood estimating function of the two parameters Weibull distribution, a simple proof on its global monotonicity is given to ensure the existence and uniqueness of its solution. The boundary of the function's…