Related papers: Aliasing-truncation Errors in Sampling Approximati…
The leading asymptotics of the truncation error for Gauss's continued fraction is determined exactly. Not only for this purpose but also for wider applicability elsewhere the discrete analogue of Laplace's method for hypergeometric series…
We consider the joint source-channel coding problem of sending a Gaussian source on a K-user Gaussian broadcast channel with bandwidth mismatch. A new outer bound to the achievable distortion region is derived using the technique of…
We perform an error analysis for numerical approximation methods of continuous time Markov chain models commonly found in the chemistry and biochemistry literature. The motivation for the analysis is to be able to compare the accuracy of…
We study the properties of several likelihood-based statistics commonly used in testing for the presence of a known signal under a mixture model with known background, but unknown signal fraction. Under the null hypothesis of no signal, all…
We consider the problem of detecting (testing) Gaussian stochastic sequences (signals) with imprecisely known means and covariance matrices. The alternative is independent identically distributed zero-mean Gaussian random variables with…
We study the convergence rate of randomly truncated stochastic algorithms, which consist in the truncation of the standard Robbins-Monro procedure on an increasing sequence of compact sets. Such a truncation is often required in practice to…
We study the convergence rate of randomly truncated stochastic algorithms, which consist in the truncation of the standard Robbins-Monro procedure on an increasing sequence of compact sets. Such a truncation is often required in practice to…
A new framework of compressive sensing (CS), namely statistical compressive sensing (SCS), that aims at efficiently sampling a collection of signals that follow a statistical distribution and achieving accurate reconstruction on average, is…
In this paper, we study random subsampling of Gaussian process regression, one of the simplest approximation baselines, from a theoretical perspective. Although subsampling discards a large part of training data, we show provable guarantees…
This paper studies the subexponential prefactor to the random-coding bound for a given rate. Using a refinement of Gallager's bounding techniques, an alternative proof of a recent result by Altu\u{g} and Wagner is given, and the result is…
This paper provides new error bounds on "consistent" reconstruction methods for signals observed from quantized random projections. Those signal estimation techniques guarantee a perfect matching between the available quantized data and a…
We consider the problem of Gaussian multiplier bootstrap procedures for the $k$th largest statistics and functions of the top $k$ order statistics, which are commonly encountered in high-dimensional statistical inference. Such a problem has…
This work analyzes the stochastic approximation algorithm with non-decaying gains as applied in time-varying problems. The setting is to minimize a sequence of scalar-valued loss functions $f_k(\cdot)$ at sampling times $\tau_k$ or to…
We propose an open loop methodology based on sample statistics to solve chance constrained stochastic optimal control problems with probabilistic safety guarantees for linear systems where the additive Gaussian noise has unknown mean and…
We introduce a new scalable approximation for Gaussian processes with provable guarantees which hold simultaneously over its entire parameter space. Our approximation is obtained from an improved sample complexity analysis for sparse…
We consider upper bounds for the approximation error E|g(X)-g(\hat X)|^p, where X and \hat X are random variables such that \hat X is an approximation of X in the L_p-norm, and the function g belongs to certain function classes, which…
A continuous-time regression model with a jointly strictly sub-Gaussian random noise is considered in the paper. Upper exponential bounds for probabilities of large deviations of the least squares estimator for the regression parameter are…
This paper is concerned with the analysis of the randomized subspace iteration for the computation of low-rank approximations. We present three different kinds of bounds. First, we derive both bounds for the canonical angles between the…
In many applications of frequency estimation, the frequencies of the signals are so high that the data sampled at Nyquist rate are hard to acquire due to hardware limitation. In this paper, we propose a novel method based on subspace…
We study the estimation error of constrained M-estimators, and derive explicit upper bounds on the expected estimation error determined by the Gaussian width of the constraint set. Both of the cases where the true parameter is on the…