Likelihood Asymptotics in Nonregular Settings: A Review with Emphasis on the Likelihood Ratio

This paper reviews the most common situations where one or more regularity conditions which underlie classical likelihood-based parametric inference fail. We identify three main classes of problems: boundary problems, indeterminate parameter problems -- which include non-identifiable parameters and singular information matrices -- and change-point problems. The review focuses on the large-sample properties of the likelihood ratio statistic. We emphasize analytical solutions and acknowledge software implementations where available. We furthermore give summary insight about the possible tools to derivate the key results. Other approaches to hypothesis testing and connections to estimation are listed in the annotated bibliography of the Supplementary Material

Systematic review and meta-analysis of surgical drain management after the diagnosis of postoperative pancreatic fistula after pancreaticoduodenectomy: draining-tract-targeted works better than standard management

Drains' role after pancreaticoduodenectomy (PD) is debated by proponents of no drain, draining selected cases, and early drain removal. The aim of the study was to assess the effect of "standard" and "draining-tract-targeted" management of abdominal drains still in situ after diagnosing a postoperative pancreatic fistula (POPF)

Accurate Parametric Inference for Small Samples

We outline how modern likelihood theory, which provides essentially exact inferences in a variety of parametric statistical problems, may routinely be applied in practice. Although the likelihood procedures are based on analytical asymptotic approximations, the focus of this paper is not on theory but on implementation and applications. Numerical illustrations are given for logistic regression, nonlinear models, and linear non-normal models, and we describe a sampling approach for the third of these classes. In the case of logistic regression, we argue that approximations are often more appropriate than `exact' procedures, even when these exist.Comment: Published in at http://dx.doi.org/10.1214/08-STS273 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Nonparametric change point estimation for survival distributions with a partially constant hazard rate

We present a new method for estimating a change point in the hazard function of a survival distribution assuming a constant hazard rate after the change point and a decreasing hazard rate before the change point. Our method is based on fitting a stump regression to p-values for testing hazard rates in small time intervals. We present three real data examples describing survival patterns of severely ill patients, whose excess mortality rates are known to persist far beyond hospital discharge. For designing survival studies in these patients and for the definition of hospital performance metrics (e.g. mortality), it is essential to define adequate and objective end points. The reliable estimation of a change point will help researchers to identify such end points. By precisely knowing this change point, clinicians can distinguish between the acute phase with high hazard (time elapsed after admission and before the change point was reached), and the chronic phase (time elapsed after the change point) in which hazard is fairly constant. We show in an extensive simulation study that maximum likelihood estimation is not robust in this setting, and we evaluate our new estimation strategy including bootstrap confidence intervals and finite sample bias correction

G-quadruplex forming sequences in the genome of all known human viruses: A comprehensive guide

G-quadruplexes are non-canonical nucleic-acid structures that control transcription, replication, and recombination in organisms. G-quadruplexes are present in eukaryotes, prokaryotes, and viruses. In the latter, mounting evidence indicates their key biological activity. Since data on viruses are scattered, we here present a comprehensive analysis of potential quadruplex-forming sequences (PQS) in the genome of all known viruses that can infect humans. We show that occurrence and location of PQSs are features characteristic of each virus class and family. Our statistical analysis proves that their presence within the viral genome is orderly arranged, as indicated by the possibility to correctly assign up to two-thirds of viruses to their exact class based on the PQS classification. For each virus we provide: i) the list of all PQS present in the genome (positive and negative strands), ii) their position in the viral genome, iii) the degree of conservation among strains of each PQS in its genome context, iv) the statistical significance of PQS abundance. This information is accessible from a database to allow the easy navigation of the results: http://www.medcomp.medicina.unipd.it/main_site/doku.php?id=g4virus. The availability of these data will greatly expedite research on G-quadruplex in viruses, with the possibility to accelerate finding therapeutic opportunities to numerous and some fearsome human diseases

Likelihood Asymptotics in Nonregular Settings: A Review and Annotated Bibliography with Emphasis on the Likelihood Ratio

This paper reviews the most common situations where one or more regularity conditions which underlie likelihood-based parametric inference fail. We identify three main classes of problems: boundary problems, indeterminate parameter problems—which include non-identifiable parameters and singular information matrices—and change-point problems. The review focuses on the large-sample properties of the likelihood ratio statistic, though other approaches to hypothesis testing and connections to estimation will be mentioned in passing. We emphasize analytical solutions and mention software implementations where available. Some summary insights about the possible tools to derivate the key results are given

hoa: An R Package Bundle for Higher Order Likelihood Inference

The likelihood function represents the basic ingredient of many commonly used statistical methods for estimation, testing and the calculation of confidence intervals. In practice, much application of likelihood inference relies on first order asymptotic results such as the central limit theorem. Th

Restricted likelihood inference for generalized linear mixed models

We aim to promote the use of the modified profile likelihood for estimating the variance parameters of a GLMM in analogy to the REML criterion for linear mixed models. Our approach is based on both Quasi-Monte Carlo integration and numerical quadrature, obtaining in either case simulation-free inferential results. The method is illustrated for regression models with binary response and independent clusters, covering also the case of two-part models. Real-data examples and simulations studies support the use of the proposed solution as a natural extension of REML for GLMMs