arXiv subjects

James H. McVittie

Publications and source records attributed to James H. McVittie.

3 recordsLinked to original sources

arXiv2026

Sample Size Determination Under Selection Bias: Robust Tolerance Limits for Prevalent Cohort Data

Tolerance limits have received considerable attention in the statistical literature, with applications reaching far beyond their initial role in quality control. The well-known formula of Scheffé and Tukey (1944) establishes a simple, distribution-free relation between sample size and population coverage by two given order statistics and a given confidence level. A key requirement in applying this formula is the availability of an unbiased, representative sample from the population of interest. However, as it often happens in biological and medical applications, various logistical constraints may preclude the possibility of obtaining an unbiased sample. We derive extensions of this formula which accommodate a large class of biased sampling schemes including weight bias and censoring. The modified formulae are validated through a simulation study and compared to its unmodified counterpart. We illustrate the use of the modified formulae using the partially observed failure times for individuals with dementia using data collected from the Canadian Study of Health and Aging.

stat.ME↗

arXiv2025

Weighted Parameter Estimators of the Generalized Extreme Value Distribution in the Presence of Missing Observations

Missing data occur in a variety of applications of extreme value analysis. In the block maxima approach to an extreme value analysis, missingness is often handled by either ignoring missing observations or dropping a block of observations from the analysis. However, in some cases, missingness may occur due to equipment failure during an extreme event, which can lead to bias in estimation. In this work, we propose weighted maximum likelihood and weighted moment-based estimators for the generalized extreme value distribution parameters to account for the presence of missing observations. We validate the procedures through an extensive simulation study and apply the estimation methods to data from multiple tidal gauges on the Eastern coast of Canada.

stat.ME↗

arXiv2025

Estimating Extreme Wave Surges in the Presence of Missing Data

The block maxima approach, which consists of dividing a series of observations into equal sized blocks to extract the block maxima, is commonly used for identifying and modelling extreme events using the generalized extreme value (GEV) distribution. In the analysis of coastal wave surge levels, the underlying data which generate the block maxima typically have missing observations. Consequently, the observed block maxima may not correspond to the true block maxima yielding biased estimates of the GEV distribution parameters. Various parametric modelling procedures are proposed to account for the presence of missing observations under a block maxima framework. The performance of these estimators is compared through an extensive simulation study and illustrated by an analysis of extreme wave surges in Atlantic Canada.

stat.ME↗