Related papers: Mean, Variance and Asymptotic Property for General…
Consider the Erd\H{o}s-Renyi random graph on n vertices where each edge is present independently with probability c/n, with c>0 fixed. For large n, a typical random graph locally behaves like a Galton-Watson tree with Poisson offspring…
We study the distribution of the maximum likelihood estimate (MLE) in high-dimensional logistic models, extending the recent results from Sur (2019) to the case where the Gaussian covariates may have an arbitrary covariance structure. We…
The central limit theorem provides the theoretical foundation for the universality of the normal distribution: under broad conditions, the asymptotic distribution of a sum of independent random variables approaches a Gaussian. Yet, physical…
Let $(M,g)$ be a Riemannian manifold. If $\mu$ is a probability measure on $M$ given by a continuous density function, one would expect the Fr\'{e}chet means of data-samples $Q=(q_1,q_2,\dots, q_N)\in M^N$, with respect to $\mu$, to behave…
We study convergence rates of variational posterior distributions for nonparametric and high-dimensional inference. We formulate general conditions on prior, likelihood, and variational class that characterize the convergence rates. Under…
Line-intensity mapping (LIM) is a promising technique to constrain the global distribution of galaxy properties. To combine LIM experiments probing different tracers with traditional galaxy surveys and fully exploit the scientific potential…
We show that the mean-model parameter is always orthogonal to the error distribution in generalized linear models. Thus, the maximum likelihood estimator of the mean-model parameter will be asymptotically efficient regardless of whether the…
This article aims to introduced a new distribution named as extended xgamma (EXg) distribution. This generalization is derived from xgamma distribution (Xg), a special finite mixture of exponential and gamma distributions [see, Sen et al.…
Symmetry is a cornerstone of much of mathematics, and many probability distributions possess symmetries characterized by their invariance to a collection of group actions. Thus, many mathematical and statistical methods rely on such…
Recent developments in extreme value statistics have established the so-called geometric approach as a powerful modelling tool for multivariate extremes. We tailor these methods to the case of spatial modelling and examine their efficacy at…
Stochastic gradient descent (SGD) is a popular algorithm for optimization problems arising in high-dimensional inference tasks. Here one produces an estimator of an unknown parameter from independent samples of data by iteratively…
The asymptotic normality of the maximum likelihood estimator (MLE) under regularity conditions is a cornerstone of statistical theory. In this paper, we give explicit upper bounds on the distributional distance between the distribution of…
Hyperbolic random graphs (HRG) and geometric inhomogeneous random graphs (GIRG) are two similar generative network models that were designed to resemble complex real world networks. In particular, they have a power-law degree distribution…
Two canonical problems in geostatistics are estimating the parameters in a specified family of stochastic process models and predicting the process at new locations. A number of asymptotic results addressing these problems over a fixed…
Gradient matching with Gaussian processes is a promising tool for learning parameters of ordinary differential equations (ODE's). The essence of gradient matching is to model the prior over state variables as a Gaussian process which…
The general limit distributions of the sum of random variables described by a finite matrix product ansatz are characterized. Using a mapping to a Hidden Markov Chain formalism, non-standard limit distributions are obtained, and related to…
The Hellinger distance between quantum states is a significant measure in quantum information theory, known for its Riemannian and monotonic properties. It is also easier to compute than the Bures distance, another measure that shares these…
With the progress of measurement apparatus and the development of automatic sensors it is not unusual anymore to get thousands of samples of observations taking values in high dimension spaces such as functional spaces. In such large…
A finite dimensional abstract approximation and convergence theory is developed for estimation of the distribution of random parameters in infinite dimensional discrete time linear systems with dynamics described by regularly dissipative…
We introduce a new random mapping model, $T_n^{\hat D}$, which maps the set $\{1,2,...,n\}$ into itself.The random mapping $T_n^{\hat D}$ is constructed using a collection of exchangeable random variables $\hat{D}_1, ....,\hat{D}_n$ which…