Multidimensional trimming based on projection depth

As estimators of location parameters, univariate trimmed means are well known for their robustness and efficiency. They can serve as robust alternatives to the sample mean while possessing high efficiencies at normal as well as heavy-tailed models. This paper introduces multidimensional trimmed means based on projection depth induced regions. Robustness of these depth trimmed means is investigated in terms of the influence function and finite sample breakdown point. The influence function captures the local robustness whereas the breakdown point measures the global robustness of estimators. It is found that the projection depth trimmed means are highly robust locally as well as globally. Asymptotics of the depth trimmed means are investigated via those of the directional radius of the depth induced regions. The strong consistency, asymptotic representation and limiting distribution of the depth trimmed means are obtained. Relative to the mean and other leading competitors, the depth trimmed means are highly efficient at normal or symmetric models and overwhelmingly more efficient when these models are contaminated. Simulation studies confirm the validity of the asymptotic efficiency results at finite samples.Comment: Published at http://dx.doi.org/10.1214/009053606000000713 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

The Impacts of the Chinese Anti-Monopoly Law on IP Commercialization in China & General Strategies for Technology-Driven Companies and Future Regulators

After thirteen years of discussion and three revisions, China\u27s Anti-Monopoly Law (AML) was promulgated on August 30, 2007 and has come into effect on August 1, 2008. It is the first anti-monopoly law in China and has been viewed as an economic constitution and a milestone of the country’s efforts in promoting a fair competition market and cracking down on monopoly activities. However, the wording of some provisions of the AML, including the sections dealing with Intellectual Property (IP) protection, is not very clear. And juridical interpretations and more specific implementing regulations on the AML have not yet appeared. This has led to a lot of uncertainty for the operations of foreign enterprises, particularly IP related enterprises in China. This iBrief will provide an overview of possible impacts of the AML on the IP protection and commercialization in China. First, it will provide a brief overview of the AML, including both major compliments and criticism. Second, it will examine both opportunities and potential legal risks of foreign IP holders and investors when operating in China, particularly focusing on the impacts of Article 55, the IP-related provision. Thirdly, it will provide some practical suggestions and strategies for foreign IP holders and technology-driven companies to operate in China, such as some useful defenses for potential IP lawsuits. Finally, it will provide some suggestions for future interpretation and implementation of Article 55 in the AML by drawing on lessons from the experiences of the United States and the European Union