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We characterise the behavior of the maximum Diaconis--Ylvisaker prior penalized likelihood estimator in high-dimensional logistic regression, where the number of covariates is a fraction $κ\in (0,1)$ of the number of observations $n$, as $n \to \infty$. We construct a rescaled estimator with zero asymptotic aggregate bias and define adjusted $Z$-statistics and rescaled penalized likelihood ratio statistics that exhibit the typical null asymptotic distributions, when the…

用于含边界观测的 [0,1] 响应的扩展支撑贝塔回归AI 解读

We introduce the XBX regression model, a continuous mixture of extended-support beta regressions for modelling bounded responses with boundary observations. The core building block of XBX regression is the extended-support beta distribution, a censored version of a four-parameter beta distribution with the same exceedance on the left and right of $(0, 1)$. Hence, XBX regression is a direct extension of beta regression. We prove that beta regression and heteroscedastic normal…

计数时间序列的贝叶斯张量分解AI 解读

We propose a flexible nonparametric Bayesian modelling framework for multivariate time series of count data based on tensor factorisations. Our models can be viewed as infinite state space Markov chains of known maximal order with non-linear serial dependence through the introduction of appropriate latent variables. Alternatively, our models can be viewed as Bayesian hierarchical models with conditionally independent Poisson distributed observations. Inference about the…