Related papers: Nonparametric Empirical Bayes Confidence Intervals
Standard blockwise empirical likelihood (BEL) for stationary, weakly dependent time series requires specifying a fixed block length as a tuning parameter for setting confidence regions. This aspect can be difficult and impacts coverage…
In this paper we consider the estimation of unknown parameters in Bayesian inverse problems. In most cases of practical interest, there are several barriers to performing such estimation, This includes a numerical approximation of a…
Approximate Bayesian Computation (ABC) are likelihood-free Monte Carlo methods. ABC methods use a comparison between simulated data, using different parameters drew from a prior distribution, and observed data. This comparison process is…
We propose a new procedure for inference on optimal treatment regimes in the model-free setting, which does not require to specify an outcome regression model. Existing model-free estimators for optimal treatment regimes are usually not…
Count endpoints are common in clinical trials, particularly for recurrent events such as hypoglycemia. When interest centers on comparing overall event rates between treatment groups, negative binomial (NB) regression is widely used because…
We study empirical Bayes estimation of the effect sizes of $N$ units from $K$ noisy observations on each unit. We show that it is possible to achieve near-Bayes optimal mean squared error, without any assumptions or knowledge about the…
This study extends the Bayesian nonparametric instrumental variable regression model to determine the structural effects of covariates on the conditional quantile of the response variable. The error distribution is nonparametrically…
We present a method for producing unbiased parameter estimates and valid confidence intervals under the constraints of differential privacy, a formal framework for limiting individual information leakage from sensitive data. Prior work in…
Given discrete time observations over a growing time interval, we consider a nonparametric Bayesian approach to estimation of the L\'evy density of a L\'evy process belonging to a flexible class of infinite activity subordinators. Posterior…
Flexible estimation of multiple conditional quantiles is of interest in numerous applications, such as studying the effect of pregnancy-related factors on low and high birth weight. We propose a Bayesian non-parametric method to…
We consider the problem of statistical inference on parameters of a target population when auxiliary observations are available from related populations. We propose a flexible empirical Bayes approach that can be applied on top of any…
We show that empirical risk minimization procedures and regularized empirical risk minimization procedures satisfy nonexact oracle inequalities in an unbounded framework, under the assumption that the class has a subexponential envelope…
In the recent paper [5], a Bayesian approach for constructing confidence intervals in monotone regression problems is proposed, based on credible intervals. We view this method from a frequentist point of view, and show that it corresponds…
This paper proposes an extension to conventional regression Neural Networks (NNs) for replacing the point predictions they produce with prediction intervals that satisfy a required level of confidence. Our approach follows a novel machine…
In the following article we consider approximate Bayesian parameter inference for observation driven time series models. Such statistical models appear in a wide variety of applications, including econometrics and applied mathematics. This…
Bayesian variable selection methods are powerful techniques for fitting and inferring on sparse high-dimensional linear regression models. However, many are computationally intensive or require restrictive prior distributions on model…
We investigate an empirical Bayesian nonparametric approach to a family of linear inverse problems with Gaussian prior and Gaussian noise. We consider a class of Gaussian prior probability measures with covariance operator indexed by a…
We develop a Nonparametric Empirical Bayes (NEB) framework for compound estimation in the discrete linear exponential family, which includes a wide class of discrete distributions frequently arising from modern big data applications. We…
Randomized quasi-Monte Carlo (RQMC) methods estimate the mean of a random variable by sampling an integrand at $n$ equidistributed points. For scrambled digital nets, the resulting variance is typically $\tilde O(n^{-\theta})$ where…
Testing network effects in weighted directed networks is a foundational problem in econometrics, sociology, and psychology. Yet, the prevalent edge dependency poses a significant methodological challenge. Most existing methods are…