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In this work, we consider a general framework of incomplete data which includes many types of censoring and truncation models. Under this framework and assuming that the distribution of interest has a parametric form, we propose local tests for simple and composite hypotheses on the parameter. These tests are based on the ϕ--divergences, Wald and Rao statistics. We study the asymptotic behaviour of these statistics under the null hypothesis. For the ϕ--divergences statistics, we study the asymptotic behaviour under the alternative as well. This allows us to approximate the power function of the proposed tests. We also propose local tests of homogeneity which serve to compare the distributions of two samples. Finally, we present the results of an application on real data. [ABSTRACT FROM AUTHOR]

Se realizó un estudio vía simulación para determinar el nivel real y la po tencia de pruebas de homogeneidad de varianza que se aplican comúnmente y de otras pruebas recientemente propuestas. Los resultados permiten a los usuarios tener criterios para escoger la prueba más adecuada de acuerdo con las circunstancias.

The objective of this paper is to analyse, for the Senegal River basin, the evolution of four classes of daily precipitation, the number of rainy days and the duration of the rainy season. The approach is to apply statistical tests of homogeneity to the series of annual rainfall over the period 1950–1998 to detect abrupt changes and to characterize the evolution of these six variables on each side of the change dates. The time series present an abrupt change (break) between 1966 and 1970. Deficits of rainy days in the period after the break compared to before vary between 6.2% at Kédougou and 38.6% at Saint Louis. The class of rain of more than 50 mm (P4) has the largest deficit, ranging from 14.8% at Mamou station to 66.6% at Nioro du Sahel.Editeur Z. W. Kundzewicz; Edithur Associé E. Gargouri [ABSTRACT FROM AUTHOR]

Determining the real level of significance and the power of homogeneity of variance tests which are currently applied is the main purpose of this study. The results allow users to have criteria to choose the best test according to the circumstances.Se realizó un estudio vía simulación para determinar el nivel real y la potencia de pruebas de homogeneidad de varianza que se aplican comúnmente y de otras pruebas recientemente propuestas. Los resultados permiten a los usuarios tener criterios para escoger la prueba más adecuada de acuerdo con las circunstancias.

Supremum score test statistics are often used to evaluate hypotheses with unidentifiable nuisance parameters under the null hypothesis. Although these statistics provide an attractive framework to address non-identifiability under the null hypothesis, little attention has been paid to their distributional properties in small to moderate sample size settings. In situations where there are identifiable nuisance parameters under the null hypothesis, these statistics may behave erratically in realistic samples as a result of a non-negligible bias induced by substituting these nuisance parameters by their estimates under the null hypothesis. In this paper, we propose an adjustment to the supremum score statistics by subtracting the expected bias from the score processes and show that this adjustment does not alter the limiting null distribution of the supremum score statistics. Using a simple example from the class of zero-inflated regression models for count data, we show empirically and theoretically that the adjusted tests are superior in terms of size and power. The practical utility of this methodology is illustrated using count data in HIV research. [ABSTRACT FROM AUTHOR]

The wet years of the 1990s have reduced the extent of the area affected by drought. But studies have shown that the rainfall deficit persisted in the Sahelian regions until the end of the 1990s. P. OZER et al., in 2003, thought that the continuity of the drought, or on the contrary the identification of a rainfall break towards weather conditions, could be verified statistically only after ten more years of data. This is the context in which the present work is conducted. It aims to analyze the recent trend of annual rainfall series of 22 stations on Senegalese territory, with data collected through 2013, to see whether the drought persists or not. These data cover the period from 1940 to 2013 and the approach includes the following: (1) review and standardization of data, (2) calculation of rain standardized indices, (3) break and trends detection in annual rainfall series by applying three rupture tests (PETTITT, LEE and HEGHINIAN, HUBERT). The applying of these tests to the rain standardized indices that was calculated from all stations and from stations grouped according to three climatic regions (South-Sahelian, South-Sudanian and North-Sudanian) highlights two rupture dates (significant at 1 % according to STUDENT's t test). The first break ranges out between 1967 and 1969, and the second one occurs between 1986 and 1998 according to the test of PETTITT and between 1992 and 2007 according to the method of LEE and HEGHINIAN and that of HUBERT. By analyzing each station, we notice that the second break in rainfall series occurs generally between 1998 and 2002. Only the HUBERT segmentation method doesn't always detect a second break, but the lack of detection covers only 18 % of the stations. So we identify a discontinuity towards wet conditions from 1998 (PETTITT) or 2003 (LEE and HEGHINIAN ; HUBERT) even though the annual rainfalls remain lower than pre 1970.