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Fujikoshi, Yasunori The Korean Statistical Society 2004 Journal of the Korean Statistical Society Vol.33 No.1
This paper is concerned with statistical methods for multivariate data when the number p of variables is large compared to the sample size n. Such data appear typically in analysis of DNA microarrays, curve data, financial data, etc. However, there is little statistical theory for high dimensional data. On the other hand, there are some asymptotic results under the assumption that both and p tend to $\infty$, in some ratio p/n ${\rightarrow}$c. The results suggest that the new asymptotic results are more useful and insightful than the classical large sample asymptotics. The main purpose of this paper is to review some asymptotic results for high dimensional statistics as well as classical statistics under a high dimensional asymptotic framework.
YASUNORI FUJIKOSHI 한국통계학회 2004 Journal of the Korean Statistical Society Vol.33 No.1
This paper is concerned with statistical methods for multivariate datawhen the number p of variables is large compared to the sample sizen. Suchdata appear typically in analysis of DNA microarrays, curve data, nancialdata,etc. However, there is little statistical theory for high dimensional data.On the other hand, there are some asymptotic results under the assumptionthat both n and p tend to 1 , in some ratiop=n ! c. The results suggestthat the new asymptotic results are more useful and insightful than theclassical large sample asymptotics. The main purpose of this paper is toreview some asymptotic results for high dimensional statistics as well asclassical statistics under a high dimensional asymptotic framework.