Related papers: A Bayesian Lower Bound for Parameter Estimation of…
We study the accuracy of a scaled Poisson approximation to the weighted sum of independent Poisson random variables, focusing on in particular the relative error of the tail distribution. A bound on the relative approximation error is…
Mathematical models of real life phenomena are highly nonlinear involving multiple parameters and often exhibiting complex dynamics. Experimental data sets are typically small and noisy, rendering estimation of parameters from such data…
We develop sharp bounds on the statistical distance between high-dimensional permutation mixtures and their i.i.d. counterparts. Our approach establishes a new geometric link between the spectrum of a complex channel overlap matrix and the…
Regression for count data is widely performed by models such as Poisson, negative binomial (NB) and zero-inflated regression. A challenge often faced by practitioners is the selection of the right model to take into account dispersion,…
The paper considers the stationary Poisson Boolean model with spherical grains and proposes a family of nonparametric estimators for the radius distribution. These estimators are based on observed distances and radii, weighted in an…
We extend a recently established asymptotic normality theorem for generalized linear mixed models to include the dispersion parameter. The new results show that the maximum likelihood estimators of all model parameters have asymptotically…
This paper provides a unified framework for analyzing tensor estimation problems that allow for nonlinear observations, heteroskedastic noise, and covariate information. We study a general class of high-dimensional models where each…
In this paper we establish lower bounds on information divergence from a distribution to certain important classes of distributions as Gaussian, exponential, Gamma, Poisson, geometric, and binomial. These lower bounds are tight and for…
In data-driven learning and inference tasks, the high cost of acquiring samples from the target distribution often limits performance. A common strategy to mitigate this challenge is to augment the limited target samples with data from a…
Suppose that $X_1,X_2,\ldots$ are a stream of independent, identically distributed Poisson random variables with mean $\mu$. This work presents a new estimate $\mu_k$ for $\mu$ with the property that the distribution of the relative error…
In this paper, tight upper and lower bounds are derived on the weighted sum of minimum mean-squared errors for additive Gaussian noise channels. The bounds are obtained by constraining the input distribution to be close to a Gaussian…
Event counts are response variables with non-negative integer values representing the number of times that an event occurs within a fixed domain such as a time interval, a geographical area or a cell of a contingency table. Analysis of…
We demonstrate that two approximations to the chi^2 statistic as popularly employed by observational astronomers for fitting Poisson-distributed data can give rise to intrinsically biased model parameter estimates, even in the high counts…
This paper studies multivariate nonparametric change point localization and inference problems. The data consists of a multivariate time series with potentially short range dependence. The distribution of this data is assumed to be…
Covariate shift arises when covariate distributions differ between source and target populations while the conditional distribution of the response remains invariant, and it underlies problems in missing data and causal inference. We…
Robust estimation is an important and timely research subject. In this paper, we investigate performance lower bounds on the mean-square-error (MSE) of any estimator for the Bayesian linear model, corrupted by a noise distributed according…
Mutual information is fundamentally important for measuring statistical dependence between variables and for quantifying information transfer by signaling and communication mechanisms. It can, however, be challenging to evaluate for…
Using techniques from Poisson approximation, we prove explicit error bounds on the number of permutations that avoid any pattern. Most generally, we bound the total variation distance between the joint distribution of pattern occurrences…
Ideally, a meta-analysis will summarize data from several unbiased studies. Here we consider the less than ideal situation in which contributing studies may be compromised by measurement error. Measurement error affects every study design,…
Bayesian optimisation has gained great popularity as a tool for optimising the parameters of machine learning algorithms and models. Somewhat ironically, setting up the hyper-parameters of Bayesian optimisation methods is notoriously hard.…