Dynamical systems based on differential equations are useful for modelling the temporal evolution of biomarkers. Such systems can characterize the temporal patterns of biomarkers and inform the detection of interactions between biomarkers. Existing statistical methods for dynamical systems deal mostly with single time-course data based on a linear model or generalized additive model. Hence, they cannot

Statistical analysis on networks has received growing attention due to demand from various emerging applications. In dynamic networks, one of the key interests is to model the event history of time-stamped interactions among nodes. We model dynamic directed networks via multivariate counting processes. A pseudo partial likelihood approach is exploited to capture the network dependence structure. Asymptotic

We consider the problem of segmented linear regression with a single breakpoint, with the focus on estimating the location of the breakpoint. If |$n$| is the sample size, we show that the global minimax convergence rate for this problem in terms of the mean absolute error is |$O(n^{-1/3})$|⁠. On the other hand, we demonstrate the construction of a super-efficient estimator that achieves the pointwise

We study posterior contraction rates in sparse high-dimensional generalized linear models using priors incorporating sparsity. A mixture of a point mass at zero and a continuous distribution is used as the prior distribution on regression coefficients. In addition to the usual posterior, the fractional posterior, which is obtained by applying the Bayes theorem on a fractional power of the likelihood

We establish a general theory of optimality for block bootstrap distribution estimation for sample quantiles under mild strong mixing conditions. In contrast to existing results, we study the block bootstrap for varying numbers of blocks. This corresponds to a hybrid between the subsampling bootstrap and the moving block bootstrap, in which the number of blocks is between 1 and the ratio of sample

We consider testing the covariance structure in statistical models. We focus on developing such tests when the random vectors of interest are not directly observable and have to be derived via estimated models. Additionally, the covariance specification may involve extra nuisance parameters which also need to be estimated. In a generic additive model setting, we develop and investigate test statistics

Eliminating the effect of confounding in observational studies typically involves fitting a model for an outcome adjusted for covariates. When, as often, these covariates are high-dimensional, this necessitates the use of sparse estimators such as the Lasso, or other regularisation approaches. Naϊve use of such estimators yields confidence intervals for the conditional treatment effect parameter that

Differential graphical models are designed to represent the difference between the conditional dependence structures of two groups, thus are of particular interest for scientific investigation. Motivated by modern applications, this manuscript considers an extended setting where each group is generated by a latent variable Gaussian graphical model. Due to the existence of latent factors, the differential

Advances in wearables and digital technology now make it possible to deliver behavioral mobile health interventions to individuals in their everyday life. The micro-randomized trial is increasingly used to provide data to inform the construction of these interventions. In a micro-randomized trial, each individual is repeatedly randomized among multiple intervention options, often hundreds or even thousands

We study a class of parameters with the so-called mixed bias property. For parameters with this property, the bias of the semiparametric efficient one-step estimator is equal to the mean of the product of the estimation errors of two nuisance functions. In nonparametric models, parameters with the mixed bias property admit so-called rate doubly robust estimators, i.e., estimators that are consistent

Information criteria are a common approach for joint fixed and random effects selection in mixed models. While straightforward to implement, a major difficultly when applying information criteria is that they are typically based on maximum likelihood estimates, yet calculating such estimates for one, let alone multiple, candidate mixed models presents a major computational hurdle. To overcome this

Large samples are generated routinely from various sources. Classic statistical models, such as smoothing spline ANOVA models, are not well equipped to analyse such large samples because of high computational costs. In particular, the daunting computational cost of selecting smoothing parameters renders smoothing spline ANOVA models impractical. In this article, we develop an asympirical, i.e., asymptotic

Posterior computation for high-dimensional data with many parameters can be challenging. This article focuses on a new method for approximating posterior distributions of a low- to moderate-dimensional parameter in the presence of a high-dimensional or otherwise computationally challenging nuisance parameter. The focus is on regression models and the key idea is to separate the likelihood into two

Exact and approximate expressions for tail probabilities and partial moments of quadratic forms in multivariate generalized hyperbolic random vectors are obtained. The derivations involve a generalization of the classic inversion formula of Gil-Pelaez (1951). Two numerical applications are considered: the distribution of the two stage least squares estimator, and the expected shortfall of a quadratic

This paper develops a unified finite-time theory for the ordinary least squares estimation of possibly unstable and even slightly explosive vector autoregressive models under linear restrictions, with the applicable region ρ(A) ≤ 1 + c/n, where ρ(A) is the spectral radius of the transition matrix A in the Var(1) representation, n is the time horizon and c > 0 is a universal constant. The linear restriction

Biometrika (2019) 106, pp. 287–302.

