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

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 2nd paragraph 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 )

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

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

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.

No abstract is available for this article.

Chris Skinner was born in London on 12 March 1953. He completed a BA in mathematics in 1975 at the University of Cambridge. He then obtained an MSc degree in statistics from the London School of Economics and Political Science (LSE) in 1976 and worked as an assistant statistician in the Central Statistical Office for 1 year. After working as a research assistant in LSE from 1977 to 1978, he joined

In this paper, we provide a detailed study of a general family of asymmetric densities. In the general framework, we establish expressions for important characteristics of the distributions and discuss estimation of the parameters via method‐of‐moments as well as maximum likelihood estimation. Asymptotic normality results for the estimators are provided. The results under the general framework are

Methods for the analysis of large numbers of p‐values, observed levels of significance, are reviewed with some emphasis placed on the Rényi decomposition hinging on the relation with independent exponentially distributed random variables. Some extensions are described. An empirical example is used in illustration, and simulation results examining potential complications are outlined.

Mann–Whitney‐type causal effects are generally applicable to outcome variables with a natural ordering, have been recommended for clinical trials because of their clinical relevance and interpretability and are particularly useful in analysing an ordinal composite outcome that combines an original primary outcome with death and possibly treatment discontinuation. In this article, we consider robust

We propose a computationally efficient and statistically principled method for kernel smoothing of point pattern data on a linear network. The point locations, and the network itself, are convolved with a two‐dimensional kernel and then combined into an intensity function on the network. This can be computed rapidly using the fast Fourier transform, even on large networks and for large bandwidths,

When sensitive issues are surveyed, collecting truthful data and obtaining reliable estimates of population parameters is a persistent problem in many fields of applied research mostly in sociological, economic, demographic, ecological and medical studies. In this context, and moving from the so‐called negative survey, we consider the problem of estimating the proportion of population units belonging

In most surveys, one is confronted with missing or, more generally, coarse data. Traditional methods dealing with these data require strong, untestable and often doubtful assumptions, for example, coarsening at random. But due to the resulting, potentially severe bias, there is a growing interest in approaches that only include tenable knowledge about the coarsening process, leading to imprecise but

W.F. Sheppard has been much overlooked in the history of statistics although his work produced significant contributions. He developed a polynomial smoothing method and corrections of moment estimates for grouped data as well as extensive normal probability tables that have been widely used since the 20th century. Sheppard presented his smoothing method for actuaries in a series of publications during

Finite mixtures offer a rich class of distributions for modelling of a variety of random phenomena in numerous fields of study. Using the sample interpoint distances (IPDs), we propose the IPD‐test statistic for testing the hypothesis of homogeneity of mixture of multivariate power series distribution or multivariate normal distribution. We derive the distribution of the IPDs that are drawn from a

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

Estimating time‐varying covariance matrices of the vector of interest is challenging both computationally and statistically due to a large number of constrained parameters. In this work, we consider an order‐averaged Cholesky‐log‐GARCH (OA‐CLGARCH) model for estimating time‐varying covariance matrices through the orthogonal transformations of the vector based on the modified Cholesky decomposition

A basic concern in statistical disclosure limitation is the re‐identification of individuals in anonymised microdata. Linking against a second dataset that contains identifying information can result in a breach of confidentiality. Almost all linkage approaches are based on comparing the values of variables that are common to both datasets. It is tempting to think that if datasets contain no common

Mixture regression models have been widely used in business, marketing and social sciences to model mixed regression relationships arising from a clustered and thus heterogeneous population. The unknown mixture regression parameters are usually estimated by maximum likelihood estimators using the expectation–maximisation algorithm based on the normality assumption of component error density. However

The widely claimed replicability crisis in science may lead to revised standards of significance. The customary frequentist confidence intervals, calibrated through hypothetical repetitions of the experiment that is supposed to have produced the data at hand, rely on a feeble concept of replicability. In particular, contradictory conclusions may be reached when a substantial enlargement of the study

Receiver operating characteristic curves are widely used as a measure of accuracy of diagnostic tests and can be summarised using the area under the receiver operating characteristic curve (AUC). Often, it is useful to construct a confidence interval for the AUC; however, because there are a number of different proposed methods to measure variance of the AUC, there are thus many different resulting

Data that have a multilevel structure occur frequently across a range of disciplines, including epidemiology, health services research, public health, education and sociology. We describe three families of regression models for the analysis of multilevel survival data. First, Cox proportional hazards models with mixed effects incorporate cluster-specific random effects that modify the baseline hazard

Recent years have seen an explosion of activity in the field of functional data analysis (FDA), in which curves, spectra, images, etc. are considered as basic functional data units. A central problem in FDA is how to fit regression models with scalar responses and functional data points as predictors. We review some of the main approaches to this problem, categorizing the basic model types as linear

Many industrial and engineering applications are built on the basis of differential equations. In some cases, parameters of these equations are not known and are estimated from measurements leading to an inverse problem. Unlike many other papers, we suggest to construct new designs in the adaptive fashion 'on the go' using the A-optimality criterion. This approach is demonstrated on determination of