On a Heuristic Method of Test Construction and its use in Multivariate Analysis

Performance of Eigenvalue-Based Signal Detectors with Known and Unknown Noise Level

“…In the asymptotical regime N → ∞, with given signal strength ρ and noise variance σ 2 v , the above criterion can be shown [16], [17] to depend only on the largest eigenvalue (λ 1 ), i.e., it reduces to Roy's largest root test [11], defined as…”

“…In this paper, we analyze the performance of two nearlyoptimal 1 detection criteria in their respective categories: for known noise variance, the largest eigenvalue test, or Roy's largest root test (RLRT), originally proposed in [11] and introduced in CR by [9] (derived as a "blindly combined energy detector"); for unknown noise variance, the test of the largest eigenvalue divided by trace of the covariance matrix, introduced in CR by [7] as a generalized likelihood ratio test (GLRT) and previously appeared in signal processing [12] and statistics literature [13], [14]. The main contributions of our analysis are: (i) derivation of novel expressions for the 1 See Sec.…”

Sufficient Reduction in Multivariate Surveillance

“…The most common way to combine the information from several univariate methods is to signal an alarm at the first time that any of the univariate methods gives an alarm. This is a special case of the unionintersection technique suggested by Roy, (1953). Sonesson & Frisén, (2005b)).…”

Multivariate empirical distribution plot and goodness-of-fit test

“…첫 번째로 확률변수들의 선형결합을 이용하여 일변량 확률변수로 변환하는 방법을 사용하고 (D'Agostino와 Stephens, 1986;Kim, 2005;Kim, 2006;Roy, 1953;Royston, 1983;Thode, 2002;Zhu 등, 1997), 두 번째로 변수변환을 이용하여 균일분포로 변환하여 사용한다 (Justel 등, 1997;Meintanis와 Hlávka, 2010;Rosenblatt, 1952). 그리고 마지막 방법으로는 표준화된 확률변수의 제곱한 카 이제곱분포를 이용한다 (Gnanadesikan와 Kettenring, 1972;Gnanadesikan 등, 1977;Kim, 2004;Koziol, 1982;Malkovich와 Afifi, 1973;Moore와 Stubblebine, 1981;Singh, 1993).…”