METHODOLOGIES IN SPECTRAL ANALYSIS OF LARGE DIMENSIONAL RANDOM MATRICES, A REVIEW

By Z. Bai. 2008

245 citations recorded by the source corpus.

Subfields: Discrete Mathematics and Combinatorics, Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/2e242ecd3224b4729e8f50cf3542ed5d52c2aa99

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In Discrete Mathematics and Combinatorics

In Mathematical Physics

In Statistics and Probability

Citations in the corpus

Determining the Number of Factors from Empirical Distribution of Eigenvalues (2010, unknown): “� � � decays as fast as n 2=3 when "it in ( 3 ) are i.i.d.”
On asymptotics of eigenvectors of large sample covariance matrix (2007, methodology): “pothesis of variance homogeneity. However, it is not the case when n increases as [cN] (the integer part of cN) with c ∈ (0,1). Using results of the limiting spectral distribution of A n (see [12] or [1]), one can show that with probability one that 1 n W n → c−1 c ln(1−c)−1≡d(c)<0, which implies”
Maximum likelihood estimation for linear Gaussian covariance models (2014, result): “We refer to [Bai99, Joh01] for a review of these results.”
High Dimensional Statistical Inference and Random Matrices (2006, background): “ms of mathematical interest, this paper concentrates largely on PCA as a leading example, together with a few remarks on related problems. Other overviews with substantial statistical content include [5], [30] and [36]. In an eﬀort to deﬁne terms and give an example, the earlier sections cover intro”
Concentration of measure and spectra of random matrices: Applications to correlation matrices, elliptical distributions and beyond (2009, methodology): “e of the vectors {ri}n i=1 other than the fact that they are independent. Proof of Lemma 6. We deﬁne Mk =M −rkr∗ k. We let Fi denote the ﬁltration generated by {rl}i l=1. The ﬁrst classical step (see [3], page 649) is to write the random variable of interest as sum of martingale diﬀerences: mp(z)−E(”
Corrections to LRT on large-dimensional covariance matrix by RMT (2009, background): “Bai, Z. D. (1999).”
ESTIMATION OF SPIKED EIGENVALUES IN SPIKED MODELS (2012, background): “Hn = H = δ{1}, it is well known [2] that the ESD of Sn converges weakly to the Marčenko–Pastur law Fγ(dx) with σ = 1 in (1.”
On the distribution of SINR for the MMSE MIMO receiver and performance analysis (2006, background): “5 in [21]), from which we can derive closed form expressions for the moments by (tedious) integration.”
Maximum-Minimum Eigenvalue Detection for Cognitive Radio (2007, background): “Bai and Yin found the limit of the smallest eigenvalue [13] as described in the following theorem.”
How many entries of a typical orthogonal matrix can be approximated by independent normals (2006, background): “ow weak convergence of certain functions of eigenvalues of matrices with independent and identically distributed random variables as entries. It is can be seen from, for example, (2.15) and (2.16) in [3]. Lemma 2.3. Let {p n;n≥1} and {q n;n≥1} be two sequences of positive integers such that p n →∞ a”