A generalized Hosmer-Lemeshow goodness-of-fit test for a family of generalized linear models.

Generalized linear models (GLMs) are very widely used, but formal goodness-of-fit (GOF) tests for the overall fit of the model seem to be in wide use only for certain classes of GLMs. We develop and apply a new goodness-of-fit test, similar to the well-known and commonly used Hosmer-Lemeshow (HL) test, that can be used with a wide variety of GLMs. The test statistic is a variant of the HL statistic, but we rigorously derive an asymptotically correct sampling distribution using methods of Stute and Zhu (Scand J Stat 29(3):535-545, 2002) and demonstrate its consistency. We compare the performance of our new test with other GOF tests for GLMs, including a naive direct application of the HL test to the Poisson problem. Our test provides competitive or comparable power in various simulation settings and we identify a situation where a naive version of the test fails to hold its size. Our generalized HL test is straightforward to implement and interpret and an R package is publicly available. Supplementary Information: The online version contains supplementary material available at 10.1007/s11749-023-00912-8.

Asymptotic behavior of an intrinsic rank-based estimator of the Pickands dependence function constructed from B-splines.

A bivariate extreme-value copula is characterized by its Pickands dependence function, i.e., a convex function defined on the unit interval satisfying boundary conditions. This paper investigates the large-sample behavior of a nonparametric estimator of this function due to Cormier et al. (Extremes 17:633-659, 2014). These authors showed how to construct this estimator through constrained quadratic median B-spline smoothing of pairs of pseudo-observations derived from a random sample. Their estimator is shown here to exist whatever the order m ≥ 3 of the B-spline basis, and its consistency is established under minimal conditions. The large-sample distribution of this estimator is also determined under the additional assumption that the underlying Pickands dependence function is a B-spline of given order with a known set of knots.

Adjusting for undercoverage of access-points in creel surveys with fewer overflights.

Creel surveys are used in recreational fisheries to estimate angling effort, catch, and harvest. Aerial-access creel surveys rely on two components: (1) a ground component in which fishing parties returning from their trips are interviewed at some access-points of the fishery; (2) an aerial component in which the number of fishing parties is counted. A common practice is to sample fewer aerial survey days than ground survey days. This is thought by practitioners to reduce the cost of the survey, but there is a lack of sound statistical methodology for this case. In this article, we propose various estimation methods to handle this situation and evaluate their asymptotic properties from a design-based perspective. We also propose formulas for the optimal allocation of the effort between the ground and the aerial portion of the survey, for given costs and budget. A simulation study investigates the performance of the estimators. Finally, we apply our methods to data from an annual Kootenay Lake survey (Canada).

The bias/variance trade-off when estimating the MR signal magnitude from the complex average of repeated measurements.

The signal-dependent bias of MR images has been considered a hindrance to visual interpretation almost since the beginning of clinical MRI. Over time, a variety of procedures have been suggested to produce less-biased images from the complex average of repeated measurements. In this work, we re-evaluate these approaches using first a survey of previous estimators in the MRI literature, then a survey of the methods statisticians employ for our specific problem. Our conclusions are substantially different from much of the previous work: first, removing bias completely is impossible if we demand the estimator have bounded variance; second, reducing bias may not be beneficial to image quality.

Marginal analysis of panel counts through estimating functions.

We develop nonparametric estimation procedures for the marginal mean function of a counting process based on periodic observations, using two types of self-consistent estimating equations. The first is derived from the likelihood studied in Wellner & Zhang (2000), assuming a Poisson counting process, and gives a nondecreasing estimator, which is the same as the nonparametric maximum likelihood estimator of Wellner & Zhang and thus is consistent without the Poisson assumption. Motivated by the construction of parametric generalized estimating equations, the second type is a set of data-adaptive quasi-score functions, which are likelihood estimating functions under a mixed-Poisson assumption. We evaluate the procedures via simulation, and illustrate them with the data from a bladder cancer study.

GENERALIZED LEAST SQUARES ESTIMATION OF THE MEAN FUNCTION OF A COUNTING PROCESS BASED ON PANEL COUNTS.

This paper considers nonparametric estimation of the mean function of a counting process based on periodic observations, i.e., panel counts. We present estimators derived through minimizing a class of generalized sums of squares subject to a monotonicity constraint. We establish consistency of the estimators and provide procedures to implement them with various weight functions. For specific weight functions, they reduce to the estimator given in Sun and Kalbfleisch (1995), and are closely related to the nonparametric maximum likelihood estimator studied in Wellner and Zhang (2000). With other weight functions, the proposed estimators provide alternatives that can have better efficiency in non-Poisson situations than previous approaches. Simulations are used to examine the finite-sample performance of the proposed estimators.