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In all areas of human knowledge, datasets are increasing in both size and complexity, creating the need for richer statistical models. This trend is also true for economic data, where high-dimensional and nonlinear/nonparametric inference…
We study the convergence rates of empirical Bayes posterior distributions for nonparametric and high-dimensional inference. We show that as long as the hyperparameter set is discrete, the empirical Bayes posterior distribution induced by…
Increasingly complex applications involve large datasets in combination with non-linear and high dimensional mathematical models. In this context, statistical inference is a challenging issue that calls for pragmatic approaches that take…
This paper develops a general method of inference for fixed effects models which is (i) automatic, (ii) computationally inexpensive, (iii) tuning parameter-free, and (iv) highly model agnostic. Specifically, we show how to combine a…
This paper develops a Bayesian approach for assessing equivalence and non-inferiority hypotheses in two-arm trials using relative belief ratios. A relative belief ratio is a measure of statistical evidence and can indicate evidence either…
The celebrated Bernstein von-Mises theorem ensures that credible regions from Bayesian posterior are well-calibrated when the model is correctly-specified, in the frequentist sense that their coverage probabilities tend to the nominal…
The American Community Survey (ACS) Public Use Microdata Sample (PUMS) provides access to a wide range of unit-level survey data consisting of correlated Gaussian and binomial distributed survey responses along with associated survey…
The paper addresses joint sparsity selection in the regression coefficient matrix and the error precision (inverse covariance) matrix for high-dimensional multivariate regression models in the Bayesian paradigm. The selected sparsity…
It is difficult to accurately estimate the rates of rape and domestic violence due to the sensitive nature of these crimes. There is evidence that bias in estimating the crime rates from survey data may arise because some women respondents…
In the sparse normal means model, convergence of the Bayesian posterior distribution associated to spike and slab prior distributions is considered. The key sparsity hyperparameter is calibrated via marginal maximum likelihood empirical…
Count outcomes in longitudinal studies are frequent in clinical and engineering studies. In frequentist and Bayesian statistical analysis, methods such as Mixed linear models allow the variability or correlation within individuals to be…
In an empirical Bayesian setting, we provide a new multiple testing method, useful when an additional covariate is available, that influences the probability of each null hypothesis being true. We measure the posterior significance of each…
Random effects model can account for the lack of fitting a regression model and increase precision of estimating area-level means. However, in case that the synthetic mean provides accurate estimates, the prior distribution may inflate an…
Energy distance is a statistical distance between the distributions of random variables, which characterizes the equality of the distributions. Utilizing the energy distance, we develop a nonparametric test for the diagonal symmetry, which…
Due to the growing adoption of deep neural networks in many fields of science and engineering, modeling and estimating their uncertainties has become of primary importance. Despite the growing literature about uncertainty quantification in…
This work develops formal statistical inference procedures for machine learning ensemble methods. Ensemble methods based on bootstrapping, such as bagging and random forests, have improved the predictive accuracy of individual trees, but…
We discuss Bayesian inference for parameters selected using the data. First, we provide a critical analysis of the existing positions in the literature regarding the correct Bayesian approach under selection. Second, we propose two types of…
Prior information often takes the form of parameter constraints. Bayesian methods include such information through prior distributions having constrained support. By using posterior sampling algorithms, one can quantify uncertainty without…
Bayesian nonparametric inferential procedures based on Markov chain Monte Carlo marginal methods typically yield point estimates in the form of posterior expectations. Though very useful and easy to implement in a variety of statistical…
Estimating the conditional quantile of the interested variable with respect to changes in the covariates is frequent in many economical applications as it can offer a comprehensive insight. In this paper, we propose a novel semiparametric…