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Journal of the Royal Statistical Society. Series B, Statistical Methodology

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https://www.readbyqxmd.com/read/29200934/sparse-graphs-using-exchangeable-random-measures
#1
François Caron, Emily B Fox
Statistical network modelling has focused on representing the graph as a discrete structure, namely the adjacency matrix. When assuming exchangeability of this array-which can aid in modelling, computations and theoretical analysis-the Aldous-Hoover theorem informs us that the graph is necessarily either dense or empty. We instead consider representing the graph as an exchangeable random measure and appeal to the Kallenberg representation theorem for this object. We explore using completely random measures (CRMs) to define the exchangeable random measure, and we show how our CRM construction enables us to achieve sparse graphs while maintaining the attractive properties of exchangeability...
November 2017: Journal of the Royal Statistical Society. Series B, Statistical Methodology
https://www.readbyqxmd.com/read/29104447/eigenprism-inference-for-high-dimensional-signal-to-noise-ratios
#2
Lucas Janson, Rina Foygel Barber, Emmanuel Candès
Consider the following three important problems in statistical inference, namely, constructing confidence intervals for (1) the error of a high-dimensional (p > n) regression estimator, (2) the linear regression noise level, and (3) the genetic signal-to-noise ratio of a continuous-valued trait (related to the heritability). All three problems turn out to be closely related to the little-studied problem of performing inference on the [Formula: see text]-norm of the signal in high-dimensional linear regression...
September 2017: Journal of the Royal Statistical Society. Series B, Statistical Methodology
https://www.readbyqxmd.com/read/29056863/estimation-of-the-false-discovery-proportion-with-unknown-dependence
#3
Jianqing Fan, Xu Han
Large-scale multiple testing with correlated test statistics arises frequently in many scientific research. Incorporating correlation information in approximating false discovery proportion has attracted increasing attention in recent years. When the covariance matrix of test statistics is known, Fan, Han & Gu (2012) provided an accurate approximation of False Discovery Proportion (FDP) under arbitrary dependence structure and some sparsity assumption. However, the covariance matrix is often unknown in many applications and such dependence information has to be estimated before approximating FDP...
September 2017: Journal of the Royal Statistical Society. Series B, Statistical Methodology
https://www.readbyqxmd.com/read/28989320/nonparametric-methods-for-doubly-robust-estimation-of-continuous-treatment-effects
#4
Edward H Kennedy, Zongming Ma, Matthew D McHugh, Dylan S Small
Continuous treatments (e.g., doses) arise often in practice, but many available causal effect estimators are limited by either requiring parametric models for the effect curve, or by not allowing doubly robust covariate adjustment. We develop a novel kernel smoothing approach that requires only mild smoothness assumptions on the effect curve, and still allows for misspecification of either the treatment density or outcome regression. We derive asymptotic properties and give a procedure for data-driven bandwidth selection...
September 2017: Journal of the Royal Statistical Society. Series B, Statistical Methodology
https://www.readbyqxmd.com/read/28983189/on-estimation-of-optimal-treatment-regimes-for-maximizing-t-year-survival-probability
#5
Runchao Jiang, Wenbin Lu, Rui Song, Marie Davidian
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 so as to maximize expected long-term clinical outcome, where larger outcomes are preferred. For chronic diseases such as cancer or HIV infection, survival time is often the outcome of interest, and the goal is to select treatment to maximize survival probability...
September 2017: Journal of the Royal Statistical Society. Series B, Statistical Methodology
https://www.readbyqxmd.com/read/28848375/change-point-estimation-in-high-dimensional-markov-random-field-models
#6
Sandipan Roy, Yves Atchadé, George Michailidis
This paper investigates a change-point estimation problem in the context of high-dimensional Markov random field models. Change-points represent a key feature in many dynamically evolving network structures. The change-point estimate is obtained by maximizing a profile penalized pseudo-likelihood function under a sparsity assumption. We also derive a tight bound for the estimate, up to a logarithmic factor, even in settings where the number of possible edges in the network far exceeds the sample size. The performance of the proposed estimator is evaluated on synthetic data sets and is also used to explore voting patterns in the US Senate in the 1979-2012 period...
September 2017: Journal of the Royal Statistical Society. Series B, Statistical Methodology
https://www.readbyqxmd.com/read/28824285/mediation-analysis-with-time-varying-exposures-and-mediators
#7
Tyler J VanderWeele, Eric J Tchetgen Tchetgen
In this paper we consider causal mediation analysis when exposures and mediators vary over time. We give non-parametric identification results, discuss parametric implementation, and also provide a weighting approach to direct and indirect effects based on combining the results of two marginal structural models. We also discuss how our results give rise to a causal interpretation of the effect estimates produced from longitudinal structural equation models. When there are time-varying confounders affected by prior exposure and mediator, natural direct and indirect effects are not identified...
