The finite-sample breakdown point of the Oja bivariate median and of the corresponding half-samples version

The purpose of this note is twofold. First it is shown that the finite-sample breakdown point of the bivariate median proposed by Oja (1983) is 2/(n + 2) which tends to zero rather than the previously conjectured . Then second, it is shown that applying a very general half-samples approach to the Oja criterion function leads to a class of estimators enjoying the 50% breakdown property and containing, as a special case, Rousseeuw's (1985, 1987) minimum covariance determinant estimator.

Behavioural and socioeconomic factors associated with the simultaneous occurrence of periodontal disease and dental caries

Abstract Objective: The aim was to evaluate the association of behavioural and socioeconomic factors with the occurrence of periodontal disease and dental caries, paying special attention to the simultaneous occurrence of these diseases. Materials and methods: The study population consisted of 5255 dentate persons aged ≥30 years from a nationally representative survey. Caries and probing pocket depth were recorded by tooth and calculated in relation to the number of existing teeth. The groups were: non-affected (A), the two most affected quintiles for periodontal disease with little or no dental caries (B), the two most affected quintiles for dental caries with little or no periodontal disease (C) and the two most affected quintiles for both periodontal disease and dental caries (D). Presence of dental plaque was determined, and behavioural and socioeconomic factors were established. Results: Dental plaque, smoking, lack of regular dental check-ups, older age and a basic level of education were strongly associated with the simultaneous occurrence of periodontal disease and dental caries. Conclusions: There are many behavioural and socioeconomic factors that associate with the occurrence of both periodontal disease and dental caries. These factors also increase the risk of individuals having these diseases simultaneously