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We propose new model selection criteria based on generalized ridge estimators dominating the maximum likelihood estimator under the squared risk and the Kullback-Leibler risk in multivariate linear regression. Our model selection criteria…

Statistics Theory · Mathematics 2016-04-08 Yuichi Mori , Taiji Suzuki

We develop a modeling framework for dynamic function-on-scalars regression, in which a time series of functional data is regressed on a time series of scalar predictors. The regression coefficient function for each predictor is allowed to…

Methodology · Statistics 2018-10-25 Daniel R. Kowal

We consider the problem of predictive density estimation under Kullback-Leibler loss in a high-dimensional Gaussian model with exact sparsity constraints on the location parameters. We study the first order asymptotic minimax risk of Bayes…

Statistics Theory · Mathematics 2019-05-24 Ujan Gangopadhyay , Gourab Mukherjee

We study a nonparametric Bayesian approach to linear inverse problems under discrete observations. We use the discrete Fourier transform to convert our model into a truncated Gaussian sequence model, that is closely related to the classical…

Statistics Theory · Mathematics 2018-10-31 Shota Gugushvili , Aad van der Vaart , Dong Yan

Global-local shrinkage hierarchies are an important innovation in Bayesian estimation. We propose the use of log-scale distributions as a novel basis for generating familes of prior distributions for local shrinkage hyperparameters. By…

Statistics Theory · Mathematics 2020-01-31 Daniel F. Schmidt , Enes Makalic

In Bayesian nonparametric models, Gaussian processes provide a popular prior choice for regression function estimation. Existing literature on the theoretical investigation of the resulting posterior distribution almost exclusively assume a…

Statistics Theory · Mathematics 2015-03-06 Debdeep Pati , Anirban Bhattacharya , Guang Cheng

Two-component mixture priors provide a traditional way to induce sparsity in high-dimensional Bayes models. However, several aspects of such a prior, including computational complexities in high-dimensions, interpretation of exact zeros and…

Statistics Theory · Mathematics 2016-05-19 Anirban Bhattacharya , David B. Dunson , Debdeep Pati , Natesh S. Pillai

In prediction problems with more predictors than observations, it can sometimes be helpful to use a joint probability model, $\pi(Y,X)$, rather than a purely conditional model, $\pi(Y \mid X)$, where $Y$ is a scalar response variable and…

Methodology · Statistics 2010-11-17 P. Richard Hahn , Sayan Mukherjee , Carlos Carvalho

Methods for choosing a fixed set of knot locations in additive spline models are fairly well established in the statistical literature. While most of these methods are in principle directly extendable to non-additive surface models, they…

Computation · Statistics 2018-07-03 Feng Li , Mattias Villani

Penalized likelihood and quasi-likelihood methods dominate inference in high-dimensional linear mixed-effects models. Sampling-based Bayesian inference is less explored due to the computational bottlenecks introduced by the random effects…

Methodology · Statistics 2025-07-24 Sreya Sarkar , Kshitij Khare , Sanvesh Srivastava

Bayesian sequence prediction is a simple technique for predicting future symbols sampled from an unknown measure on infinite sequences over a countable alphabet. While strong bounds on the expected cumulative error are known, there are only…

Machine Learning · Computer Science 2013-07-02 Tor Lattimore , Marcus Hutter , Peter Sunehag

We consider nonparametric Bayesian estimation and prediction for nonhomogeneous Poisson process models with unknown intensity functions. We propose a class of improper priors for intensity functions. Nonparametric Bayesian inference with…

Statistics Theory · Mathematics 2021-08-17 Fumiyasu Komaki

The quantile varying coefficient (VC) model can flexibly capture dynamical patterns of regression coefficients. In addition, due to the quantile check loss function, it is robust against outliers and heavy-tailed distributions of the…

Methodology · Statistics 2023-07-11 Fei Zhou , Jie Ren , Shuangge Ma , Cen Wu

Spatial models are used in a variety research areas, such as environmental sciences, epidemiology, or physics. A common phenomenon in many spatial regression models is spatial confounding. This phenomenon takes place when spatially indexed…

Methodology · Statistics 2021-06-08 Isa Marques , Thomas Kneib , Nadja Klein

We propose a shrinkage procedure for simultaneous variable selection and estimation in generalized linear models (GLMs) with an explicit predictive motivation. The procedure estimates the coefficients by minimizing the Kullback-Leibler…

Methodology · Statistics 2010-09-14 Minh-Ngoc Tran , David Nott , Chenlei Leng

Simultaneous predictive densities for independent Poisson observables are investigated. The observed data and the target variables to be predicted are independently distributed according to different Poisson distributions parametrized by…

Statistics Theory · Mathematics 2021-05-27 Fumiyasu Komaki

In this paper we forecast daily returns of crypto-currencies using a wide variety of different econometric models. To capture salient features commonly observed in financial time series like rapid changes in the conditional variance,…

Econometrics · Economics 2018-02-14 Christian Hotz-Behofsits , Florian Huber , Thomas O. Zörner

In multivariate statistics, estimating the covariance matrix is essential for understanding the interdependence among variables. In high-dimensional settings, where the number of covariates increases with the sample size, it is well known…

Statistics Theory · Mathematics 2025-10-24 Seongmin Kim , Kwangmin Lee , Sewon Park , Jaeyong Lee

Statistical modelling of covariate distributions allows to generate virtual populations or to impute missing values in a covariate dataset. Covariate distributions typically have non-Gaussian margins and show nonlinear correlation…

Applications · Statistics 2025-03-20 Niklas Hartung , Aleksandra Khatova

For estimating the large covariance matrix with a limited sample size, we propose the covariance model with general linear structure (CMGL) by employing the general link function to connect the covariance of the continuous response vector…

Methodology · Statistics 2022-05-17 Xinyan Fan , Wei Lan , Tao Zou , Chih-Ling Tsai
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