Predicting the Number of Future Events

Tian, Qinglong; Meng, Fanqi; Nordman, Daniel J.; Meeker, William Q.

doi:10.1080/01621459.2020.1850461

Cited by 8 publications

(9 citation statements)

References 28 publications

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“…Liu et al 2014Liu et al , 2015Shen et al 2020;Cai et al 2021;Liu et al 2021), prediction (e.g. Shen et al 2018;Xie and Zheng 2021;Tian et al 2021), and fields such as Fisher randomization tests (Luo et al 2021) and survival studies (Tian et al 2011).…”

Section: Review On Confidence Distributions and Rank-and Pseudo-rank-...mentioning

confidence: 99%

A unifying framework for rank and pseudo-rank based inference using nonparametric confidence distributions

Beck

Bathke

2023

Stat Papers

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Nonparametric confidence distributions estimate statistical functionals by a distribution function on the parameter space, instead of the classical point or interval estimators. The concept bears analogy to the Bayesian posterior, but is nevertheless a completely frequentist concept. In order to ensure the desired statistical properties, we require that the cumulative distribution function on the parameter space is, evaluated at the true parameter, uniformly distributed over the unit interval. Our main focus lies on developing confidence distributions for the nonparametric relative effect and some natural extensions thereof. We develop asymptotic, range preserving and—especially important in the case of small sample sizes—approximate confidence distributions based on rank and pseudo-rank procedures. Due to the close relationship between point estimators, confidence intervals and p-values, these can all be approached in a unified manner within the framework of confidence distributions. The main goal of our contribution is to make the powerful theory of confidence distributions available in a nonparametric context, that is, for situations where methods relying on parametric assumptions are not justifiable. Application of the proposed methods and interpretation of the results is demonstrated using real data sets, including ordinal, non-metric data.

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Section: Review On Confidence Distributions and Rank-and Pseudo-rank-...mentioning

confidence: 99%

A unifying framework for rank and pseudo-rank based inference using nonparametric confidence distributions

Beck

Bathke

2023

Stat Papers

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“…For the PI constructions, those studies commonly utilized the calibration approach as in Lawless and Fredette (2005). Lastly, Tian et al (2021) considered failure-time event processes and introduced several PI procedures, including the calibration and bootstrap approaches.…”

Section: Prediction Intervals For Poisson Regressionmentioning

confidence: 99%

Prediction intervals for Poisson‐based regression models

Kim

Lieberman

Luta

et al. 2021

WIREs Computational Stats

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This paper provides a review of the literature regarding methods for constructing prediction intervals for counting variables, with particular focus on those whose distributions are Poisson or derived from Poisson and with an over‐dispersion property. Independent and identically distributed models and regression models are both considered. The motivating problem for this review is that of predicting the number of daily and cumulative cases or deaths attributable to COVID‐19 at a future date. This article is categorized under: Applications of Computational Statistics > Clinical Trials Statistical Learning and Exploratory Methods of the Data Sciences > Modeling Methods Statistical Models > Generalized Linear Models

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“…Similar problems have been studied in Nelson (2000) and Nordman and Meeker (2002) based on an LR statistic without calibration. Tian et al (2020) showed that the simple plug-in method (where ML estimates replace the unknown parameters in the distribution of the predictand and the α/2 and 1 − α/2 quantiles of the resulting distribution define an approximate 1 − α prediction interval procedure) is not asymptotically correct and proposed three alternative methods, based on parametric bootstrap samples, that are asymptotically correct. In this paper, we propose another solution based on an LR statistic, that does not require bootstrap samples.…”

Section: Predicting the Number Of Future Eventsmentioning

confidence: 99%

“…As mentioned earlier, the plug-in method, which replaces the unknown parameter θ = (β, η) with a consistent estimate θ n , fails to provide asymptotically correct prediction intervals (cf. Tian et al 2020). The last three methods are from Tian et al (2020) and have been established to be asymptotically correct.…”

Section: A Simulation Studymentioning

confidence: 99%

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Constructing Prediction Intervals Using the Likelihood Ratio Statistic

Tian¹,

Nordman²,

Meeker³

2021

Preprint

Self Cite

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Statistical prediction plays an important role in many decision processes such as university budgeting (depending on the number of students who will enroll), capital budgeting (depending on the remaining lifetime of a fleet of systems), the needed amount of cash reserves for warranty expenses (depending on the number of warranty returns), and whether a product recall is needed (depending on the number of potentially lifethreatening product failures). In statistical inference, likelihood ratios have a long history of use for decision making relating to model parameters (e.g., in evidence-based medicine and forensics). We propose a general prediction method, based on a likelihood ratio (LR) involving both the data and a future random variable. This general approach provides a way to identify prediction interval methods that have excellent statistical properties. For example, if a prediction method can be based on a pivotal quantity, our LR-based method will often identify it. For applications where a pivotal quantity does not exist, the LR-based method provides a procedure with good coverage properties for both continuous or discrete-data prediction applications.

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Predicting the Number of Future Events

Cited by 8 publications

References 28 publications

A unifying framework for rank and pseudo-rank based inference using nonparametric confidence distributions

A unifying framework for rank and pseudo-rank based inference using nonparametric confidence distributions

Prediction intervals for Poisson‐based regression models

Constructing Prediction Intervals Using the Likelihood Ratio Statistic

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