Distribution Free Tests for Stochastic Ordering in the Competing Risks Model

Bagai, Isha; Deshpandé, Jayant V.; Kochar, Subhash C.

doi:10.2307/2336637

Cited by 5 publications

(9 citation statements)

References 3 publications

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“…. , T n , Bagai et al (1989) proposed a test statistic Bagai et al (1989) provided the explicit expressions for the important statistical quantities such as the mean and variance…”

Section: The Bagai Statisticmentioning

confidence: 99%

“…It should also be mentioned that for the cases of n = 9 and 15, the Bagai approximation is better than other approximations. Table 3 shows the numerical results for the saddlepoint and the tenth degree Gaussian-polynomial approximations in the case of a 5 % significance level in addition to the exact probability and Bagai approximation calculated in Bagai et al (1989). The differences between the exact probability of the Bagai statistic and the approximations are given in Table 4.…”

Section: Gaussian-polynomial Approximationmentioning

confidence: 99%

“…The three approximation methods are the Bagai approximation, the saddlepoint approximation and the Gaussianpolynomial approximation. Bagai et al (1989) provided numerical comparisons with the normal approximation and the exact distribution, and Mukarami (2009) utilized the saddlepoint approximation which is based on the cumulant generating function of the Bagai statistic and compared it to the Bagai approximation. For fair numerical comparisons of those three approximation methods, the cases involving moderate sample sizes for 5 ≤ n ≤ 20, which was used in Murakami (2009), are revisited.…”

Section: Introductionmentioning

confidence: 99%

“…

Abstract Bagai et al (1989) proposed a distribution-free test for stochastic ordering in the competing risk model, and recently Murakami (2009) utilized a standard saddlepoint approximation to provide tail probabilities for the Bagai statistic under finite sample sizes. In the present paper, we consider the Gaussian-polynomial approximation proposed in Ha and Provost (2007) and compare it to the saddlepoint approximation in terms of approximating the percentiles of the Bagai statistic.

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confidence: 99%

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Numerical Comparisons for the Null Distribution of the Bagai Statistic

2012

Communications for Statistical Applications and Methods

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Bagai et al. (1989) proposed a distribution-free test for stochastic ordering in the competing risk model, and recently Murakami (2009) utilized a standard saddlepoint approximation to provide tail probabilities for the Bagai statistic under finite sample sizes. In the present paper, we consider the Gaussian-polynomial approximation proposed in Ha and Provost (2007) and compare it to the saddlepoint approximation in terms of approximating the percentiles of the Bagai statistic. We make numerical comparisons of these approximations for moderate sample sizes as was done in Murakami (2009). From the numerical results, it was observed that the Gaussianpolynomial approximation provides comparable or greater accuracy in the tail probabilities than the saddlepoint approximation. Unlike saddlepoint approximation, the Gaussian-polynomial approximation provides a simple explicit representation of the approximated density function. We also discuss the details of computations.

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“…. , T n , Bagai et al (1989) proposed a test statistic Bagai et al (1989) provided the explicit expressions for the important statistical quantities such as the mean and variance…”

Section: The Bagai Statisticmentioning

confidence: 99%

Section: Gaussian-polynomial Approximationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…

…”

mentioning

confidence: 99%

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Numerical Comparisons for the Null Distribution of the Bagai Statistic

2012

Communications for Statistical Applications and Methods

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“…• BAGAI, I., DESHPANDE, J.V., and KOCHAR, S.C. (1989). • BAGAI, I., see JAIN, K., SINGH, H., and BAGAI, I.…”

Section: Ardittimentioning

confidence: 99%

Stochastic Orders and Applications

Mosler¹,

Scarsini²

1993

Lecture Notes in Economics and Mathematical Systems

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X ::;maj y. 11. X = IIy, for some doubly stochastic matrix II.iii. I:i=l g(Xi) ::; I:i=l g(y;) for all 9 convex.Another important paper in the history of stochastic orderings is due to Karamata (1932), who provided an analysis of concepts that will then be known as dilation and second degree stochastic dominance, both of which can be considered as a generalization of majorization.After World War II more results have been discovered and new areas of research have been developed. Many results now originate from applications: for instance Blackwell's 1. J

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On Testing Dependence between Time to Failure and Cause of Failure via Conditional Probabilities

Dewan¹,

Deshpandé²,

Kulathinal³

2004

Scandinavian J Statistics

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Dependence structures between the failure time and the cause of failure are expressed in terms of the monotonicity properties of the conditional probabilities involving the cause of failure and the failure time. These properties of the conditional probabilities are used for testing four types of departures from the independence of the failure time and the cause of failure and tests based on "U"-statistics are proposed. In the process, a concept of concordance and discordance between a continuous and a binary variable is introduced to propose a statistical test. The proposed tests are applied to two illustrative applications. Copyright Board of the Foundation of the Scandinavian Journal of Statistics 2004.

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Distribution Free Tests for Stochastic Ordering in the Competing Risks Model

Cited by 5 publications

References 3 publications

Numerical Comparisons for the Null Distribution of the Bagai Statistic

Numerical Comparisons for the Null Distribution of the Bagai Statistic

Stochastic Orders and Applications

On Testing Dependence between Time to Failure and Cause of Failure via Conditional Probabilities

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