In this paper we introduce the least-trimmed squares estimator for multivariate regression. We give three equivalent formulations of the estimator and obtain its breakdown point. A fast algorithm for its computation is proposed. We prove Fisher-consistency at the multivariate regression model with elliptically symmetric error distribution and derive the influence function. Simulations investigate the finite-sample efficiency and robustness of the estimator. To increase the efficiency of the estimator, we also consider a one-step reweighted estimator.

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We propose two finite algorithms to compute the exact least median of squares (LMS) estimates of parameters of a linear regression model with p coefficients. The first algorithm is similar to Stromberg's (1993) exact algorithm. It is based on the exact fit to subsets of p cases and uses impossibility conditions to avoid unnecessary calculations. The second one is based on a branch and bound (BAB) technique. Empirical results suggest that the proposed algorithms are faster than the finite exact algorithms described earlier in the literature.

El objetivo del estudio fue determinar las lesiones más frecuentes en jugadores españoles de élite de balonmano playa. Ochenta deportistas de élite de, procedentes de veinte diferentes clubs participantes en el Arena Handball Tour de la Real Federación Española de Balonmano, participaron voluntariamente en el estudio. Para el tratamiento de los datos se realizó el test Chi-cuadrado (x2) para pruebas no paramétricas. El análisis estadístico de los resultados (p < .05) indicó que la región corporal en la que se produjeron más lesiones fueron las extremidades inferiores (54.2%), más concretamente los músculos isquiotibiales (23.7%) y el diagnóstico más repetido esguince (28.8%). El tipo de lesión más reiterada fue la nueva lesión (66.1%), siendo el impacto (57.6%) el modo más frecuente. También se obtuvieron datos acerca del momento en el que se produjeron más lesiones, la competición (61.0%). El 26.3% sufre dolor crónico a causa de una vieja lesión. Este estudio ofrece información determinante a especialistas para la prevención de lesiones en la preparación de jugadores de élite.Abstract: The aim of the study was to determine the most frequent injuries in elite Spanish beach handball players. Eighty elite athletes from twenty different clubs participating in the Arena Handball Tour of the Royal Spanish Handball Federation voluntarily participated in the study. For the treatment of the data, the Chi-square test was performed (x2) for non-parametric tests. The statistical analysis of the results (p < .05) indicated that the body region in which there were more injuries were the lower extremities (54.2%), more specifically the hamstring muscles (23.7%) and the most repeated diagnosis was the sprain (28.8%). The most repeated type of injury was firs-time lesion (66.1%), with impact (57.6%) being the most frequent mode. Data were also obtained about the moment in which injuries occur, competition (61.0%). 26.3% suffer chronic pain due to a recurring injury. This study offers decisive information to specialists for the prevention of injuries in the preparation of elite players.

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