Related papers: A uniform estimate for rate functions in large dev…

Uniform deviation bounds limit the difference between a model's expected loss and its loss on an empirical sample uniformly for all models in a learning problem. As such, they are a critical component to empirical risk minimization. In this…

This paper provides new uniform rate results for kernel estimators of absolutely regular stationary processes that are uniform in the bandwidth and in infinite-dimensional classes of dependent variables and regressors. Our results are…

Consider the inhomogeneous Erd\H{o}s-R\'enyi random graph (ERRG) on $n$ vertices for which each pair $i,j\in\{1,\ldots,n\}$, $i\neq j$ is connected independently by an edge with probability $r_n(\frac{i-1}{n},\frac{j-1}{n})$, where…

In this paper, some global existence and uniform asymptotic stability results for fractional functional differential equations are proved. It is worthy mentioning that when $\alpha=1$ the initial value problem (1.1) reduces to a classical…

We consider an isolated macroscopic quantum system in a pure state $\psi_t$ evolving unitarily in a separable Hilbert space $\mathcal{H}$ and take for granted that different macro states $\nu$ correspond to mutually orthogonal subspaces…

We consider the problem of estimating an arbitrary smooth functional of $k \geq 1 $ distribution functions (d.f.s.) in terms of random samples from them. The natural estimate replaces the d.f.s by their empirical d.f.s. Its bias is…

We give stationary estimates for the derivative of the expectation of a non-smooth function of bounded variation f of the workload in a G/G/1/$\infty$ queue, with respect to a parameter influencing the distribu- tion of the input process.…

For the functions from sets $C_\beta^\psi C$ and $C_\beta^\psi L_s, \ 1\leq s\leq\infty$, generated by sequences $\psi(k)>0$ satisfying the condition d'Alembert $\mathop {\rm \lim}\limits_{k\rightarrow\infty}\frac{\psi(k+1)}{\psi(k)}=q, \…

We consider estimating the proportion of random variables for two types of composite null hypotheses: (i) the means or medians of the random variables belonging to a non-empty, bounded interval; (ii) the means or medians of the random…

While statistics focusses on hypothesis testing and on estimating (properties of) the true sampling distribution, in machine learning the performance of learning algorithms on future data is the primary issue. In this paper we bridge the…

We establish H\"older regularity and gradient estimates for the transition semigroup of the solutions to the following SDE: $$ {\rm d} X_t=\sigma (t, X_{t-}){\rm d} Z_t+b (t, X_t){\rm d} t,\ \ X_0=x\in{\mathbb R}^d, $$ where $( Z_t)_{t\geq…

We derive the large deviation principle for radial Schramm-Loewner evolution ($\operatorname{SLE}$) on the unit disk with parameter $\kappa \rightarrow \infty$. Restricting to the time interval $[0,1]$, the good rate function is finite only…

For a decreasing real valued function $\psi$, a pair $(A,\mathbf{b})$ of a real $m\times n$ matrix $A$ and $\mathbf{b}\in\mathbb{R}^m$ is said to be $\psi$-Dirichlet improvable if the system $$\|A\mathbf{q}+\mathbf{b}-\mathbf{p}\|^m <…

We consider large deviations of empirical measures of diffusion processes. In a first part, we present conditions to obtain a large deviations principle (LDP) for a precise class of unbounded functions. This provides an analogue to the…

We derive a large deviation principle for random permutations induced by probability measures of the unit square, called permutons. These permutations are called $\mu$-random permutations. We also introduce and study a new general class of…

Large deviation principles for hyperbolic systems are well studied and provide exponential rates for the deviations of Birkhoff averages from their limit. This short article presents a local large deviation principle for Smale spaces, in…

On the sets of $2\pi$-periodic functions $f$, which are defined with a help of $(\psi, \beta)$-integrals of the functions $\varphi$ from $L_{1}$, we establish Lebesgue-type inequalities, in which the uniform norms of deviations of Fourier…

We obtained order estimations for the best uniform approximations by trigonometric polynomials and approximations by Fourier sums of classes of $2\pi$-periodic continuous functions, which $(\psi,\beta)$-derivatives $f_{\beta}^{\psi}$ belong…

In this work, we establish, for a strong Feller process, the large deviation principle for the occupation measure conditioned not to exit a given subregion. The rate function vanishes only at a unique measure, which is the so-called…

I--MR charts commonly estimate the process standard deviation $\sigma$ via the span-2 average moving range divided by the unbiasing constant $d_2$; unlike the unbiased sample standard deviation ($S/c_4$), this estimator depends on ordering…