Building on Yu and Kumbier's predictability, computability and stability (PCS) framework and for randomised experiments, we introduce a novel methodology for Stable Discovery of Interpretable Subgroups via Calibration (StaDISC), with large heterogeneous treatment effects. StaDISC was developed during our re‐analysis of the 1999–2000 VIGOR study, an 8076‐patient randomised controlled trial that compared

The statistical literature is known to be inconsistent in the use of the terms ‘permutation test’ and ‘randomisation test’. Several authors successfully argue that these terms should be used to refer to two distinct classes of tests and that there are major conceptual differences between these classes. The present paper explains an important difference in mathematical reasoning between these classes:

This paper discusses several modern approaches to regression analysis involving time series data where some of the predictor variables are also indexed by time. We discuss classical statistical approaches as well as methods that have been proposed recently in the machine learning literature. The approaches are compared and contrasted, and it will be seen that there are advantages and disadvantages

The statistical challenges in using big data for making valid statistical inference in the finite population have been well documented in literature. These challenges are due primarily to statistical bias arising from under‐coverage in the big data source to represent the population of interest and measurement errors in the variables available in the data set. By stratifying the population into a big

Analysing data from large‐scale, multiexperiment studies requires scientists to both analyse each experiment and to assess the results as a whole. In this article, we develop double empirical Bayes testing (DEBT), an empirical Bayes method for analysing multiexperiment studies when many covariates are gathered per experiment. DEBT is a two‐stage method: in the first stage, it reports which experiments

Sparse generalised additive models (GAMs) are an extension of sparse generalised linear models that allow a model's prediction to vary non‐linearly with an input variable. This enables the data analyst build more accurate models, especially when the linearity assumption is known to be a poor approximation of reality. Motivated by reluctant interaction modelling, we propose a multi‐stage algorithm,

No abstract is available for this article.

Paul Embrechts was born in Schoten, Belgium, on 3 February 1953. He holds a Licentiaat in Mathematics from Universiteit Antwerpen (1975) and a DSc from Katholieke Universiteit Leuven (1979), where he was also a Research Assistant from 1975 to 1983. He then held a lectureship in Statistics at Imperial College, London (1983–1985) and was a Docent at Limburgs Universitair Centrum, Belgium (1985–1989)

We show that the family of asymmetric distributions studied in a recent publication in the International Statistical Review is equivalent to the family of two‐piece distributions. Moreover, we show that the location‐scale asymmetric family proposed in that publication is non‐identifiable (overparameterised), and it coincides with the family of two‐piece distributions after removing the redundant parameters

Rubio (2020) points out an identification problem for the four‐parameter family of two‐piece asymmetric densities introduced by Nassiri & Loris (2013). This implies that statistical inference for that family is problematic. Establishing probabilistic properties for this four‐parameter family however still makes sense. For the three‐parameter family, there is no identification problem. The main contribution

We review some recent works on removing hidden confounding and causal regularisation from a unified viewpoint. We describe how simple and user‐friendly techniques improve stability, replicability and distributional robustness in heterogeneous data. In this sense, we provide additional thoughts on the issue of concept drift, raised recently by Efron, when the data generating distribution is changing

Rank‐based inference methods are applied in various disciplines, typically when procedures relying on standard normal theory are not justifiable. Various specific rank‐based methods have been developed for two and more samples and also for general factorial designs (e.g. Kruskal–Wallis test or Akritas–Arnold–Brunner test). It is the aim of the present paper (1) to demonstrate that traditional rank

Multivariate count data arise naturally in practice. In analysing such data, it is critical to define a model that can accurately capture the underlying dependence structure between the counts. To this end, this paper develops a multivariate model wherein correlated Poisson margins are generated by a comonotonic shock vector. The proposed model allows for greater flexibility in the dependence structure

In Bayesian inference, predictive distributions are typically in the form of samples generated via Markov chain Monte Carlo or related algorithms. In this paper, we conduct a systematic analysis of how to make and evaluate probabilistic forecasts from such simulation output. Based on proper scoring rules, we develop a notion of consistency that allows to assess the adequacy of methods for estimating

Usually, in spatial generalised linear models, covariates that are spatially smooth are collinear with spatial random effects. This affects the bias and precision of the regression coefficients. This is known in the spatial statistics literature as spatial confounding. We discuss the problem of confounding in the case of multilevel spatial models wherein there are multiple observations within clusters

