Estimation of a relative risk function using a ratio of two kernel density estimates is considered, concentrating on the problem of choosing the smoothing parameters. A cross-validation method is proposed, compared with a range of other methods and found to be an improvement when the actual risk is close to constant. In particular, theoretical and empirical comparisons demonstrate the advantage of choosing the smoothing parameters jointly. The methodology was motivated by a class of problems in environmental epidemiology, and an application in this area is described.
Bernoulli is published jointly by the Bernoulli Society for Mathematical Statistics and Probability and the International Statistical Institute (ISI). The journal provides a comprehensive account of important developments in the fields of statistics and probability, offering an international forum for both theoretical and applied work. Bernoulli publishes papers containing original and significant research contributions with background, derivation and discussion of the results in suitable detail and, where appropriate, with discussion of interesting data sets in relation to the methodology proposed. Papers of the following types are also considered for publication, provided they are judged to enhance the dissemination of research: Review papers that provide an integrated critical survey of some area of probability and statistics and discuss important recent developments. Scholarly written papers on some historically significant aspect of statistics and probability.
Established in 1885, the International Statistical Institute (ISI) is one of the oldest scientific associations operating in the modern world. Its success can be attributed to the increasing worldwide demand for professional statistical information, its leadership in the development of statistical methods and their application, and in the collective dedication of its members. Our influence can be seen in the improvements in information and analysis throughout the economic, social, biological and industrial sectors. Its industrial influence is evidenced in advanced statistical practises, resulting in improved quality assurance. The ISI is also proud of its continuing support of statistical progress in the developing world. The ISI is composed of more than 2,000 individual elected members who are internationally recognised as the definitive leaders in the field of statistics. Its membership crosses all borders, representing more than 133 countries worldwide. This reservoir of expertise is supplemented by approximately 3,000 + additional individual members of the Institute's specialised sections: The Bernoulli Society for Mathematical Statistics and Probability (BS) The International Association for Official Statistics (IAOS) The International Association for Statistical Computing (IASC) The International Association for Statistical Education (IASE) The International Association of Survey Statisticians (IASS) The International Society for Business and Industrial Statistics (ISBIS) Irving Fisher Society for Financial and Monetary Statistics (ISI transitional Section) The ISI publishes a variety of professional books, journals, newsletters and reports, representing the cutting edge in the development of contemporary statistical knowledge. The ISI is especially renowned for its biennial meetings in which the entire membership congregates to exchange innovative ideas, develop new links and discuss current trends and developments in the statistical world.
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Bernoulli
© 1995 Bernoulli Society for Mathematical Statistics and Probability
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