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1. High-quantile regression for tail-dependent time series

   https://doi.org/10.1093/biomet/asaa046  

   Zhang, Ting ( July 2020 , Biometrika)

   null (Ed.)

   Summary Quantile regression is a popular and powerful method for studying the effect of regressors on quantiles of a response distribution. However, existing results on quantile regression were mainly developed for cases in which the quantile level is fixed, and the data are often assumed to be independent. Motivated by recent applications, we consider the situation where (i) the quantile level is not fixed and can grow with the sample size to capture the tail phenomena, and (ii) the data are no longer independent, but collected as a time series that can exhibit serial dependence in both tail and non-tail regions. To study the asymptotic theory for high-quantile regression estimators in the time series setting, we introduce a tail adversarial stability condition, which had not previously been described, and show that it leads to an interpretable and convenient framework for obtaining limit theorems for time series that exhibit serial dependence in the tail region, but are not necessarily strongly mixing. Numerical experiments are conducted to illustrate the effect of tail dependence on high-quantile regression estimators, for which simply ignoring the tail dependence may yield misleading $p$-values. 

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2. A mark-specific quantile regression model

   https://doi.org/10.1093/biomet/asad039  

   Qu, Lianqiang ; Sun, Liuquan ; Sun, Yanqing ( June 2023 , Biometrika)

   Quantile regression has become a widely used tool for analysing competing risk data. However, quantile regression for competing risk data with a continuous mark is still scarce. The mark variable is an extension of cause of failure in a classical competing risk model where cause of failure is replaced by a continuous mark only observed at uncensored failure times. An example of the continuous mark variable is the genetic distance that measures dissimilarity between the infecting virus and the virus contained in the vaccine construct. In this article, we propose a novel mark-specific quantile regression model. The proposed estimation method borrows strength from data in a neighbourhood of a mark and is based on an induced smoothed estimation equation, which is very different from the existing methods for competing risk data with discrete causes. The asymptotic properties of the resulting estimators are established across mark and quantile continuums. In addition, a mark-specific quantile-type vaccine efficacy is proposed and its statistical inference procedures are developed. Simulation studies are conducted to evaluate the finite sample performances of the proposed estimation and hypothesis testing procedures. An application to the first HIV vaccine efficacy trial is provided.

    

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3. Identifying meteorological drivers of PM 2.5 levels via a Bayesian spatial quantile regression

   https://doi.org/10.1002/env.2669  

   Self, Stella W. ; McMahan, Christopher S. ; Russell, Brook T. ( February 2021 , Environmetrics)

   Recently, due to accelerations in urban and industrial development, the health impact of air pollution has become a topic of key concern. Of the various forms of air pollution, fine atmospheric particulate matter (PM_2.5; particles less than 2.5 micrometers in diameter) appears to pose the greatest risk to human health. While even moderate levels of PM_2.5can be detrimental to health, spikes in PM_2.5to atypically high levels are even more dangerous. These spikes are believed to be associated with regionally specific meteorological factors. To quantify these associations, we develop a Bayesian spatiotemporal quantile regression model to estimate the spatially varying effects of meteorological variables purported to be related to PM_2.5levels. By adopting a quantile regression model, we are able to examine the entire distribution of PM_2.5levels; for example, we are able to identify which meteorological drivers are related to abnormally high PM_2.5levels. Our approach uses penalized splines to model the spatially varying meteorological effects and to account for spatiotemporal dependence. The performance of the methodology is evaluated through extensive numerical studies. We apply our modeling techniques to 5 years of daily PM_2.5data collected throughout the eastern United States to reveal the effects of various meteorological drivers.

    

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4. Bayesian inference for finite populations under spatial process settings

   https://doi.org/10.1002/env.2606  

   Chan‐Golston, Alec M. ; Banerjee, Sudipto ; Handcock, Mark S. ( November 2019 , Environmetrics)

   We develop a Bayesian model–based approach to finite population estimation accounting for spatial dependence. Our innovation here is a framework that achieves inference for finite population quantities in spatial process settings. A key distinction from the small area estimation setting is that we analyze finite populations referenced by their geographic coordinates. Specifically, we consider a two‐stage sampling design in which the primary units are geographic regions, the secondary units are point‐referenced locations, and the measured values are assumed to be a partial realization of a spatial process. Estimation of finite population quantities from geostatistical models does not account for sampling designs, which can impair inferential performance, whereas design‐based estimates ignore the spatial dependence in the finite population. We demonstrate by using simulation experiments that process‐based finite population sampling models improve model fit and inference over models that fail to account for spatial correlation. Furthermore, the process‐based models offer richer inference with spatially interpolated maps over the entire region. We reinforce these improvements and demonstrate scalable inference for groundwater nitrate levels in the population of California Central Valley wells by offering estimates of mean nitrate levels and their spatially interpolated maps.

    

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5. Improving structured population models with more realistic representations of non‐normal growth

   https://doi.org/10.1111/2041-210X.13240  

   DeMarche, Megan L. ; Morris, William ; Linares, Cristina ; Doak, Daniel ; Altwegg, ed., Res ( July 2019 , Methods in Ecology and Evolution)

   Structured population models are among the most widely used tools in ecology and evolution. Integral projection models (IPMs) use continuous representations of how survival, reproduction and growth change as functions of state variables such as size, requiring fewer parameters to be estimated than projection matrix models (PPMs). Yet, almost all published IPMs make an important assumption that size‐dependent growth transitions are or can be transformed to be normally distributed. In fact, many organisms exhibit highly skewed size transitions. Small individuals can grow more than they can shrink, and large individuals may often shrink more dramatically than they can grow. Yet, the implications of such skew for inference from IPMs has not been explored, nor have general methods been developed to incorporate skewed size transitions into IPMs, or deal with other aspects of real growth rates, including bounds on possible growth or shrinkage.

   Here, we develop a flexible approach to modelling skewed growth data using a modified beta regression model. We propose that sizes first be converted to a (0,1) interval by estimating size‐dependent minimum and maximum sizes through quantile regression. Transformed data can then be modelled using beta regression with widely available statistical tools. We demonstrate the utility of this approach using demographic data for a long‐lived plant, gorgonians and an epiphytic lichen. Specifically, we compare inferences of population parameters from discrete PPMs to those from IPMs that either assume normality or incorporate skew using beta regression or, alternatively, a skewed normal model.

   The beta and skewed normal distributions accurately capture the mean, variance and skew of real growth distributions. Incorporating skewed growth into IPMs decreases population growth and estimated life span relative to IPMs that assume normally distributed growth, and more closely approximate the parameters of PPMs that do not assume a particular growth distribution. A bounded distribution, such as the beta, also avoids the eviction problem caused by predicting some growth outside the modelled size range.

   Incorporating biologically relevant skew in growth data has important consequences for inference from IPMs. The approaches we outline here are flexible and easy to implement with existing statistical tools.

    

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