Using social media data for statistical analysis of general population faces commonly two basic obstacles: firstly, social media data are collected for different objects than the population units of interest; secondly, the relevant measures are typically not available directly but need to be extracted by algorithms or machine learning techniques. In this paper, we examine and summarise two existing

The concepts of isotropy/anisotropy and separability/non‐separability of a covariance function are strictly related. If a covariance function is separable, it cannot be isotropic or geometrically anisotropic, except for the Gaussian covariance function, which is the only model both separable and isotropic. In this paper, some interesting results concerning the Gaussian covariance model and its properties

One way of evaluating the quality of a simulation study methodology is to estimate the Monte Carlo Error (MCE). The formula for this calculation was incorrectly implemented in Nagaraja & Nagaraja (2020). The correct formula that replaces equation (24) on page 96 of the original paper is as follows. Borrowing the notation from Koehler et al. (2009), let φ ^ r be an indicator of confidence interval r

In the 2ndparagraph of Merikoski (2020), the equal symbol in (1 = k= n– 1) should be corrected to ≤. The correct equation should be as follows: ( 1 ≤ k ≤ n − 1 )

No abstract is available for this article.

A variety of demographic statistical models exist for studying population dynamics when individuals can be tracked over time. In cases where data are missing due to imperfect detection of individuals, the associated measurement error can be accommodated under certain study designs (e.g. those that involve multiple surveys or replication). However, the interaction of the measurement error and the underlying

Multi‐compartment models have been playing a central role in modelling infectious disease dynamics since the early 20th century. They are a class of mathematical models widely used for describing the mechanism of an evolving epidemic. Integrated with certain sampling schemes, such mechanistic models can be applied to analyse public health surveillance data, such as assessing the effectiveness of preventive

As the coronavirus disease 2019 outbreak evolves, statistical network analysis is playing an essential role in informing policy decisions. Therefore, researchers who are new to such studies need to understand the techniques available to them. As a field, statistical network analysis aims to develop methods that account for the complex dependencies found in network data. Over the last few decades, the

Differential privacy is a framework for data analysis that provides rigorous privacy protections for database participants. It has increasingly been accepted as the gold standard for privacy in the analytics industry, yet there are few techniques suitable for statistical inference in the health sciences. This is notably the case for regression, one of the most widely used modelling tools in clinical

Small area estimation (SAE) entails estimating characteristics of interest for domains, often geographical areas, in which there may be few or no samples available. SAE has a long history and a wide variety of methods have been suggested, from a bewildering range of philosophical standpoints. We describe design‐based and model‐based approaches and models that are specified at the area level and at

In the last two decades, several methods for estimating Value at Risk have been proposed in the literature. Four of the most successful approaches are conditional autoregressive Value at Risk, extreme value theory, filtered historical simulation and time‐varying higher order conditional moments. In this paper, we compare their performances under both an empirical investigation using 80 assets and a

Appropriate modelling of Likert‐type items should account for the scale level and the specific role of the neutral middle category, which is present in most Likert‐type items that are in common use. Powerful hierarchical models that account for both aspects are proposed. To avoid biased estimates, the models separate the neutral category when modelling the effects of explanatory variables on the outcome

Adrian Smith joined The Alan Turing Institute as Institute Director and Chief Executive in September 2018. In May 2020, he was confirmed as President Elect of the Royal Society. He is also a member of the government's AI Council, which helps boost AI growth in the UK and promote its adoption and ethical use in businesses and organisations across the country. Professor Smith's previous role was Vice‐Chancellor

I thoroughly enjoyed reading the article by Bhadra et. al. (2020) and convey my congratulations to the authors for providing a comprehensive and coherent review of horseshoe‐based regularization approaches for machine learning models. I am thankful to the editors for providing this opportunity to write a discussion on this useful article, which I expect will turn out to be a good guide in the future

During the last years, graphical models have become a popular tool to represent dependencies among variables in many scientific areas. Typically, the objective is to discover dependence relationships that can be represented through a directed acyclic graph (DAG). The set of all conditional independencies encoded by a DAG determines its Markov property. In general, DAGs encoding the same conditional

Social and economic studies are often implemented as complex survey designs. For example, multistage, unequal probability sampling designs utilised by federal statistical agencies are typically constructed to maximise the efficiency of the target domain level estimator (e.g. indexed by geographic area) within cost constraints for survey administration. Such designs may induce dependence between the

A brief historical introduction to nine women who were trailblazers in the statistical sciences is presented. During their times, men dominated the profession. Yet we see how these women in their various ways blazed trails and as such became mentors and inspirations for generations of women practitioners who worked with them and followed in their footsteps.

