The Exact and Asymptotic Distributions of Cramér-Von Mises Statistics

Csörgő, Sándor; Faraway, Julian J.

doi:10.1111/j.2517-6161.1996.tb02077.x

Cited by 103 publications

(43 citation statements)

References 21 publications

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“…Based on the model in (2), the m variables in r are generated from a Beta(θ,1) distribution, and the elements of r in the set (r m−k+1:m ,··· , r m:m ) represent the k largest order statistics from r.…”

Section: Goodness Of Fitmentioning

confidence: 99%

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Comparing Hall of Fame Baseball Players Using Most Valuable Player Ranks

Kvam¹

2011

Journal of Quantitative Analysis in Sports

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We propose a rank-based statistical procedure for comparing performances of top major league baseball players who performed in different eras. The model is based on using the player ranks from voting results for the most valuable player awards in the American and National Leagues. The current voting procedure has remained the same since 1932, so the analysis regards only data for players whose career blossomed after that time. Because the analysis is based on quantiles, its basis is nonparametric and relies on a simple link function. Results are stratified by fielding position, and we compare 73 Hall of Fame players up to 2010. We also consider the players on the 2011 Hall of Fame ballot as well as other potential Hall of Fame candidates. The analysis is based on the method of maximum likelihood, and results are illustrated graphically.

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Section: Goodness Of Fitmentioning

confidence: 99%

“…We approximated ψby treating θas a known parameter, so the computation of the test statistic is more straightforward (see Chapter 6.3.2 in Kvam and Vidakovic (2008), for example). For players who appeared in six or more MVP lists, Csörgo and Faraway (1996) showed the approximation to the Cramér-von-Mises test statistic…”

Section: Goodness Of Fitmentioning

confidence: 99%

Comparing Hall of Fame Baseball Players Using Most Valuable Player Ranks

Kvam¹

2011

Journal of Quantitative Analysis in Sports

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“…This statistic is designed to pick up sustained but modest departures from the zero mean. The distribution of the test statistic is approximated [7] by…”

Section: Test Statisticsmentioning

confidence: 99%

Tests for Hazard Transformation

Henderson

Philipson

2010

Stat Biosci

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The semiparametric Cox proportional hazards model is routinely adopted to model time-to-event data. Proportionality is a strong assumption, especially when follow-up time, or study duration, is long. Zeng and Lin (J. R. Stat. Soc., Ser. B, 69:1-30, 2007) proposed a useful generalisation through a family of transformation models which allow hazard ratios to vary over time. In this paper we explore a variety of tests for the need for transformation, arguing that the Cox model is so ubiquitous that it should be considered as the default model, to be discarded only if there is good evidence against the model assumptions. Since fitting an alternative transformation model is more complicated than fitting the Cox model, especially as procedures are not yet incorporated in standard software, we focus mainly on tests which require a Cox fit only. A score test is derived, and we also consider performance of omnibus goodness-of-fit tests based on Schoenfeld residuals. These tests can be extended to compare different transformation models. In addition we explore the consequences of fitting a misspecified Cox model to data generated under a true transformation model. Data on survival of 1043 leukaemia patients are used for illustration.

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“…These ranges do not contain any absolute information about the significance. The calculation of the significance value p is rather complex [40][41][42] and can be obtained upon request from the authors.…”

Section: Appendix a Rank-order Testsmentioning

confidence: 99%