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Tests de la razón de verosimilitud para medias de poblaciones normales, sujetas a restricciones.

José Antonio Menéndez Fernández (1984)

Trabajos de Estadística e Investigación Operativa

This paper shows the statistics that define the likelihood ratio tests about the mean of a k-dimensional normal population, when the hypotheses to test are H0: θ = 0; H0*: θ ∈ τφ; H1: θ ∈ τ; H2: θ ∈ Rk, being τ a closed and poliedric convex cone in Rk, and τφ the minima dimension face in τ.It is proved that the obtained statistics distributions are certain combinations of chi-squared distributions, when θ = 0.At last, it is proved that the power functions of the tests satisfy some desirable properties....

Tests for profile analysis based on two-step monotone missing data

Mizuki Onozawa, Sho Takahashi, Takashi Seo (2013)

Discussiones Mathematicae Probability and Statistics

In this paper, we consider profile analysis for the observations with two-step monotone missing data. There exist three interesting hypotheses - the parallelism hypothesis, level hypothesis, and flatness hypothesis - when comparing the profiles of some groups. The T²-type statistics and their asymptotic null distributions for the three hypotheses are given for two-sample profile analysis. We propose the approximate upper percentiles of these test statistics. When the data do not have missing observations,...

Tests in weakly nonlinear regression model

Lubomír Kubáček, Eva Tesaříková (2005)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

In weakly nonlinear regression model a weakly nonlinear hypothesis can be tested by linear methods if an information on actual values of model parameters is at our disposal and some condition is satisfied. In other words we must know that unknown parameters are with sufficiently high probability in so called linearization region. The aim of the paper is to determine this region.

Tests lineales para contrastes con hipótesis oblicuas.

Cristina Rueda Sabater (1991)

Trabajos de Estadística

En contrastes de hipótesis oblicuas para medias normales se ha demostrado la dominación del test de razón de verosimilitud (TRV). En este contexto consideramos estadísticos definidos por combinaciones lineales de las medias muestrales obteniendo tests para coeficientes fijos y aleatorios. En ambos casos los tests óptimos no tienen en cuenta toda la información del modelo original siendo adecuados para situaciones con hipótesis menos restrictivas. En la obtención de tests con coeficientes aleatorios...

Tests of independence of normal random variables with known and unknown variance ratio

Edward Gąsiorek, Andrzej Michalski, Roman Zmyślony (2000)

Discussiones Mathematicae Probability and Statistics

In the paper, a new approach to construction test for independenceof two-dimensional normally distributed random vectors is given under the assumption that the ratio of the variances is known. This test is uniformly better than the t-Student test. A comparison of the power of these two tests is given. A behaviour of this test forsome ε-contamination of the original model is also shown. In the general case when the variance ratio is unknown, an adaptive test is presented. The equivalence between...

Tests of some hypotheses on characteristic roots of covariance matrices not requiring normality assumptions

František Rublík (2001)

Kybernetika

Test statistics for testing some hypotheses on characteristic roots of covariance matrices are presented, their asymptotic distribution is derived and a confidence interval for the proportional sum of the characteristic roots is constructed. The resulting procedures are robust against violation of the normality assumptions in the sense that they asymptotically possess chosen significance level provided that the population characteristic roots are distinct and the covariance matrices of certain quadratic...

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