arXiv research

This paper considers asymptotically hyperbolic manifolds with a finite boundary intersecting the usual infinite boundary -- cornered asymptotically hyperbolic manifolds -- and proves a theorem of Cartan-Hadamard type near infinity for the normal exponential map on the finite boundary. As a main application, a normal fo…

We consider a skew ruled surface $Φ$ in the Euclidean space $E^{3}$ and relative normalizations of it, so that the relative normals at each point lie in the corresponding asymptotic plane of $Φ$. We call such relative normalizations and the resulting relative images of $Φ$ \emph{asymptotic}. We determine all ruled surf…

Paper proposes a debiased estimator for adaptive linear regression.

Local asymptotic minimax risk bounds in a locally asymptotically mixture of normal family of distributions have been investigated under asymmetric loss functions and the asymptotic distribution of the optimal estimator that attains the bound has been obtained.

Paper explores weighted averaging schemes for SGD, achieving asymptotic normality and optimality.

The paper proves asymptotic normality for multinomial logistic regression on null covariates.

Paper proves robust M-estimators' coordinates' normality in high dimensions.

Operational risk models commonly employ maximum likelihood estimation (MLE) to fit loss data to heavy-tailed distributions. Yet several desirable properties of MLE (e.g. asymptotic normality) are generally valid only for large sample-sizes, a situation rarely encountered in operational risk. In this paper, we study how…

Normal distributions ensure asymptotic variance reduction in moment matching Monte Carlo.

Proves mass-capacity inequalities for critical area-normalized capacitors, improving Schwarzschild metric uniqueness.

Defines mass for non-smooth hyperbolic spaces using a modified flow.

Kernel smoothing on unknown manifolds with bounds and asymptotic normality.

As bandit algorithms are increasingly utilized in scientific studies and industrial applications, there is an associated increasing need for reliable inference methods based on the resulting adaptively-collected data. In this work, we develop methods for inference on data collected in batches using a bandit algorithm. …

The study explores normal generators for mapping class groups and their properties.

We study asymptotic properties of maximum likelihood estimators of drift parameters for a jump-type Heston model based on continuous time observations, where the jump process can be any purely non-Gaussian Lévy process of not necessarily bounded variation with a Lévy measure concentrated on $(-1,\infty)$. We prove stro…

Stochastic approximation proves asymptotic normality for non-smooth problems.

Gradient descent on normalized networks reveals sparsity preferences.

We consider a jump-type Cox--Ingersoll--Ross (CIR) process driven by a standard Wiener process and a subordinator, and we study asymptotic properties of the maximum likelihood estimator (MLE) for its growth rate. We distinguish three cases: subcritical, critical and supercritical. In the subcritical case we prove weak …

Study shows stability in X-ray transform on specific hyperbolic manifolds.

We provide non-asymptotic convergence rates of the Polyak-Ruppert averaged stochastic gradient descent (SGD) to a normal random vector for a class of twice-differentiable test functions. A crucial intermediate step is proving a non-asymptotic martingale central limit theorem (CLT), i.e., establishing the rates of conve…

Stochastic algo learns from evolving data, achieving optimal performance.

We address challenges in estimating parameters from adaptively collected data.

Study improves BN TTA under distribution shift using higher-order asymptotics.

The paper improves the empirical bootstrap method for non-normal estimators.

We study the dynamics of the normal implied volatility in a local volatility model, using a small-time expansion in powers of maturity T. At leading order in this expansion, the asymptotics of the normal implied volatility is similar, up to a different definition of the moneyness, to that of the log-normal volatility. …

Asymptotic net is an important concept in discrete differential geometry. In this paper, we show that we can associate affine discrete geometric concepts to an arbitrary non-degenerate asymptotic net. These concepts include discrete affine area, mean curvature, normal and co-normal vector fields and cubic form, and the…

Proposes online debiasing estimators for adaptive linear regression.

The paper addresses statistical inference issues in adaptive experiments.

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 turns out to depend on the correlation between the components, and the explicit s…

We consider a stable Cox--Ingersoll--Ross process driven by a standard Wiener process and a spectrally positive strictly stable Lévy process, and we study asymptotic properties of the maximum likelihood estimator (MLE) for its growth rate based on continuous time observations. We distinguish three cases: subcritical, c…

Study on neural networks' performance under different normalizations as N grows.

This paper analyzes the distribution of genera in 2-bridge knots and proves their asymptotic normality.

We study some asymptotic behavior of the first nonzero eigenvalue of the Lalacian along the normalized Ricci flow and give a direct short proof for an asymptotic upper limit estimate.

We consider the evolution of the asymptotically hyperbolic mass under the curvature-normalized Ricci flow of asymptotically hyperbolic, conformally compactifiable manifolds. In contrast to asymptotically flat manifolds, for which ADM mass is constant during Ricci flow, we show that the mass of an asymptotically hyperbo…

Paper proposes CIV estimator for categorical instruments in small sample settings.

There are many models, often called unnormalized models, whose normalizing constants are not calculated in closed form. Maximum likelihood estimation is not directly applicable to unnormalized models. Score matching, contrastive divergence method, pseudo-likelihood, Monte Carlo maximum likelihood, and noise contrastive…

Defines and analyzes generalized normal ruled surfaces of curves in 3D space.

The paper addresses statistical inference for online decision-making in a contextual bandit setting.

We consider the Laplace normal vector field of relatively normalized ruled surfaces with non-vanishing Gaussian curvature in the three-dimensional Euclidean space $\mathbb{R}^{3}$. We determine all ruled surfaces and all relative normalizations for which the Laplace normal image degenerates into a point or into a curve…

The paper analyzes the randomized midpoint method for Langevin diffusions, revealing biases and asymptotic properties.

New relation found between ADM mass and generalized Komar energy for dynamical spacetimes.

We derive formulas for F measures' standard error and confidence intervals.

Semi-supervised method boosts two-sample testing with covariate data.

Considering the tangent plane at a point to a surface in the four-dimensional Euclidean space, we find an invariant of a pair of two tangents in this plane. If this invariant is zero, the two tangents are said to be conjugate. When the two tangents coincide with a given tangent, then we obtain the normal curvature of t…

SGDM accelerates faster than SGD with large batch sizes and permits broader learning rates.

The paper develops approximations for Pearson's chi-square statistic and applies them to confidence intervals.

The study connects surface geometry in 5D to 4D projections and umbilic curvatures.

SGD's uncertainty quantified in non-convex learning problems.