Comparison of Confidence Intervals for a Poisson Mean – Further Considerations

I make recommendations in choosing a confidence interval for the Poisson mean, from twelve different methods, that are based on four general principles: actual coverage should closely match the nominal coverage; narrower expected widths of confidence intervals are better; the right and left non-coverage should be fairly balanced; and some investigators may prefer closed-form intervals. The interval chosen depends on the relative importance the investigator places on each of these principles. The confidence intervals are examined through graphs of their coverage probability, interval widths and shapes.     

Confidence Intervals for Conditional Tail Risk Measures in ARMA–GARCH Models

ABSTRACT

ARMA–GARCH models are widely used to model the conditional mean and conditional variance dynamics of returns on risky assets. Empirical results suggest heavy-tailed innovations with positive extreme value index for these models. Hence, one may use extreme value theory to estimate extreme quantiles of residuals. Using weak convergence of the weighted sequential tail empirical process of the residuals, we derive the limiting distribution of extreme conditional Value-at-Risk (CVaR) and conditional expected shortfall (CES) estimates for a wide range of extreme value index estimators. To construct confidence intervals, we propose to use self-normalization. This leads to improved coverage vis-à-vis the normal approximation, while delivering slightly wider confidence intervals. A data-driven choice of the number of upper order statistics in the estimation is suggested and shown to work well in simulations. An application to stock index returns documents the improvements of CVaR and CES forecasts.     

Transformed Logit Confidence Intervals for Small Populations in Single Capture–Recapture Estimation

The good performance of logit confidence intervals for the odds ratio with small samples is well known. This is true unless the actual odds ratio is very large. In single capture–recapture estimation the odds ratio is equal to 1 because of the assumption of independence of the samples. Consequently, a transformation of the logit confidence intervals for the odds ratio is proposed in order to estimate the size of a closed population under single capture–recapture estimation. It is found that the transformed logit interval, after adding .5 to each observed count before computation, has actual coverage probabilities near to the nominal level even for small populations and even for capture probabilities near to 0 or 1, which is not guaranteed for the other capture–recapture confidence intervals proposed in statistical literature. Thus, given that the .5 transformed logit interval is very simple to compute and has a good performance, it is appropriate to be implemented by most users of the single capture–recapture method.     

Asymptotic and Resampling-Based Confidence Intervals for P(X < Y)

ABSTRACT

We consider asymptotic and resampling-based interval estimation procedures for the stress-strength reliability P(X < Y). We developed and studied several types of intervals. Their performances are investigated using simulation techniques and compared in terms of attainment of the nominal confidence level, symmetry of lower and upper error rates, and expected length. Recommendations concerning their use are given.     

Wilson Confidence Intervals for the Two-Sample Log-Odds-Ratio in Stratified 2 × 2 Contingency Tables

Large-sample Wilson-type confidence intervals (CIs) are derived for a parameter of interest in many clinical trials situations: the log-odds-ratio, in a two-sample experiment comparing binomial success proportions, say between cases and controls. The methods cover several scenarios: (i) results embedded in a single 2 × 2 contingency table; (ii) a series of K 2 × 2 tables with common parameter; or (iii) K tables, where the parameter may change across tables under the influence of a covariate. The calculations of the Wilson CI require only simple numerical assistance, and for example are easily carried out using Excel. The main competitor, the exact CI, has two disadvantages: It requires burdensome search algorithms for the multi-table case and results in strong over-coverage associated with long confidence intervals. All the application cases are illustrated through a well-known example. A simulation study then investigates how the Wilson CI performs among several competing methods. The Wilson interval is shortest, except for very large odds ratios, while maintaining coverage similar to Wald-type intervals. An alternative to the Wald CI is the Agresti-Coull CI, calculated from the Wilson and Wald CIs, which has same length as the Wald CI but improved coverage.     

What Difference Does the Dependence Between Durations Make? Insights for Population Studies of Aging

The interpretation of age-specific changes in hazards, relative risks, genetic parameters and other indicators of aging calculated from data on related individuals should take into account the regularities of bivariate selection. Due to such selection the hazard rate calculated for twins who have survived to a certain age may be lower than for singletons, even if marginal chances of survival for all individuals are the same. In a mixed population of relatives the proportion of pairs with closer family links increases with age, even if all marginal individual chances of survival are the same. The proportion of chronic conditions for MZ twins observed in a cross-sectional study may be different from that of DZ twins. The age-dependence of relative risks calculated in genetic-epidemiological studies of twins does not necessarily reflect changes in genetic influence on individual susceptibility to disease and death during the aging process. The age-related changes in heritability of susceptibility estimated in twin studies may have nothing to do with changes in the genetic determination of diseases with age. These issues are illustrated by empirical graphs together with the results of modeling and statistical analysis.     