High-dimensional |$k$|-sample comparison is a common task in applications. We construct a class of easy-to-implement distribution-free tests based on new nonparametric tools and unexplored connections with spectral graph theory. The test is shown to have various desirable properties and a characteristic exploratory flavour that has practical consequences for statistical modelling. Numerical examples

Penalization of the likelihood by Jeffreys’ invariant prior, or a positive power thereof, is shown to produce finite-valued maximum penalized likelihood estimates in a broad class of binomial generalized linear models. The class of models includes logistic regression, where the Jeffreys-prior penalty is known additionally to reduce the asymptotic bias of the maximum likelihood estimator, and models

Paradata refers to survey variables which are not of direct interest themselves, but are related to the quality of data on survey variables which are of interest. We focus on a categorical paradata variable, which reflects the presence of measurement error in a variable of interest. We propose a quasi-score test of the hypothesis of no measurement error bias in the estimation of regression coefficients

We propose a general framework based on selectively traversed accumulation rules for interactive multiple testing with generic structural constraints on the rejection set. It combines accumulation tests from ordered multiple testing with data-carving ideas from post-selection inference, allowing for highly flexible adaptation to generic structural information. Our procedure defines an interactive protocol

We discuss Poisson reduced-rank models for low-dimensional summaries of high-dimensional Poisson vectors that allow for inference on the location of individuals in a low-dimensional space. We show that under weak dependence conditions, which allow for certain correlations between the Poisson random variables, the locations can be consistently estimated using Poisson maximum likelihood estimation. Moreover

Sketching is a probabilistic data compression technique that has been largely developed in the computer science community. Numerical operations on big datasets can be intolerably slow; sketching algorithms address this issue by generating a smaller surrogate dataset. Typically, inference proceeds on the compressed dataset. Sketching algorithms generally use random projections to compress the original

Quantile matching is a strictly monotone transformation that sends the observed response values to the quantiles of a given target distribution. A profile likelihood-based criterion is developed for comparing one target distribution with another in a linear-model setting.

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

We consider testing marginal independence versus conditional independence in a trivariate Gaussian setting. The two models are nonnested, and their intersection is a union of two marginal independences. We consider two sequences of such models, one from each type of independence, that are closest to each other in the Kullback–Leibler sense as they approach the intersection. They become indistinguishable

We propose a new method for functional nonparametric regression with a predictor that resides on a finite-dimensional manifold, but is observable only in an infinite-dimensional space. Contamination of the predictor due to discrete or noisy measurements is also accounted for. By using functional local linear manifold smoothing, the proposed estimator enjoys a polynomial rate of convergence that adapts

We investigate optimal subsampling for quantile regression. We derive the asymptotic distribution of a general subsampling estimator and then derive two versions of optimal subsampling probabilities. One version minimizes the trace of the asymptotic variance-covariance matrix for a linearly transformed parameter estimator and the other minimizes that of the original parameter estimator. The former

Classifiers label data as belonging to one of a set of groups based on input features. It is challenging to achieve accurate classification when the feature distributions in the different classes are complex, with nonlinear, overlapping and intersecting supports. This is particularly true when training data are limited. To address this problem, we propose a new type of classifier based on obtaining

Stochastic gradient Markov chain Monte Carlo algorithms have received much attention in Bayesian computing for big data problems, but they are only applicable to a small class of problems for which the parameter space has a fixed dimension and the log-posterior density is differentiable with respect to the parameters. This paper proposes an extended stochastic gradient Markov chain Monte Carlo algorithm

Quantitative comparison of microbial composition from different populations is a fundamental task in various microbiome studies. We consider two-sample testing for microbial compositional data by leveraging the phylogenetic tree information. Motivated by existing phylogenetic distances, we take a minimum-cost flow perspective to study such testing problems. We first show that multivariate analysis

