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Binary spatial observations arise in environmental and ecological studies, where Markov random field (MRF) models are often applied. Despite the prevalence and the long history of MRF models for spatial binary data, appropriate model diagnostics have remained an unresolved issue in practice. A complicating factor is that such models involve neighborhood specifications, which are difficult to assess for binary data. To address this, we propose a formal goodness-of-fit (GOF) test for diagnosing an MRF model for spatial binary values. The test statistic involves a type of conditional Moran's I based on the fitted conditional probabilities, which can detect departures in model form, including neighborhood structure. Numerical studies show that the GOF test can perform well in detecting deviations from a null model, with a focus on neighborhoods as a difficult issue. We illustrate the spatial test with an application to Besag's historical endive data as well as the breeding pattern of grasshopper sparrows across Iowa. [ABSTRACT FROM AUTHOR]

Bootstrapping spectral mean statistics has been a notoriously difficult problem over the past 25 years. Many frequency domain bootstraps are valid only for certain time series structures, e.g. linear processes, or for special types of statistics, i.e. ratio statistics, because such bootstraps fail to capture the limiting variance of spectral statistics in general settings. We address this issue with a different form of resampling, namely, subsampling. While not considered previously, subsampling provides consistent variance estimation under much weaker conditions than any existing bootstrap in the frequency domain. Mixing is not used, as is often standard with subsampling. Rather, subsampling can be generally justified under the same conditions needed for original spectral mean statistics to have distributional limits in the first place. This result has impacts for other bootstrap methods. Subsampling then applies to extending the validity of recent state-of-the-art bootstraps in the frequency domain. We nontrivially link subsampling to such bootstraps, which broadens their range, as moment and block assumptions needed for these are cut by more than half. Essentially, state-of-the-art bootstraps then require no more stringent assumptions than those needed for a target limit distribution to exist, which is unusual in the bootstrap world. We also close a gap in the theory of subsampling for time series with distributional approximations, in addition to variance estimation, for frequency domain statistics. [ABSTRACT FROM AUTHOR]

This article describes prediction methods for the number of future events from a population of units associated with an on-going time-to-event process. Examples include the prediction of warranty returns and the prediction of the number of future product failures that could cause serious threats to property or life. Important decisions such as whether a product recall should be mandated are often based on such predictions. Data, generally right-censored (and sometimes left truncated and right-censored), are used to estimate the parameters of a time-to-event distribution. This distribution can then be used to predict the number of events over future periods of time. Such predictions are sometimes called within-sample predictions and differ from other prediction problems considered in most of the prediction literature. This article shows that the plug-in (also known as estimative or naive) prediction method is not asymptotically correct (i.e., for large amounts of data, the coverage probability always fails to converge to the nominal confidence level). However, a commonly used prediction calibration method is shown to be asymptotically correct for within-sample predictions, and two alternative predictive-distribution-based methods that perform better than the calibration method are presented and justified. for this article are available online. [ABSTRACT FROM AUTHOR]