Theory of multivariate statistics

By M. Bilodeau, D. Brenner. 1999

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Citations in the corpus

Interpretable Distribution Features with Maximum Testing Power (2016, background): “The bound may be of independent interest in other Hotelling’s T-squared statistics, since apart from the Gaussian case (e.g. Bilodeau and Brenner, 2008, Ch. 8), the characterization of such statistics under the alternative distribution is challenging.”
A Non-parametric Learning Method for Confidently Estimating Patient's Clinical State and Dynamics (2016, methodology): “To test for the null hypothesis H(1) 0 we utilize Hotelling’s T 2 test as it is asymptotically the most powerful invariant test when the data associated with k and k′ are normally distributed [4].”
Some Tests Concerning the Covariance Matrix in High Dimensional Data (2005, background): “For proof , see Bilodeau and Brenner (1999, p. 79) .”
Applied Multivariate Analysis (2002, methodology): “The vech (·) operator is most often used when evaluating the distribution of symmetric matrices which occur in multivariate analysis; see McCulloch (1982), Fuller (1987), and Bilodeau and Brenner (1999).”
An Appraisal and Bibliography of Tests for Multivariate Normality (2004, background): “It is well known (e.g. Bilodeau & Brenner, 1999) that a data vector is distributed as ap-dimensional multivariate normal distributionif and only if all linear combinations of that vector are univariate normal.”
A cautionary note on robust covariance plug-in methods (2014, background): “We first recall the definitio of elliptical distributions (see e.g. Bilodeau & Brenner, 1999).”
Whishart Quadratic Term Structure Models (2003, unknown): “These results are reconciled after a 10 See e.g. Dai and Singleton (2000), the introduction and Section 2, Piazzes (2003), Dai and Singleton (2003a), Section 3, Levendorskiy (2003) for presentation of this condition as necessary and sufficient in recent surveys on affine term structure models, or e.”
Theory and numerical analysis for exact distributions of functionals of a Dirichlet process (2002, unknown): “3 in Bilodeau and Brenner (1999). The notations Q(·;α) and Q1(·;α) are used here to designate the probability distributions of ξα and ξ1α , respectively.”
Invariant co‐ordinate selection (2009, background): “, if Z ∼ QZ for any p × p orthogonal matrix Q, then the distribution of Y = AZ +μ is said to have an elliptically symmetric distribution with centre μ∈ p and shape matrix Γ=AA′; see for example Bilodeau and Brenner (1999). If the distribution of Y is also absolutely continuous, then it has a density”
Complex Elliptically Symmetric Distributions: Survey, New Results and Applications (2012, background): “The real elliptically symmetric (RES) distributions have become a standard part of multivariate analysis and results for RES distributions are incorporated into most multivariate analysis textbooks [11], [40], [62] and textbooks on robust multivariate statistics [37], [60].”
SEMIPARAMETRICALLY EFFICIENT RANK-BASED INFERENCE FOR SHAPE I. OPTIMAL RANK-BASED TESTS FOR SPHERICITY (2006, background): “ction A.1). Note that the structure of the information matrix for shape (2.7) is not unfamiliar, having been previously obtained under much more restrictive assumptions; see, for example, page 219 of [8]. 3. Parametrically eﬃcient tests for shape. 14 M. HALLIN AND D. PAINDAVEINE 3.1. An eﬃcient cent”
ECA: High-Dimensional Elliptical Component Analysis in Non-Gaussian Distributions (2013, background): “In particular, it can be shown (check, e.g., Section 3 in Bilodeau and Brenner (1999)) that Y 2j Y 21 + · · · +Y 2q ∼ Beta ( 1 2 , q− 1 2 ) , for j = 1, . . . , q, where Beta(α, β) is the beta distribution with parameters α and β .”
Robust Trend Inference with Series Variance Estimator and Testing-Optimal Smoothing Parameter (2011, background): “…distribution with degrees of freedom (p;K p+ 1) and noncentrality parameter 2 = (~c)0 ~c = c0 12R R0 1=2 12R R0 1=2 c = c0 12R R0 1 c: This result follows from Proposition 8.2 in Bilodeau and Brenner (1999) where the notation Fc is the canonical F distribution (Bilodeau and Brenner, 1999, page 42).”