The pseudo-marginal algorithm is a variant of the Metropolis–Hastings algorithm which samples asymptotically from a probability distribution when it is only possible to estimate unbiasedly an unnormalized version of its density. Practically, one has to trade off the computational resources used to obtain this estimator against the asymptotic variances of the ergodic averages obtained by the pseudo-marginal

Modularity is a popular metric for quantifying the degree of community structure within a network. The distribution of the largest eigenvalue of a network’s edge weight or adjacency matrix is well studied and is frequently used as a substitute for modularity when performing statistical inference. However, we show that the largest eigenvalue and modularity are asymptotically uncorrelated, which suggests

We consider an extension of Aalen’s additive regression model allowing covariates to have effects that vary on two different time-scales. The two time-scales considered are equal up to a constant that varies for each individual, such as follow-up time and age in medical studies or calendar time and age in longitudinal studies. The model was introduced in Scheike (2001) where it was solved via smoothing

We propose and prove the optimality of a Bayesian approach for estimating the latent positions in random dot product graphs, which we call posterior spectral embedding. Unlike classical spectral-based adjacency, or Laplacian spectral embedding, posterior spectral embedding is a fully likelihood-based graph estimation method that takes advantage of the Bernoulli likelihood information of the observed

Experimental designs that spread out points apart from each other on projections are important for computer experiments when not necessarily all factors have substantial influence on the response. We provide a theoretical framework to generate designs that possess quasi-optimal separation distance on all of the projections and quasi-optimal fill distance on univariate margins. The key is to use special

Measurement error in covariates has been extensively studied in many conventional regression settings where covariate information is typically expressed in a vector form. However, there has been little work on error-prone matrix-variate data which commonly arise from studies with imaging, spatial-temporal structures, etc. In this paper, we consider analysis of matrix-variate data which are error-contaminated

Envelopes have been proposed in recent years as a nascent methodology for sufficient dimension reduction and efficient parameter estimation in multivariate linear models. We extend the classical definition of envelopes in Cook et al. (2010) to incorporate a nonlinear conditional mean function and a heteroscedastic error. Given any two random vectors |${X}\in\mathbb{R}^{p}$| and |${Y}\in\mathbb{R}^{r}$|⁠

Left-truncation poses extra challenges for the analysis of complex time-to-event data. We propose a general semiparametric regression model for left-truncated and right-censored competing risks data that is based on a novel weighted conditional likelihood function. Targeting the subdistribution hazard, our parameter estimates are directly interpretable with regard to the cumulative incidence function

Classification with high-dimensional data is of widespread interest and often involves dealing with imbalanced data. Bayesian classification approaches are hampered by the fact that current Markov chain Monte Carlo algorithms for posterior computation become inefficient as the number |$p$| of predictors or the number |$n$| of subjects to classify gets large, because of the increasing computational

Linear regression is often used in the analysis of randomized experiments to improve treatment effect estimation by adjusting for imbalances of covariates in the treatment and control groups. This article proposes a randomization-based inference framework for regression adjustment in stratified randomized experiments. We re-establish, under mild conditions, the finite-population central limit theorem

The infinite-dimensional information operator for the nuisance parameter plays a key role in semiparametric inference, as it is closely related to the regular estimability of the target parameter. Calculation of information operators has traditionally proceeded in a case-by-case manner and has often entailed lengthy derivations with complicated arguments. We develop a unified framework for this task

Composite likelihood functions are often used for inference in applications where the data have a complex structure. While inference based on the composite likelihood can be more robust than inference based on the full likelihood, the inference is not valid if the associated conditional or marginal models are misspecified. In this paper, we propose a general class of specification tests for composite

In an observational study matched for observed covariates, an association between treatment received and outcome exhibited may indicate not an effect caused by the treatment, but merely some bias in the allocation of treatments to individuals within matched pairs. The evidence that distinguishes moderate biases from causal effects is unevenly dispersed among possible comparisons in an observational

This paper proposes general methods for the problem of multiple testing of a single hypothesis, with a standard goal of combining a number of |$p$|-values without making any assumptions about their dependence structure. A result by Rüschendorf (1982) and, independently, Meng (1993) implies that the |$p$|-values can be combined by scaling up their arithmetic mean by a factor of 2, and no smaller factor

Discrete nonparametric priors play a central role in a variety of Bayesian procedures, most notably when used to model latent features, such as in clustering, mixtures and curve fitting. They are effective and well-developed tools, though their infinite dimensionality is unsuited to some applications. If one restricts to a finite-dimensional simplex, very little is known beyond the traditional Dirichlet

