Approximate Distributions of Order Statistics

Reiss, Rolf–Dieter

doi:10.1007/978-1-4613-9620-8

Cited by 420 publications

(123 citation statements)

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“…The main argument is that participation at the Games is not proportional to population, since the number of athletes that represent their country at the Games is restricted. Another argument which is based on Reiss (1989) states that the maximum performing individual of a population of size N it will be of the order (log N it ) 1/2 . In our model, we use population shares n it and we approximate log (1+n it ) with n it (first-order Taylor series approximation).…”

Section: Modeling Successmentioning

confidence: 99%

Forecasts and evaluation of the 2011 Pan American Games

Kuper

Sterken

2012

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Abstract:The current paper predicts the medal tally for the 2011 Pan American Games. The forecast procedure consists of analyzing success at the four latest editions of the Pan American Games at the country level. Potential explanatory variables for medal winning are GDP, population, geographical distance to the Games and home advantage. Our forecasts show that the US takes first place in the medal tally. We expect Mexico to take fourth place wining 37 gold medals. The final results as they were published after the Games prove us right in this respect. However, the forecasts are less precise than similar predictions for the Olympic Games.n Resumen: Este ensayo pronostica el número de medallas para los Juegos Panamericanos del 2011. El procedimiento del pronóstico consiste en analizar a los ganadores de las últimas cuatro ediciones de los Juegos Panamericanos por país. Las posibles variables explicativas de las medallas ganadoras son PIB, población, distancia geográfica con respecto al sitio donde se celebran los Juegos y la ventaja del país sede. Nuestro pronóstico muestra que Estados Unidos obtendrá el primer lugar en el total de medallas ganadas. Esperamos que México ocupe el cuarto lugar obteniendo 37 medallas de oro. Los resultados finales publicados después de los Juegos prueban nuestras predicciones. Sin embargo, los pronósticos son menos precisos que otras predicciones similares hechas para los Juegos Olímpicos.

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Section: Modeling Successmentioning

confidence: 99%

Forecasts and evaluation of the 2011 Pan American Games

Kuper

Sterken

2012

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“…(see, e.g., Reiss, 1989). A crucial step of the proof is approximating the conditional distributions of the ξ nj 's by appropriate exponential distributions.…”

Section: Proof Of Theoremmentioning

confidence: 99%

Untitled

AntosAndrás

LugosiGábor

1998

Machine Learning

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Abstract. Minimax lower bounds for concept learning state, for example, that for each sample size n and learning rule g n , there exists a distribution of the observation X and a concept C to be learnt such that the expected error of g n is at least a constant times V /n, where V is the VC dimension of the concept class. However, these bounds do not tell anything about the rate of decrease of the error for a fixed distribution-concept pair.In this paper we investigate minimax lower bounds in such a (stronger) sense. We show that for several natural k-parameter concept classes, including the class of linear halfspaces, the class of balls, the class of polyhedra with a certain number of faces, and a class of neural networks, for any sequence of learning rules {g n }, there exists a fixed distribution of X and a fixed concept C such that the expected error is larger than a constant times k/n for infinitely many n. We also obtain such strong minimax lower bounds for the tail distribution of the probability of error, which extend the corresponding minimax lower bounds.

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“…1. Denote by the conditional distribution of (X l:n' ... , Xn:n) given (XI:", ... , X k :,,) =(Xl' ... , Xk)='~ under the parameter t. It is well known (see Reiss 1989, Theorem 1.8.1) that where 8 y denotes the Dirac measure at y and the 1';, ie{l, ... , n-k}, are Li.d. random variables with common distribution Pr,Xk (the restriction of Pr to the interval (Xk' 00».…”

Section: Upper Bound For the Deficiency Between E And Enkmentioning

confidence: 99%

“…Applying the exponential bound for order statistics as given in Lemma 3.1.1 of Reiss (1989) [compare with (2.2)J we see that…”

Section: F Marohnmentioning

confidence: 99%