Heteroscedastic One-Way ANOVA and Lack-of-Fit Tests

Akritas, Michaël G.; Papadatos, Nickos

doi:10.1198/016214504000000412

Cited by 76 publications

(66 citation statements)

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“…Wang and Akritas (2006) followed Akritas and Papadatos (2004) and extended the results to two-way designs. However application of this technique, which involves writing M ST − M SE in matrix form, becomes almost intractable in the present multi-way setting.…”

Section: Techniques For Obtaining the Asymptotic Distributionsmentioning

confidence: 99%

“…As a tool for developing asymptotics in non-classical situations, Akritas and Papadatos (2004) suggested a bold use of Hájek's projection method applied to the difference between the mean squares for treatment and the mean squares for error, M ST − M SE. Wang and Akritas (2006) followed Akritas and Papadatos (2004) and extended the results to two-way designs.…”

Section: Techniques For Obtaining the Asymptotic Distributionsmentioning

confidence: 99%

“…For example, Akritas and Papadatos (2004) and Wang and Akritas (2006) used a representation of the observations under the local alternatives as the observations under the null plus an integral of a continuous function. Specifically, both references considered local alternatives of the form Y ij = X ij + α i (a), where X ij is a sequence of random variables satisfying the null hypothesis and α i (a) = a 3/4 n(a) −1/2 i/a (i−1)/a g(t)dt, with g(t) being a continuous function on [0,1].…”

Section: Introductionmentioning

confidence: 99%

“…Boos and Brownie (1995), Akritas and Arnold (2000), Bathke (2002), and Bathke (2004) are mainly focused on showing that the ANOVA F-statistics can still be used under homoscedastic or a special form of heteroscedastic variances when there are a large number of treatments for balanced design. Akritas and Papadatos (2004) considered heteroscedastic one-way layout; Wang and Akritas (2006) gave results for heteroscedastic two-way designs; Wang and Akritas (2004) and Bathke and Harrar (2008) considered methods based on ranks. None of the references above allow a combination of unbalanced design with arbitrary number of factors in the presence of arbitrary heteroscedastic variances.…”

Section: Introductionmentioning

confidence: 99%

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Asymptotically distribution free tests in heteroscedastic unbalanced high dimensional ANOVA

Wang¹,

Akritas²

2011

STAT. SINICA

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In this paper, we develop the asymptotic theory for hypotheses testing in high-dimensional analysis of variance (HANOVA) when the distributions are completely unspecified. Most results in the literature have been restricted to observations of no more than two-way designs for continuous data. Here we formulate the local alternatives in terms of departures from the null distribution so that the responses can be either continuous or categorical. The asymptotic theory is presented for testing of main factor and interaction effects of up to order three in Primary: 62E20, 62G30, 62G10; secondary: 62J12, 62J10.

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Section: Techniques For Obtaining the Asymptotic Distributionsmentioning

confidence: 99%

Section: Techniques For Obtaining the Asymptotic Distributionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Asymptotically distribution free tests in heteroscedastic unbalanced high dimensional ANOVA

Wang¹,

Akritas²

2011

STAT. SINICA

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“…It was found that the distributions were not normal in the dependent variable. The distributions were not normal because n = 110, but by the Central Limit Theorem (Maroco and Bispo, 2003;Pedrosa and Gama, 2004) we assumed a normal distribution (Akritas and Papadatos, 2004). The analysis of homogeneity was performed using the Levene test.…”

Section: Discussionmentioning

confidence: 99%

Intelligent systems for analyzing soccer games: The weighted centroid

Clemente¹,

Couceiro²,

Martins³

et al. 2014

ing.inv.

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New, intelligent systems have been developed recently to improve the quality of match analysis. These systems analyze the tactical behavior of the teams. However, the existing methods leave room for improvement. Thus, the main goal of this study is to refine the team centroid metric by considering all of the players on the team and the ball position. Furthermore, this study analyzes the relationship between the centroids of the two opposing teams. One 11-on-11 soccer match was analyzed to test the new centroid algorithm. The results provided strong evidence of the positive relation between the centroids of the two teams over time in the ‫-ݔ‬axis ‫ݎ(‬ ௦ = 0.781) and the ‫-ݕ‬axis ‫ݎ(‬ ௦ = 0.707). This study confirmed the results of previous studies that analyzed the relationship between team centroids. Furthermore, it was possible to prove the effectiveness of the new tactical metric and its relevance for adding information during a match.Keywords: Match Analysis, Soccer, Tactics, Collective Behavior, Centroid. RESUMENNuevos sistemas inteligentes se han desarrollado recientemente, con el fin de mejorar la calidad de análisis del partido. Estos sistemas basan su análisis en el comportamiento táctico de los equipos, sin embargo, todos los métodos innovadores necesitan algunos cambios para aumentar su potencial en las implicaciones prácticas. Por lo tanto, el objetivo principal de este trabajo es proponer una actualización del centroide y métrica del equipo, teniendo en cuenta a todos los jugadores del equipo y también la posición de la bola, además, tiene como objetivo analizar la relación entre los centroides de los equipos oponentes. Un partido de fútbol 11, fue analizado con el fin de aplicar el nuevo algoritmo del centroide; los principales resultados mostraron una fuerte evidencia de la relación positiva entre centroides en el eje x ‫ݎ(‬ ௦ = 0.781) y el eje y ‫ݎ(‬ ௦ = 0.707). Este estudio, confirma trabajos previos que analizaron la relación positiva y fuerte entre equipos centroides. Además, fue posible demostrar la pertinencia de la nueva actualización de métrica táctica y su importancia para el aumento de la información en las aplicaciones prácticas durante el partido.Palabras clave: análisis del partido de fútbol, táctica, comportamiento colectivo y Centroide.

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Some contributions to the analysis of multivariate data

Bathke

Harrar

Ahmad³

2009

Biometrical J

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In this paper, we provide an overview of recently developed methods for the analysis of multivariate data that do not necessarily emanate from a normal universe. Multivariate data occur naturally in the life sciences and in other research fields. When drawing inference, it is generally recommended to take the multivariate nature of the data into account, and not merely analyze each variable separately. Furthermore, it is often of major interest to select an appropriate set of important variables. We present contributions in three different, but closely related, research areas: first, a general approach to the comparison of mean vectors, which allows for profile analysis and tests of dimensionality; second, non-parametric and parametric methods for the comparison of independent samples of multivariate observations; and third, methods for the situation where the experimental units are observed repeatedly, for example, over time, and the main focus is on analyzing different time profiles when the number p of repeated observations per subject is larger than the number n of subjects.

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Heteroscedastic One-Way ANOVA and Lack-of-Fit Tests

Cited by 76 publications

References 1 publication

Asymptotically distribution free tests in heteroscedastic unbalanced high dimensional ANOVA

Asymptotically distribution free tests in heteroscedastic unbalanced high dimensional ANOVA

Intelligent systems for analyzing soccer games: The weighted centroid

Some contributions to the analysis of multivariate data

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