Algorithm AS 122: Weights for One-Sided Multivariate Inference

Bohrer, Robert; Chow, W. L.

doi:10.2307/2346250

Cited by 58 publications

(18 citation statements)

References 12 publications

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“…There are various numerical methods available for the cases that P 2 5. Bohrer and Chow (1978) give an algorithm which is designed to calculate these weights up to the case that P = 10. However, for P 2 8, the complexity of the calculations could make these numerical methods prohibitively expensive or simply intractable.…”

Section: Corollary 2 For the Hypothesis Test H: P = 0 Versus K: P 2 mentioning

confidence: 99%

Testing inequality constraints in linear econometric models

Wolak

1989

Journal of Econometrics

211

129

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This paper develops three asymptotically equivalent tests for examining the validity of imposing linear inequality restrictions on the parameters of linear econometric models. First we consider the model .v = X/3 + e. where r is N(O,8), and the hypothesis test H: R/l 1 r versus K: p E R". Later we generalize this testing framework to the linear simultaneous equations model. We show that the Joint asymptotic distribution of these test statistics and the test statistics from the hypothesis test H: RP = I versus K: R/3 2 r is a weighted sum of two sets of independent X'-distributions. We also derive a useful duality relation between the multivariate inequality constraints test developed here and the multivariate one-sided hypothesis test. In small samples, these three test statistics satisfy inequalities similar to those derived by Berndt and Savin (1977) for the case of equality constraints.The paper also contains an illustrative application of this testing technique.

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Section: Corollary 2 For the Hypothesis Test H: P = 0 Versus K: P 2 mentioning

confidence: 99%

Testing inequality constraints in linear econometric models

Wolak

1989

Journal of Econometrics

211

129

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“…Kud6 (1963) gives expressions for these level probabilities in terms of orthant probabilities for a multivariate normal distribution, but numerical techniques are needed to compute arbitrary orthant probabilities of dimension four or greater. The FORTRAN program given in Bohrer and Chow (1978) can be used to compute these mixing coefficients. For the computations discussed in Section 7, we used their program along with that given by Sun (1988) to compute orthant probabilities.…”

Section: Level Probabifitiesmentioning

confidence: 99%

“…For estimation of the regression coefficient,/~, was obtained by solving (2.3) using the IMSL routine N2QNJ, the projections, ~ and/~, were obtained by the IMSL routine QPROG, the level probabilities in (4.7) and (5.3) were computed by the program in Bohrer and Chow (1978) using Sun's (1988) program to compute multivariate normal orthant probabilities and then (4.7) and (5.3) were computed using the IMSL routine CHIDE However, for OLR2 and PLRT2 the approximating projections were computed using the PAVA, see Section 6, and for OLR1, OLR2, PLRT1 and PLRT2, the critical values were taken from Table A.4 Robertson et al (1988) for equal sample sizes, and for N1 = 2N2 and N2 .....…”

Section: Nm = N and Nl = 2nmentioning

confidence: 99%

Testing order restricted hypotheses with proportional hazards

Singh¹,

Wright²

1996

Lifetime Data Anal

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Inferences for survival curves based on right censored continuous or grouped data are studied. Testing homogeneity with an ordered restricted alternative and testing the order restriction as the null hypothesis are considered. Under a proportional hazards model, the ordering on the survival curves corresponds to an ordering on the regression coefficients. Approximate likelihood methods are obtained by applying order restricted procedures to the estimates of the regression coefficients. Ordered analogues to the log rank test which are based on the score statistics are considered also. Chi-bar-squared distributions, which have been studied extensively, are shown to provide reasonable approximations to the null distributions of these tests statistics. Using Monte Carlo techniques, the powers of these two types of tests are compared with those that are available in the literature.

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“…For k~10, a subroutine of computing the level probabilities was given by Bohrer and Chow (1978), in which a subroutine of computing the orthant probability is needed and can be found in Sun (1988).…”

Section: Shi: a Test Of Homogeneity Of Odds Ratiosmentioning

confidence: 99%

A Test of Homogeneity of Odds Ratios against Order Restrictions

Shi

1991

Journal of the American Statistical Association

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This article deals with testing the homogeneity of the odds ratios 1/1" ... , 1/1.. taken relative to the first column of a given 2 x (k + 1) cross-classification table of ordinal variables, against a partial order restriction. The inference of these odds ratios is considered 011 an extended hypergeometric distribution, a conditional distribution of cell frequencies N 2 " ••• , N». say, given both marginal totals. Take a transformation such that the order restriction on the odds ratios tends to be in some linear inequalities restriction on means of the N 2 / s based on the conditional distribution. A test is proposed from the transformation as a one-sided likelihood ratio test in the normal case and its asymptotic null distribution is the fi distribution. The test is applied to a numerical example and its power is compared with Mantel's test and the ordinary X 2 test. In practice, many odds ratios exhibit a trend. For example, there is usually a simple order on the odds ratios: I~1/1,~••.~1/1•. In the study of dose-response relationships, a unimodal trend may be considered, that is, there is a positive integer p such that I~1/1.~...~I/Ip~..•~1/1.. which is said to be the umbrella order by Mack and Wolfe (1981) and includes the simple order with p = k. A simple tree order may be denoted by I~1/1,~I/I J for j = 2, ... , k. The test proposed in this article can be applied to test homogeneity of the odds ratios: 1/1, = ... = 1/1. = 1 against the simple or any other partial order restricted alternatives.

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Algorithm AS 122: Weights for One-Sided Multivariate Inference

Cited by 58 publications

References 12 publications

Testing inequality constraints in linear econometric models

Testing inequality constraints in linear econometric models

Testing order restricted hypotheses with proportional hazards

A Test of Homogeneity of Odds Ratios against Order Restrictions

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