Simultaneous Logit-Based Confidence Intervals for Odds Ratios in 2 × k Classification Tables with a Fixed Reference Level

In this article, we consider the problem of constructing simultaneous confidence intervals for odds ratios in 2 × k classification tables with a fixed reference level. We discuss six methods designed to control the familywise error rate and investigate these methods in terms of simultaneous coverage probability and mean interval length. We illustrate the importance and the implementation of these methods using two {sc hiv} public health studies.     

Linked Data: What Is It and What Can It Do?

There has been a lot of talk, discussion (and even buzz) on the Internet and in the library world recently on the whole issue of linked data and what it may mean, accomplish, and even change in the Internet and library worlds. This article will attempt to clarify what linked data is, some of the issues surrounding it, and explore some possible implications.     

Linked Data: What Is It and What Can It Do?

Abstract

There has been a lot of talk, discussion (and even buzz) on the Internet and in the library world recently on the whole issue of linked data and what it may mean, accomplish, and even change in the Internet and library worlds. This article will attempt to clarify what linked data is, some of the issues surrounding it, and explore some possible implications.     

The Institutional Repository Rediscovered: What Can a University Do for Open Access Publishing?

Universities have always been one of the key players in open access publishing and have encountered the particular obstacle that faces this Green model of open access, namely, disappointing author uptake. Today, the university has a unique opportunity to reinvent and to reinvigorate the model of the institutional repository. This article explores what is not working about the way we talk about repositories to authors today and how can we better meet faculty needs. More than an archive, a repository can be a showcase that allows scholars to build attractive scholarly profiles, and a platform to publish original content in emerging open-access journals.     

What have private schools done for (some of) us?

Many parents in Britain make huge financial sacrifices to send their children to private schools. Are those sacrifices worthwhile? What return, if any, do they get? Do their children end up in better careers, earning more, than if they have been educated at the expense of the state? Francis Green, Stephen Machin, Richard Murphy and Yu Zhu examine who exactly benefits from the privileges of the Old School Tie.     

Do we need the constant term in the heterogenous autoregressive model for forecasting realized volatilities?

No-constant strategy is considered for the heterogenous autoregressive (HAR) model of Corsi, which is motivated by smaller biases of its estimated HAR coefficients than those of the constant HAR model. The no-constant model produces better forecasts than the constant model for four real datasets of the realized volatilities (RVs) of some major assets. Robustness of forecast improvement is verified for other functions of realized variance and log RV and for the extended datasets of all 20 RVs of Oxford-Man realized library. A Monte Carlo simulation also reveals improved forecasts for some historic HAR model estimated by Corsi.     

What matters most? Different stakeholder perspectives on estimands for an invented case study in COPD

In drug development, we ask ourselves which population, endpoint and treatment comparison should be investigated. In this context, we also debate what matters most to the different stakeholders that are involved in clinical drug development, for example, patients, physicians, regulators and payers. With the publication of draft ICH E9 addendum on estimands in 2017, we now have a common framework and language to discuss such questions in an informed and transparent way. This has led to the estimand discussion being a key element in study development, including design, analysis and interpretation of a treatment effect. At an invited session at the 2018 PSI annual conference, PSI hosted a role‐play debate where the aim of the session was to mimic a regulatory and payer scientific advice discussion for a COPD drug. Including role‐play views from an industry sponsor, a patient, a regulator and a payer. This paper presents the invented COPD case‐study design and considerations relating to appropriate estimands are discussed by each of the stakeholders from their differing viewpoints with the additional inclusion of a technical (academic) perspective. The rationale for each perspective on approaches for handling intercurrent events is presented, with a key emphasis on the application of while‐on‐treatment and treatment policy estimands in this context. It is increasingly recognised that the treatment effect estimated by the treatment policy approach may not always be of primary clinical interest and may not appropriately communicate to patients the efficacy they can expect if they take the treatment as directed.     

The Tale of Cochran's Rule: My Contingency Table has so Many Expected Values Smaller than 5, What Am I to Do?

In an informal way, some dilemmas in connection with hypothesis testing in contingency tables are discussed. The body of the article concerns the numerical evaluation of Cochran's Rule about the minimum expected value in r × c contingency tables with fixed margins when testing independence with Pearson's X² statistic using the χ² distribution.