Related papers: Constrained correlation functions
This paper extends the standard chaining technique to prove excess risk upper bounds for empirical risk minimization with random design settings even if the magnitude of the noise and the estimates is unbounded. The bound applies to many…
We prove lower bounds for energy in the Gaussian core model, in which point particles interact via a Gaussian potential. Under the potential function $t \mapsto e^{-\alpha t^2}$ with $0 < \alpha < 4\pi/e$, we show that no point…
Let X_n=(x_{ij}) be an n by p data matrix, where the n rows form a random sample of size n from a certain p-dimensional population distribution. Let R_n=(\rho_{ij}) be the p\times p sample correlation matrix of X_n; that is, the entry…
In this paper, I revisit the constraints obtained by several authors (Reichart et al. 1999; Eke et al. 1998; Henry 2000) on the estimated values of $\Omega_{\rm m}$, $n$ and $\sigma_8$ in the light of recent theoretical developments: 1) new…
We present constraints on the evolution of large-scale structure from a catalog of 710,000 galaxies with I_AB <= 24 derived from a KPNO 4m CCD imaging survey of a contiguous 4 deg x 4 deg region. The advantage of using large contiguous…
Understanding $\textit{galaxy bias}$ -- that is the statistical relation between matter and galaxies -- is of key importance for extracting cosmological information from galaxy surveys. While the bias function $f$ -- that is the probability…
Strain correlation functions in two-dimensional isotropic elastic bodies are shown both theoretically (using the general structure of isotropic tensor fields) and numerically (using a glass-forming model system) to depend on the coordinates…
Let $\{X_{n}(t), t\in[0,\infty)\}, n\in\mathbb{N}$ be a sequence of centered dependent stationary Gaussian processes. The limit distribution of $\sup_{t\in[0,T(n)]}|X_{n}(t)|$ is established as $r_{n}(t)$, the correlation function of…
Due to their flexibility, Gaussian processes (GPs) have been widely used in nonparametric function estimation. A prior information about the underlying function is often available. For instance, the physical system (computer model output)…
The computation of global radial basis function (RBF) approximations requires the solution of a linear system which, depending on the choice of RBF parameters, may be ill-conditioned. We study the stability and accuracy of approximation…
In this article we continue the study of properties of squeezing functions and geometry of bounded domains. The limit of squeezing functions of a sequence of bounded domains is studied. We give comparisons of intrinsic positive forms and…
Consider fixed and bounded trace Gaussian orthogonal, unitary and symplectic ensembles, closely related to Gaussian ensembles without any constraint. For three restricted trace Gaussian ensembles, we prove universal limits of correlation…
We prove that for $c>0$ a sufficiently small universal constant that a random set of $c d^2/\log^4(d)$ independent Gaussian random points in $\mathbb{R}^d$ lie on a common ellipsoid with high probability. This nearly establishes a…
We prove bounds for the covering numbers of classes of convex functions and convex sets in Euclidean space. Previous results require the underlying convex functions or sets to be uniformly bounded. We relax this assumption and replace it…
There is a result of Diaconis and Freedman which says that, in a limiting sense, for large collections of high-dimensional data most one-dimensional projections of the data are approximately Gaussian. This paper gives quantitative versions…
We consider the problem of providing nonparametric confidence guarantees for undirected graphs under weak assumptions. In particular, we do not assume sparsity, incoherence or Normality. We allow the dimension $D$ to increase with the…
Tests of cosmological models via measurements of galaxy correlations will require increasing modeling accuracy, given the high precision of measurements promised by forthcoming galaxy surveys. In this work we investigate the biases…
Linear regression is arguably the most widely used statistical method. With fixed regressors and correlated errors, the conventional wisdom is to modify the variance-covariance estimator to accommodate the known correlation structure of the…
We consider functional linear regression models where functional outcomes are associated with scalar predictors by coefficient functions with shape constraints, such as monotonicity and convexity, that apply to sub-domains of interest. To…
Elicitable functionals and (strictly) consistent scoring functions are of interest due to their utility of determining (uniquely) optimal forecasts, and thus the ability to effectively backtest predictions. However, in practice, assuming…