In this paper, we modify small area estimators, based on the unit‐level model, so that they add up to reliable higher‐level estimates of population totals. These modifications result in benchmarked small area estimators. We consider two benchmarking procedures. One is based on augmenting the unit‐level model with a suitable variable. The other one uses the calibrated weights of the direct estimators

Justifying ridge regression from a geometrical perspective is one of the main contributions of this paper. To the best of our knowledge, this question has not been treated previously. This paper shows that ridge regression is a particular case of raising procedures that provide greater flexibility by transforming the matrix X associated with the model. Thus, raising procedures, based on a geometrical

There has been considerable and controversial research over the past two decades into how successfully random effects misspecification in mixed models (i.e. assuming normality for the random effects when the true distribution is non‐normal) can be diagnosed and what its impacts are on estimation and inference. However, much of this research has focused on fixed effects inference in generalised linear

Starting from the pioneering works of Shannon and Weiner in 1948, a plethora of works have been reported on entropy in different directions. Entropy‐related review work in the direction of statistical inference, to the best of our knowledge, has not been reported so far. Here, we have tried to collect all possible works in this direction during the last seven decades so that people interested in entropy

Readership: Graduate students and researchers interested in random matrices. Chapters: 1. Circulants, 2. Symmetric and reverse circulant, 3. LSD: normal approximation, 4. LSD: dependent input, 5. Spectral radius: light tail, 6. Spectral radius: k‐circulant, 7. Maximum of scaled eigenvalues: dependent input, 8. Poisson convergence, 9. Heavy‐tailed input: LSD, 10. Heavy‐tailed input: spectral radius

Readership: Researchers and practitioners in the area of quality control. I have been involved in the field of quality and reliability engineering for more than 40 years. I have taught courses at both undergraduate and graduate levels, taught many short courses for a wide range of industries, conducted research, authored and coauthored books and papers in this field and was a consultant for many companies

Readership: Teachers and students of a first course in probability. Chapters: 1. The Concept of Probability, 2. Finite Sample Spaces – Combinatorial Methods, 3. Conditional Probability – Independent Events, 4. Discrete Random Variables and Distributions, 5. Some Important Discrete Distributions, 6. Continuous Random Variables, 7. Some Important Continuous Distributions. Appendices: A. Sums and Products

Causal Inference in Statistics: A Primer Judea Pearl, Madelyn Glymour and Nicholas P. Jewell John Wiley & Sons, 2019, 156 pages, $46.75, paperback ISBN: 978‐1‐1191‐8684‐7 Readership: Graduate students and researchers interested in causal inference. This book, initially originating from course notes, covers the basics of causal inference in statistics. Often classical statistical methods fail to uncover

Readership: Statistics/machine learning graduate students and researchers. This is an excellent book. It provides a lucid, accessible and in‐depth treatment of non‐asymptotic high‐dimensional statistical theory, which is critical as the underpinning of modern statistics and machine learning. It succeeds brilliantly in providing a self‐contained overview of high‐dimensional statistics, suitable for

Readership: Graduate students, practitioners and researchers interested in calculus, matrices, optimisation problems, statistical models and/or their applications. The book has become the standard reference on matrix differential calculus since first published in 1988. This is the third edition of the book, with seven parts devoted to the theory and application of matrix differential calculus. Matrix

Readership: Graduate students and researchers in statistics. Table of contents. Chapter 1: Introduction, Chapter 2: Model‐based Clustering: Basic Ideas, Chapter 3: Dealing with Difficulties, Chapter 4: Model‐based Classification, Chapter 5: Semi‐supervised Clustering and Classification, Chapter 6: Discrete Data Clustering, Chapter 7: Variable Selection, Chapter 8: High‐dimensional Data Chapter, 9:

No abstract is available for this article.

