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作者：Sen, Bodhisattva; Meyer, Mary
作者单位：Columbia University; Colorado State University System; Colorado State University Fort Collins
摘要：A formal likelihood ratio hypothesis test for the validity of a parametric regression function is proposed, using a large dimensional, non-parametric double-cone alternative. For example, the test against a constant function uses the alternative of increasing or decreasing regression functions, and the test against a linear function uses the convex or concave alternative. The test proposed is exact and unbiased and the critical value is easily computed. The power of the test increases to 1 as ...
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作者：Bandyopadhyay, Soutir; Rao, Suhasini Subba
作者单位：Lehigh University; Texas A&M University System; Texas A&M University College Station
摘要：The analysis of spatial data is based on a set of assumptions, which in practice need to be checked. A commonly used assumption is that the spatial random field is second-order stationary. In the paper, a test for spatial stationarity for irregularly sampled data is proposed. The test is based on a transformation of the data (a type of Fourier transform), where the correlations between the transformed data are close to 0 if the random field is second-order stationary. However, if the random fi...
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作者：Nandy, Siddhartha; Lim, Chae Young; Maiti, Tapabrata
作者单位：Michigan State University; Seoul National University (SNU)
摘要：Spatial regression is an important predictive tool in many scientific applications and an additive model provides a flexible regression relationship between predictors and a response variable. We develop a regularized variable selection technique for building a spatial additive model. We find that the methods developed for independent data do not work well for spatially dependent data. This motivates us to propose a spatially weighted l2-error norm with a group lasso type of penalty to select ...
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作者：Rao, Vinayak; Adams, Ryan P.; Dunson, David D.
作者单位：Purdue University System; Purdue University; Harvard University; Twitter, Inc.; Duke University
摘要：In many applications involving point pattern data, the Poisson process assumption is unrealistic, with the data exhibiting a more regular spread. Such repulsion between events is exhibited by trees for example, because of competition for light and nutrients. Other examples include the locations of biological cells and cities, and the times of neuronal spikes. Given the many applications of repulsive point processes, there is a surprisingly limited literature developing flexible, realistic and ...
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作者：Drton, Mathias; Plummer, Martyn
作者单位：University of Washington; University of Washington Seattle; World Health Organization; International Agency for Research on Cancer (IARC)
摘要：We consider approximate Bayesian model choice for model selection problems that involve models whose Fisher information matrices may fail to be invertible along other competing submodels. Such singular models do not obey the regularity conditions underlying the derivation of Schwarz's Bayesian information criterion BIC and the penalty structure in BIC generally does not reflect the frequentist large sample behaviour of the marginal likelihood. Although large sample theory for the marginal like...
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作者：Fan, Jianqing; Liu, Han; Ning, Yang; Zou, Hui
作者单位：Princeton University; University of Minnesota System; University of Minnesota Twin Cities
摘要：We propose a semiparametric latent Gaussian copula model for modelling mixed multivariate data, which contain a combination of both continuous and binary variables. The model assumes that the observed binary variables are obtained by dichotomizing latent variables that satisfy the Gaussian copula distribution. The goal is to infer the conditional independence relationship between the latent random variables, based on the observed mixed data. Our work has two main contributions: we propose a un...
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作者：Soriano, Jacopo; Ma, Li
作者单位：Duke University
摘要：We propose a multi-resolution scanning approach to identifying two-sample differences. Windows of multiple scales are constructed through nested dyadic partitioning on the sample space and a hypothesis regarding the two-sample difference is defined on each window. Instead of testing the hypotheses on different windows independently, we adopt a joint graphical model, namely a Markov tree, on the null or alternative states of these hypotheses to incorporate spatial correlation across windows. Th...
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作者：Fan, Jianqing; Li, Quefeng; Wang, Yuyan
作者单位：Princeton University; Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS; University of North Carolina; University of North Carolina Chapel Hill; Princeton University
摘要：Data subject to heavy-tailed errors are commonly encountered in various scientific fields. To address this problem, procedures based on quantile regression and least absolute deviation regression have been developed in recent years. These methods essentially estimate the conditional median (or quantile) function. They can be very different from the conditional mean functions, especially when distributions are asymmetric and heteroscedastic. How can we efficiently estimate the mean regression f...
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作者：Ji, Hao; Mueller, Hans-Georg
作者单位：University of California System; University of California Davis
摘要：We propose novel optimal designs for longitudinal data for the common situation where the resources for longitudinal data collection are limited, by determining the optimal locations in time where measurements should be taken. As for all optimal designs, some prior information is needed to implement the optimal designs proposed. We demonstrate that this prior information may come from a pilot longitudinal study that has irregularly measured and noisy measurements, where for each subject one ha...
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作者：Jiang, Runchao; Lu, Wenbin; Song, Rui; Davidian, Marie
作者单位：North Carolina State University
摘要：A treatment regime is a deterministic function that dictates personalized treatment based on patients' individual prognostic information. There is increasing interest in finding optimal treatment regimes, which determine treatment at one or more treatment decision points to maximize expected long-term clinical outcomes, where larger outcomes are preferred. For chronic diseases such as cancer or human immunodeficiency virus infection, survival time is often the outcome of interest, and the goal...
