An Introduction to Multivariate Statistical Analysis

By A. Vogler. 2004

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Adaptivity and Computation-Statistics Tradeoffs for Kernel and Distance based High Dimensional Two Sample Testing (2015, background): “T H is consistent for MDA whenever P, Q have different means, and further, it is known to be the “uniformly most powerful” test when P, Q are univariate Gaussians under fairly general assumptions [Kariya, 1981, Simaika, 1941, Anderson, 1958, Salaevskii, 1971].”
Estimating High-Dimensional Directed Acyclic Graphs with the PC-Algorithm (2005, background): “A proof can be found in Fisher (1924); see also Anderson (1984). Lemma 1 and 2 yield then the following.”
Approximation of Rectangular Beta-Laguerre Ensembles and Large Deviations (2013, background): “…study the spectral properties of a Wishart matrix formed by a random sample of p-dimensional data with sample size n, where p is larger than n.Wishart matrices are very popular and useful objects in multivariate analysis, see, for example, the classical books by Muirhead (1982) and Anderson (1984).”
Statistical Tests and Estimators of the Rank of a Matrix and Their Applications in Econometric Modelling (2009, neutral): “11 ECB Working Paper Series No 850 January 2008 the case, it is possible to make use of a well known result in canonical correlation analysis; namely, that given two random stationary vector series yt and xt of dimensions m and n respectively, the rank of the covariance matrix between those two rand”
Synthetic controls with imperfect pretreatment fit (2016, background): “, Bai (2003) and Anderson (1984)). Therefore, the asymptotic bias we find for the SC estimator is consistent with the results from a large literature on factor models. We also revisit the conditions for validity of alternative estimators, such as the ones proposed by Hsiao et al. (2012), Li and Bell”
From Visual Data Exploration to Visual Data Mining: A Survey (2003, methodology): “Some common techniques are Principal Component Analysis [2], Factor Analysis [37], Multidimensional Scaling [92], and FastMap [27].”
GLS Estimation of Dynamic Factor Models (2011, methodology): “An important problem with maximizing this likelihood function is that the likelihood function is unbounded in general (see, e.g., Anderson 1984, p. 570).”
State-Varying Factor Models of Large Dimensions (2018, neutral): “6Generalized correlations or canonical correlations have been studied in Anderson (1958), Yuan and Bentler (2000), Bai and Ng (2006), Pelger (2019), and Andreou et al. (2019).”
Enhancing Interpretability in Factor Analysis by Means of Mathematical Optimization (2019, background): “In this paper, we focus on latent variable models to uncover the hidden information enclosed in raw data, Anderson (2003), Bartholomew, Knott, and Moustaki (2011), and Blei (2014).”
Directional MEWMA Schemes for Multistage Process Monitoring and Diagnosis (2008, methodology): “Because our pro- Journal of Quality Technology Vol. 40, No. 4, October 2008 posed chart is base on the GLRT test, we can investigate the root cause by tracing if from a particular stage that provides the largest value of the statistic MZyj , i.e., the estimate of ζ is as follows: ζ̂D = arg 1≤k≤N max”
On the High-dimensional Power of Linear-time Kernel Two-Sample Testing under Mean-difference Alternatives (2014, background): “GA, it is unclear how exactly tests designed for general alternatives fare when when faced with a mean-shift alternative. 2 1.3 Related Work (MSA) It is well known (see Kariya (1981); Simaika (1941); Anderson (1958); Salaevskii (1971)) that if P;Q are Gaussians, then the uniformly most powerful test”
Large-Scale Correlation Screening (2011, background): “It is well known that when the rows of the data matrix X are iid and follow a diagonal elliptical distribution, the U-scores are uniformly distributed on Sn−2 (see, e.g., Anderson 2003, section 2.7).”
Autocorrelation-Based Decentralized Sequential Detection of OFDM Signals in Cognitive Radios (2009, methodology): “Then [6] is given by (10) Equivalently can be rewritten in terms of the observations as Using the approximation for the low SNR case, and substituting the value of from (10) in (9), we get (11) where is the maximum likelihood estimate of from the vectors and [6] given by (12) Equivalently can be…”
Controlling for Individual Heterogeneity in Longitudinal Models, with Applications to Student Achievement (2007, background): “These assumptions imply that R1 := V (A1δi + ǫi) = A1S1A ′ 1+Ψ1, the usual form considered in factor analysis when S1 = I (4; 35).”
Random matrix theory for modeling uncertainties in computational mechanics (2005, methodology): “This figure corresponds to the base 10 logarithm of the random normalized response spectrum for the considered observation (vertical axis) as a function of the base 10 logarithm of the frequency in Hertz for the [1 , 200] Hz frequency band.”