Dominance of Likelihood Ratio Tests under Cone Constraints

Menéndez, José A.; Rueda, Cristina; Salvador, Bonifacio

doi:10.1214/aos/1176348904

Cited by 18 publications

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“…Under suitable regularity conditions, the distribution of T has proven to be conditionally distributed as a χ 2 d when r t 1 = · · · = r tn (in what follows we denote r 0 a vector whose components are equal), and d is the observed value of D , i.e, Menéndez et al, 1992 andHu andWright, 1994). The conditional α level test rejects when…”

Section: The Conditional Likelihood Ratio Testmentioning

confidence: 99%

“…The conditional test is easy to formulate using the results by Menéndez et al (1992). The F distribution is then used instead of the chi-squared distribution for the test statistic.…”

Section: The Conditional Likelihood Ratio Testmentioning

confidence: 99%

“…(i) From Lemma 1 (ii), Lemma 2.2. in Menéndez et al (1992), and basic properties of polar cones, T 0q is given by…”

Section: Proof Of Theoremmentioning

confidence: 99%

See 2 more Smart Citations

Checking unimodality using isotonic regression: an application to breast cancer mortality rates

Rueda

Ugarte

Militino

2015

Stoch Environ Res Risk Assess

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In some diseases it is well-known that a unimodal mortality pattern exists. A clear example in developed countries is breast cancer, where mortality increased sharply until the nineties and then decreased. This clear unimodal pattern is not necessarily applicable to all regions within a country. In this paper, we develop statistical tools to check if the unimodality pattern persists within regions using order restricted inference. Break points as well as confidence intervals are also provided. In addition, a new test for checking monotonicity against unimodality is derived allowing to discriminate between a simple increasing pattern and an up-then-down response pattern. A comparison with the widely used joinpoint regression technique under unimodality is provided. We show that the joinpoint technique could fail when the underlying function is not piecewise linear. Results will be illustrated using age-specific breast cancer mortality data from Spain in the period 1975-2005.

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Section: The Conditional Likelihood Ratio Testmentioning

confidence: 99%

“…The conditional test is easy to formulate using the results by Menéndez et al (1992). The F distribution is then used instead of the chi-squared distribution for the test statistic.…”

Section: The Conditional Likelihood Ratio Testmentioning

confidence: 99%

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Checking unimodality using isotonic regression: an application to breast cancer mortality rates

Rueda

Ugarte

Militino

2015

Stoch Environ Res Risk Assess

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“…Generally it seems to lead to satisfactory tests. However , counter-examples are also known in which the test is quite unsatisfactory; see for example Perlman and Wu [7] and Menendez, Rueda, and Salvador [6].…”

Section: Lx(b) = Po(x)mentioning

confidence: 99%

On likelihood ratio tests

Lehmann

2011

Selected Works of E. L. Lehmann

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Likelihood ratio tests are intuitively appealing. Nevertheless, a number of examples are known in which they perform very poorly. The present paper discusses a la rge class of situations in which this is the case, and analyzes just how intuition misleads us; it also presents an alternative approach which in these situations is optimal. The popularity of likelihood ratio testsFaced with a new testing problem, the most common approach is the likelihood ratio (LR) test. Introduced by Neyman and Pearson in 1928, it compares the maximum likelihood under the alternatives with that under the hypothesis. It owes its popularity to a number of facts.(i) It is intuitively appealing. The likelihood of B,i.e. the probability density (or probability) of x considered as a function of B, is widely considered a (relative) measure of support that the observation x gives to the parameter B. compares the best explanation the data provide for the alternatives with the best explanations for the hypothesis. This seems quite persuasive.(ii) In many standard problems, the LR test agrees with tests obtained from other principles (for example it is UMP unbiased or UMP invariant). Generally it seems to lead to satisfactory tests. However , counter-examples are also known in which the test is quite unsatisfactory; see for example Perlman and Wu [7] and Menendez, Rueda, and Salvador [6].(iii) The LR test, under suitable conditons, has good asymptotic properties.None of these three reasons are convincing.(iii) tells us little about small samples.(i) has no strong logical grounding.(ii) is the most persuasive, but in these standard problems (in which there typically exist a complete set of sufficient statistics) all principles typically lead to tests that are the same or differ only by little.

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“…Se ha obtenido la distribución del estadístico razón de verosimilitudes en distintas situaciones [Bartholomew (1961), Barlow et al (1972), Sasabuchi et al (1983), Kulatunga y Sasabuchi (1984), Shapiro (1988), , Cohen et al (2000)], así como propiedades de la función de potencia de los mismos [Perlman (1969), Mukerjee et al (1986), Tsai (1992), Praestgaard (2012)]. Se han detectado anomalías en estos tests de razón de verosimilitudes bajo restricciones, habiéndose estudiado y caracterizado las situaciones en que están dominados por otros tests que no tienen en cuenta la información dada por las restricciones: Menéndez et al ( , 1992aMenéndez et al ( , 1992b, Menéndez y Salvador (1991, 1992, Hu y Wright (1994), Cohen et al (2000), Perlman y Wu (2002), Cohen y Sackrowitz (2004). También se han considerado procedimientos ajenos a la razón de verosimilitudes con resultados positivos, como los tests lineales como el que proponen Abelson y Tukey (1963) y que después extienden, entre otros, Schaafsma y Smid (1966), Shi y Kudô (1987), Rueda (1989) y Tsai y Sen (1993).…”

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Dominance of Likelihood Ratio Tests under Cone Constraints

Cited by 18 publications

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Checking unimodality using isotonic regression: an application to breast cancer mortality rates

Checking unimodality using isotonic regression: an application to breast cancer mortality rates

On likelihood ratio tests

Mejoras en reglas de clasificación mediante incorporación de información adicional

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