Related papers: Asymptotic Normality of Extensible Grid Sampling

We study the partition function from random matrix theory using a well known connection to orthogonal polynomials, and a recently developed Riemann-Hilbert approach to the computation of detailed asymptotics for these orthogonal…

Parametric high-dimensional regression analysis requires the usage of regularization terms to get interpretable models. The respective estimators can be regarded as regularized M-functionals which are naturally highly nonlinear. We study…

A common method for estimating the Hessian operator from random samples on a low-dimensional manifold involves locally fitting a quadratic polynomial. Although widely used, it is unclear if this estimator introduces bias, especially in…

In this paper, we present the asymptotic theory for integrated functions of increments of Brownian local times in space. Specifically, we determine their first-order limit, along with the asymptotic distribution of the fluctuations. Our key…

We analytically compute asymptotic expansions of a 1-dimensional sub-manifold of stable and unstable manifolds in a 4-dimensional symplectic mapping by using the method called asymptotic expansions beyond all orders. This method enables us…

Asymptotic uniform confidence bands are constructed for a multivariate nonparametric regression model with heteroscedastic noise, employing histogram estimators under flexible partition conditions. The construction is especially applicable…

In this paper, we study parametric nonlinear regression under the Harris recurrent Markov chain framework. We first consider the nonlinear least squares estimators of the parameters in the homoskedastic case, and establish asymptotic theory…

We consider covariance asymptotics for linear statistics of general stationary random measures in terms of their truncated pair correlation measure. We give exact infinite series-expansion formulas for covariance of smooth statistics of…

We consider covariance parameter estimation for Gaussian processes with functional inputs. From an increasing-domain asymptotics perspective, we prove the asymptotic consistency and normality of the maximum likelihood estimator. We extend…

For a simple finite graph G denote by {G \brace k} the number of ways of partitioning the vertex set of G into k non-empty independent sets (that is, into classes that span no edges of G). If E_n is the graph on n vertices with no edges…

We consider a modified quadratic variation of the Hermite process based on some well-chosen increments of this process. These special increments have the very useful property to be independent and identically distributed up to…

The objective of this paper is to obtain asymptotic results for shifted sums of multiplicative functions of the form $g \ast 1$, where the function $g$ satisfies the Ramanujan conjecture and has conjectured upper bounds on square moments of…

We study asymptotic normality of the randomized periodogram estimator of quadratic variation in the mixed Brownian--fractional Brownian model. In the semimartingale case, that is, where the Hurst parameter $H$ of the fractional part…

We first establish a local gradient estimate for anisotropic $p$-harmonic functions. A key feature of our estimate is that the constant remains bounded as $p\to 1$; consequently, in the limit $p\to 1$, this estimate yields the local…

A spectral problem is considered in a thin $3D$ graph-like junction that consists of three thin curvilinear cylinders that are joined through a domain (node) of the diameter $\mathcal{O}(\varepsilon),$ where $\varepsilon$ is a small…

The paper concerns the asymptotic distribution of the mixture density estimator, proposed by Oppenheim et al 2006, in the aggregation/disaggregation problem of random parameter AR(1) process. We prove that, under mild conditions on the…

We show, through local estimates and simulation, that if one constrains simple graphs by their densities $\varepsilon$ of edges and $\tau$ of triangles, then asymptotically (in the number of vertices) for over $95\%$ of the possible range…

In this paper, we study the asymptotic behavior of a semi-linear slow-fast stochastic partial differential equation with singular coefficients. Using the Poisson equation in Hilbert space, we first establish the strong convergence in the…

We establish the asymptotic expansion in $\beta$ matrix models with a confining, off-critical potential, in the regime where the support of the equilibrium measure is a union of segments. We first address the case where the filling…

We study the asymptotic properties of an estimator of Hurst parameter of a stochastic differential equation driven by a fractional Brownian motion with $H > 1/2$. Utilizing the theory of asymptotic expansion of Skorohod integrals introduced…