June 2017: Journal of the Royal Statistical Society. Series B, Statistical Methodology
https://www.readbyqxmd.com/read/28458613/causal-analysis-of-ordinal-treatments-and-binary-outcomes-under-truncation-by-death
#8
Linbo Wang, Thomas S Richardson, Xiao-Hua Zhou
It is common that in multi-arm randomized trials, the outcome of interest is "truncated by death," meaning that it is only observed or well-defined conditioning on an intermediate outcome. In this case, in addition to pairwise contrasts, the joint inference for all treatment arms is also of interest. Under a monotonicity assumption we present methods for both pairwise and joint causal analyses of ordinal treatments and binary outcomes in presence of truncation by death. We illustrate via examples the appropriateness of our assumptions in different scientific contexts...
June 2017: Journal of the Royal Statistical Society. Series B, Statistical Methodology
https://www.readbyqxmd.com/read/28529445/regression-models-on-riemannian-symmetric-spaces
#9
Emil Cornea, Hongtu Zhu, Peter Kim, Joseph G Ibrahim
The aim of this paper is to develop a general regression framework for the analysis of manifold-valued response in a Riemannian symmetric space (RSS) and its association with multiple covariates of interest, such as age or gender, in Euclidean space. Such RSS-valued data arises frequently in medical imaging, surface modeling, and computer vision, among many others. We develop an intrinsic regression model solely based on an intrinsic conditional moment assumption, avoiding specifying any parametric distribution in RSS...
March 2017: Journal of the Royal Statistical Society. Series B, Statistical Methodology
https://www.readbyqxmd.com/read/28239261/efficient-estimation-of-semiparametric-transformation-models-for-the-cumulative-incidence-of-competing-risks
#10
Lu Mao, D Y Lin
The cumulative incidence is the probability of failure from the cause of interest over a certain time period in the presence of other risks. A semiparametric regression model proposed by Fine and Gray (1999) has become the method of choice for formulating the effects of covariates on the cumulative incidence. Its estimation, however, requires modeling of the censoring distribution and is not statistically efficient. In this paper, we present a broad class of semiparametric transformation models which extends the Fine and Gray model, and we allow for unknown causes of failure...
March 2017: Journal of the Royal Statistical Society. Series B, Statistical Methodology
https://www.readbyqxmd.com/read/28479862/estimation-of-high-dimensional-mean-regression-in-the-absence-of-symmetry-and-light-tail-assumptions
#11
Jianqing Fan, Quefeng Li, Yuyan Wang
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 (LAD) 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 functions in ultra-high dimensional setting with existence of only the second moment? To solve this problem, we propose a penalized Huber loss with diverging parameter to reduce biases created by the traditional Huber loss...
January 2017: Journal of the Royal Statistical Society. Series B, Statistical Methodology
https://www.readbyqxmd.com/read/27840585/a-general-framework-for-updating-belief-distributions
#12
P G Bissiri, C C Holmes, S G Walker
We propose a framework for general Bayesian inference. We argue that a valid update of a prior belief distribution to a posterior can be made for parameters which are connected to observations through a loss function rather than the traditional likelihood function, which is recovered as a special case. Modern application areas make it increasingly challenging for Bayesians to attempt to model the true data-generating mechanism. For instance, when the object of interest is low dimensional, such as a mean or median, it is cumbersome to have to achieve this via a complete model for the whole data distribution...
November 2016: Journal of the Royal Statistical Society. Series B, Statistical Methodology
https://www.readbyqxmd.com/read/27570475/making-the-cut-improved-ranking-and-selection-for-large-scale-inference
#13
Nicholas C Henderson, Michael A Newton
Identifying leading measurement units from a large collection is a common inference task in various domains of large-scale inference. Testing approaches, which measure evidence against a null hypothesis rather than effect magnitude, tend to overpopulate lists of leading units with those associated with low measurement error. By contrast, local maximum likelihood (ML) approaches tend to favor units with high measurement error. Available Bayesian and empirical Bayesian approaches rely on specialized loss functions that result in similar deficiencies...
September 2016: Journal of the Royal Statistical Society. Series B, Statistical Methodology
https://www.readbyqxmd.com/read/27346982/globally-efficient-non-parametric-inference-of-average-treatment-effects-by-empirical-balancing-calibration-weighting
#14
Kwun Chuen Gary Chan, Sheung Chi Phillip Yam, Zheng Zhang
The estimation of average treatment effects based on observational data is extremely important in practice and has been studied by generations of statisticians under different frameworks. Existing globally efficient estimators require non-parametric estimation of a propensity score function, an outcome regression function or both, but their performance can be poor in practical sample sizes. Without explicitly estimating either functions, we consider a wide class calibration weights constructed to attain an exact three-way balance of the moments of observed covariates among the treated, the control, and the combined group...