We present a multivariate one-sided sensitivity analysis for matched observational studies, appropriate when the researcher has specified that a given causal mechanism should manifest itself in effects on multiple outcome variables in a known direction. The test statistic can be thought of as the solution to an adversarial game, where the researcher determines the best linear combination of test statistics

We propose a robust method to estimate the average treatment effects in observational studies when the number of potential confounders is possibly much greater than the sample size. Our method consists of three steps. We first use a class of penalized |$M$|-estimators for the propensity score and outcome models. We then calibrate the initial estimate of the propensity score by balancing a carefully

The dimension of the parameter space is typically unknown in a variety of models that rely on factorizations. For example, in factor analysis the number of latent factors is not known and has to be inferred from the data. Although classical shrinkage priors are useful in such contexts, increasing shrinkage priors can provide a more effective approach that progressively penalizes expansions with growing

For estimating the population mean of a response variable subject to ignorable missingness, a new class of methods, called multiply robust procedures, has been proposed. The advantage of multiply robust procedures over the traditional doubly robust methods is that they permit the use of multiple candidate models for both the propensity score and the outcome regression, and they are consistent if any

Parameter estimation in linear errors-in-variables models typically requires that the measurement error distribution be known or estimable from replicate data. A generalized method of moments approach can be used to estimate model parameters in the absence of knowledge of the error distributions, but it requires the existence of a large number of model moments. In this paper, parameter estimation based

Fully Bayesian inference in the presence of unequal probability sampling requires stronger structural assumptions on the data-generating distribution than frequentist semiparametric methods, but offers the potential for improved small-sample inference and convenient evidence synthesis. We demonstrate that the Bayesian exponentially tilted empirical likelihood can be used to combine the practical benefits

We thank the authors for their new contribution to network modelling. Data reuse, encompassing methods such as bootstrapping and cross-validation, is an area that to date has largely resisted obvious and rapid development in the network context. One of the major reasons is that mimicking the original sampling mechanisms is challenging if not impossible. To avoid deleting edges and destroying some of

One of the main novelties of the method is the use of matrix completion to...

We congratulate the authors for a nice contribution to the literature on model selection and assessment for complex network data. The article of Li et al. (2020) enriches the collection of tools available for network data analysis, bringing together different fields such as low-rank matrix estimation, cross-validation and network modelling. This discussion will focus on the |$V$|-fold variant of the

We thank the editor for organizing this discussion and giving us the opportunity to read experts’ perspectives on our work. We are grateful to all the discussants for their insightful contributions, which raise many important points and offer suggestions for potential improvements and generalizations of our method. In this rejoinder we provide some clarifications, remarks and selected numerical results

We consider the problem of approximating smoothing spline estimators in a nonparametric regression model. When applied to a sample of size |$n$|⁠, the smoothing spline estimator can be expressed as a linear combination of |$n$| basis functions, requiring |$O(n^3)$| computational time when the number |$d$| of predictors is two or more. Such a sizeable computational cost hinders the broad applicability

In multivariate extreme value analysis, the nature of the extremal dependence between variables should be considered when selecting appropriate statistical models. Interest often lies in determining which subsets of variables can take their largest values simultaneously while the others are of smaller order. Our approach to this problem exploits hidden regular variation properties on a collection of

We consider the weighted bootstrap approximation to the distribution of a class of M-estimators for the parameters of the generalized autoregressive conditional heteroscedastic model. We prove that the bootstrap distribution, given the data, is a consistent estimate in probability of the distribution of the M-estimator, which is asymptotically normal. We propose an algorithm for the computation of

We present a new general method for constrained likelihood ratio testing which, when few constraints are violated, improves upon the existing approach in the literature that compares the likelihood ratio with the quantile of a mixture of chi-squared distributions; the improvement is in terms of both simplicity and power. The proposed method compares the constrained likelihood ratio statistic against

Mediation analysis is difficult when the number of potential mediators is larger than the sample size. In this paper we propose new inference procedures for the indirect effect in the presence of high-dimensional mediators for linear mediation models. We develop methods for both incomplete mediation, where a direct effect may exist, and complete mediation, where the direct effect is known to be absent