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

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

We establish the inferential properties of the mean‐difference estimator for the average treatment effect in randomised experiments where each unit in a population is randomised to one of two treatments and then units within treatment groups are randomly sampled. The properties of this estimator are well understood in the experimental design scenario where first units are randomly sampled and then

When two surveys carried out separately in the same population have common variables, it might be desirable to adjust each survey's weights so that they give equal estimates for the common variables. This problem has been studied extensively and has often been referred to as alignment or numerical consistency. We develop a design‐based empirical likelihood approach for alignment and estimation of complex

Factor analysis models are used in data dimensionality reduction problems where the variability among observed variables can be described through a smaller number of unobserved latent variables. This approach is often used to estimate the multidimensionality of well‐being. We employ factor analysis models and use multivariate empirical best linear unbiased predictor (EBLUP) under a unit‐level small

Quantile estimation is important for a wide range of applications. While point estimates based on one or two order statistics are common, constructing confidence intervals around them, however, is a more difficult problem. This paper has two goals. First, it surveys the numerous distribution‐free methods for constructing approximate confidence intervals for quantiles. These techniques can be divided

Non‐negative matrix factorisation (NMF) is an increasingly popular unsupervised learning method. However, parameter estimation in the NMF model is a difficult high‐dimensional optimisation problem. We consider algorithms of the alternating least squares type. Solutions to the least squares problem fall in two categories. The first category is iterative algorithms, which include algorithms such as the

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

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

The aim of this study was to assess spatial co-occurrence of acute respiratory infections (ARI), diarrhoea and stunting among children of the age between 6 and 59 months in Somalia. Data were obtained from routine biannual nutrition surveys conducted by the Food and Agriculture Organization 2007-2010. A Bayesian hierarchical geostatistical shared component model was fitted to the residual spatial components

This article gives a formal definition of a lognormal family of probability distributions on the set of symmetric positive definite (SPD) matrices, seen as a matrix-variate extension of the univariate lognormal family of distributions. Two forms of this distribution are obtained as the large sample limiting distribution via the central limit theorem of two types of geometric averages of i.i.d. SPD

The growth of nonresponse rates for social science surveys has led to increased concern about the risk of nonresponse bias. Unfortunately, the nonresponse rate is a poor indicator of when nonresponse bias is likely to occur. We consider in this paper a set of alternative indicators. A large-scale simulation study is used to explore how each of these indicators performs in a variety of circumstances

This paper uses semidefinite programming (SDP) to construct Bayesian optimal design for nonlinear regression models. The setup here extends the formulation of the optimal designs problem as an SDP problem from linear to nonlinear models. Gaussian quadrature formulas (GQF) are used to compute the expectation in the Bayesian design criterion, such as D-, A- or E-optimality. As an illustrative example

Good statistical practice dictates that summaries in Monte Carlo studies should always be accompanied by standard errors. Those standard errors are easy to provide for summaries that are sample means over the replications of the Monte Carlo output: for example, bias estimates, power estimates for tests, and mean squared error estimates. But often more complex summaries are of interest: medians (often

We demonstrate that many current approaches for marginal modeling of correlated binary outcomes produce likelihoods that are equivalent to the copula-based models herein. These general copula models of underlying latent threshold random variables yield likelihood-based models for marginal fixed effects estimation and interpretation in the analysis of correlated binary data with exchangeable correlation

Modern computational statistics is turning more and more to high-dimensional optimization to handle the deluge of big data. Once a model is formulated, its parameters can be estimated by optimization. Because model parsimony is important, models routinely include nondifferentiable penalty terms such as the lasso. This sober reality complicates minimization and maximization. Our broad survey stresses

Summarizing the effect of many covariates through a few linear combinations is an effective way of reducing covariate dimension and is the backbone of (sufficient) dimension reduction. Because the replacement of high-dimensional covariates by low-dimensional linear combinations is performed with a minimum assumption on the specific regression form, it enjoys attractive advantages as well as encounters

Survey calibration (or generalized raking) estimators are a standard approach to the use of auxiliary information in survey sampling, improving on the simple Horvitz-Thompson estimator. In this paper we relate the survey calibration estimators to the semiparametric incomplete-data estimators of Robins and coworkers, and to adjustment for baseline variables in a randomized trial. The development based

According to the law of likelihood, statistical evidence is represented by likelihood functions and its strength measured by likelihood ratios. This point of view has led to a likelihood paradigm for interpreting statistical evidence, which carefully distinguishes evidence about a parameter from error probabilities and personal belief. Like other paradigms of statistics, the likelihood paradigm faces

Hot deck imputation is a method for handling missing data in which each missing value is replaced with an observed response from a "similar" unit. Despite being used extensively in practice, the theory is not as well developed as that of other imputation methods. We have found that no consensus exists as to the best way to apply the hot deck and obtain inferences from the completed data set. Here we

"China has conducted four population censuses since 1949. A large amount of important information about population, education, employment, migration and urbanization was collected in the most recent 1990 census. This paper will examine main features and key issues of the Chinese population census and the census data. Some fundamental considerations in building a computerized census data system and

"For some years it has been the policy of Statistics Norway to collaborate with various governmental agencies in order to use administrative registers in statistics production. This policy has been supported politically, and a new Statistics Act has been useful in these efforts. The purpose of this paper is to present the strategy and methodology used to produce statistics in general, census statistics

"This paper discusses possible sources for statistics to be used for describing and analysing the number, structure, situation, development and impact of migrant workers. The discussion is focused on key, intrinsic features of the different sources, important for the understanding of their strengths and weaknesses, and draws the reader's attention to features which may tend to undermine the quality

"Sampling errors and design effects from 48 nationally representative surveys conducted under the Demographic and Health Surveys Program for a large number of variables concerning fertility, family planning, fertility intentions, child health and mortality etc. are analysed for the total sample, and for urban-rural domains, sub-national regions and various demographic and socio-economic subclasses

"Five types of multipopulation surveys are defined and described: periodic surveys; multidomain designs; multinational survey designs; cumulated and combined samples; and controlled observations or quasi- experimental designs. I emphasize the deliberate designs of these surveys, not the mere post hoc or ad hoc utilization of survey results. Most importantly, I emphasize a sharp distinction between

"The paper summarises the findings of an international survey of census processing methods used in the 1990 round. Extensive use is made of computers, although the technologies involved vary considerably from country to country. There is more extensive discussion of the use made of computer-assisted and automatic coding, non-keyboard data entry methods and the establishment of population databases

This is an exploratory study of geographical factors affecting cancer mortality in the United States. Data were collected by the National Cancer Institute for the years 1950-1969 and concern mortality from cancer of the trachea, bronchus, and lung combined for white males. The authors discuss differences in mortality by level of urbanization and how these might be affected by differences in smoking