June 2016: Journal of the Royal Statistical Society. Series B, Statistical Methodology
https://www.readbyqxmd.com/read/26924939/joint-estimation-of-multiple-graphical-models-from-high-dimensional-time-series
#15
Huitong Qiu, Fang Han, Han Liu, Brian Caffo
In this manuscript we consider the problem of jointly estimating multiple graphical models in high dimensions. We assume that the data are collected from n subjects, each of which consists of T possibly dependent observations. The graphical models of subjects vary, but are assumed to change smoothly corresponding to a measure of closeness between subjects. We propose a kernel based method for jointly estimating all graphical models. Theoretically, under a double asymptotic framework, where both (T, n) and the dimension d can increase, we provide the explicit rate of convergence in parameter estimation...
March 1, 2016: Journal of the Royal Statistical Society. Series B, Statistical Methodology
https://www.readbyqxmd.com/read/27656104/the-lasso-for-high-dimensional-regression-with-a-possible-change-point
#16
Sokbae Lee, Myung Hwan Seo, Youngki Shin
We consider a high dimensional regression model with a possible change point due to a covariate threshold and develop the lasso estimator of regression coefficients as well as the threshold parameter. Our lasso estimator not only selects covariates but also selects a model between linear and threshold regression models. Under a sparsity assumption, we derive non-asymptotic oracle inequalities for both the prediction risk and the l1-estimation loss for regression coefficients. Since the lasso estimator selects variables simultaneously, we show that oracle inequalities can be established without pretesting the existence of the threshold effect...
January 2016: Journal of the Royal Statistical Society. Series B, Statistical Methodology
https://www.readbyqxmd.com/read/26834506/semiparametric-estimation-in-the-secondary-analysis-of-case-control-studies
#17
Yanyuan Ma, Raymond J Carroll
We study the regression relationship among covariates in case-control data, an area known as the secondary analysis of case-control studies. The context is such that only the form of the regression mean is specified, so that we allow an arbitrary regression error distribution, which can depend on the covariates and thus can be heteroscedastic. Under mild regularity conditions we establish the theoretical identifiability of such models. Previous work in this context has either (a) specified a fully parametric distribution for the regression errors, (b) specified a homoscedastic distribution for the regression errors, (c) has specified the rate of disease in the population (we refer this as true population), or (d) has made a rare disease approximation...
January 2016: Journal of the Royal Statistical Society. Series B, Statistical Methodology
https://www.readbyqxmd.com/read/26778916/variable-selection-for-support-vector-machines-in-moderately-high-dimensions
#18
Xiang Zhang, Yichao Wu, Lan Wang, Runze Li
The support vector machine (SVM) is a powerful binary classification tool with high accuracy and great flexibility. It has achieved great success, but its performance can be seriously impaired if many redundant covariates are included. Some efforts have been devoted to studying variable selection for SVMs, but asymptotic properties, such as variable selection consistency, are largely unknown when the number of predictors diverges to infinity. In this work, we establish a unified theory for a general class of nonconvex penalized SVMs...
January 2016: Journal of the Royal Statistical Society. Series B, Statistical Methodology
https://www.readbyqxmd.com/read/26568699/regression-analysis-of-sparse-asynchronous-longitudinal-data
#19
Hongyuan Cao, Donglin Zeng, Jason P Fine
We consider estimation of regression models for sparse asynchronous longitudinal observations, where time-dependent responses and covariates are observed intermittently within subjects. Unlike with synchronous data, where the response and covariates are observed at the same time point, with asynchronous data, the observation times are mismatched. Simple kernel-weighted estimating equations are proposed for generalized linear models with either time invariant or time-dependent coefficients under smoothness assumptions for the covariate processes which are similar to those for synchronous data...
September 2015: Journal of the Royal Statistical Society. Series B, Statistical Methodology
https://www.readbyqxmd.com/read/26512210/sparsifying-the-fisher-linear-discriminant-by-rotation
#20
Ning Hao, Bin Dong, Jianqing Fan
Many high dimensional classification techniques have been proposed in the literature based on sparse linear discriminant analysis (LDA). To efficiently use them, sparsity of linear classifiers is a prerequisite. However, this might not be readily available in many applications, and rotations of data are required to create the needed sparsity. In this paper, we propose a family of rotations to create the required sparsity. The basic idea is to use the principal components of the sample covariance matrix of the pooled samples and its variants to rotate the data first and to then apply an existing high dimensional classifier...
September 1, 2015: Journal of the Royal Statistical Society. Series B, Statistical Methodology
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