A brief survey on methods to handle non‐proportional hazards in survival analysis is given with emphasis on short‐term and long‐term hazard ratio modelling. A drawback of the existing model of this nature is that except at time zero or infinity, the hazard ratio for a unit increase in the value of a covariate depends on the starting value. With two or more covariates, the hazard ratio for a unit increase

Small area estimation is concerned with methodology for estimating population parameters associated with a geographic area defined by a cross‐classification that may also include non‐geographic dimensions. In this paper, we develop constrained estimation methods for small area problems: those requiring smoothness with respect to similarity across areas, such as geographic proximity or clustering by

This article reviews the application of some advanced Monte Carlo techniques in the context of multilevel Monte Carlo (MLMC). MLMC is a strategy employed to compute expectations, which can be biassed in some sense, for instance, by using the discretization of an associated probability law. The MLMC approach works with a hierarchy of biassed approximations, which become progressively more accurate and

In the first phase of pharmaceutical development, and assuming that the probability of positive response increases with dose, the main statistical goal is to estimate a percentile of the dose–response function for a given target value Γ . We compare the Maximum Likelihood and centred isotonic regression estimators of the target dose and we discuss several performance criteria to assess inferential

The paper is concerned with testing normality in samples of curves and error curves estimated from functional regression models. We propose a general paradigm based on the application of multivariate normality tests to vectors of functional principal components scores. We examine finite sample performance of a number of such tests and select the best performing tests. We apply them to several extensively

Since the advent of the horseshoe priors for regularisation, global–local shrinkage methods have proved to be a fertile ground for the development of Bayesian methodology in machine learning, specifically for high‐dimensional regression and classification problems. They have achieved remarkable success in computation and enjoy strong theoretical support. Most of the existing literature has focused

The envelope model was first introduced as a parsimonious version of multivariate linear regression. It uses dimension reduction techniques to remove immaterial variation in the data and has the potential to gain efficiency in estimation and improve prediction. Many advances have taken place since its introduction, and the envelope model has been applied to many contexts in multivariate analysis, including

We consider groups of observations in R d and present a simultaneous plot of the empirical cumulative distribution functions of the within and between interpoint distances to visualise and examine the equality of the underlying distribution functions of the observations. We provide several examples to illustrate how such plots can be utilised to envision and canvass the relationship between the two

Rising nonresponse rates in social surveys make the issue of nonresponse bias contentious. There are conflicting messages about the importance of high response rates and the hazards of low rates. Some articles (e.g. Groves and Peytcheva, 2008) suggest that the response rate is in general not a good predictor of survey quality. Equally, it is well known that nonresponse may induce bias and increase

Recently, a number of statistical problems have found an unexpected solution by inspecting them through a ‘modal point of view'. These include classical tasks such as clustering or regression. This has led to a renewed interest in estimation and inference for the mode. This paper offers an extensive survey of the traditional approaches to mode estimation and explores the consequences of applying this

We consider least squares method for partially linear models based on polynomial splines. We derive the asymptotic property for the estimator, focusing on the estimation of the non‐parametric function, in particular whether and how the estimation of the linear part will affect the non‐parametric part (the converse relation, that is, how the linear part will be affected by the non‐parametric part is

In this study, we suggest pretest and shrinkage methods based on the generalised ridge regression estimation that is suitable for both multicollinear and high‐dimensional problems. We review and develop theoretical results for some of the shrinkage estimators. The relative performance of the shrinkage estimators to some penalty methods is compared and assessed by both simulation and real‐data analysis

A key requirement of repeated surveys conducted by national statistical institutes is the comparability of estimates over time, resulting in uninterrupted time series describing the evolution of finite population parameters. This is often an argument to keep survey processes unchanged as long as possible. It is nevertheless inevitable that a survey process will need to be redesigned from time to time

We study properties of the maximum h‐likelihood estimators for random effects in clustered data. To define optimality in random effects predictions, several foundational concepts of statistics such as likelihood, unbiasedness, consistency, confidence distribution and the Cramer–Rao lower bound are extended. Exact probability statements about interval estimators for random effects can be made asymptotically

Bayesian networks (BNs) are graphical probabilistic models used for reasoning under uncertainty. These models are becoming increasingly popular in a range of fields including engineering, ecology, computational biology, medical diagnosis and forensics. In most of these cases, the BNs are quantified using information from experts or from users' opinions. While this quantification is straightforward

Many National Statistical Institutes (NSIs), especially in Europe, are moving from single‐source statistics to multi‐source statistics. By combining data sources, NSIs can produce more detailed and more timely statistics and respond more quickly to events in society. By combining survey data with already available administrative data and Big Data, NSIs can save data collection and processing costs