| Autor: |
Yang, Jeha, Johnstone, Iain M. |
| Rok vydání: |
2017 |
| Předmět: |
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| Druh dokumentu: |
Working Paper |
| Popis: |
We study improved approximations to the distribution of the largest eigenvalue $\hat{\ell}$ of the sample covariance matrix of $n$ zero-mean Gaussian observations in dimension $p+1$. We assume that one population principal component has variance $\ell > 1$ and the remaining `noise' components have common variance $1$. In the high dimensional limit $p/n \to \gamma > 0$, we begin study of Edgeworth corrections to the limiting Gaussian distribution of $\hat{\ell}$ in the supercritical case $\ell > 1 + \sqrt \gamma$. The skewness correction involves a quadratic polynomial as in classical settings, but the coefficients reflect the high dimensional structure. The methods involve Edgeworth expansions for sums of independent non-identically distributed variates obtained by conditioning on the sample noise eigenvalues, and limiting bulk properties \textit{and} fluctuations of these noise eigenvalues. |
| Databáze: |
arXiv |
| Externí odkaz: |
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