A generalized likelihood ratio test for normal mean when <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si27.gif" display="inline" overflow="scroll"><mml:mi>p</mml:mi></mml:math> is greater than <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si28.gif" display="inline" overflow="scroll"><mml:mi>n</mml:mi></mml:math>

Zhao, Junguang; Xu, Xingzhong

doi:10.1016/j.csda.2016.01.006

Cited by 13 publications

(4 citation statements)

References 44 publications

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“…, if the autocorrelation function of { 1 , … , } decays rapidly as the lag increases, 1 will converge to the standard normal distribution under appropriate centering and scaling. Finally, we note that similar mixing conditions were also adopted in Gregory et al (2015) and Zhao and Xu (2016) The asymptotic variance of 1∕2 1 , 2 1 , depends on the autocovariance of the sequence { 1 , 2 , …} and is unknown. To establish the null distribution in practice, we need an estimate,̂2 1 , to replace 2 1 .…”

Section: =1mentioning

confidence: 99%

“…Finally, we note that similar mixing conditions were also adopted in Gregory et al (2015) and Zhao and Xu (2016). The asymptotic variance of p 1/2 T 1 , τ 2 1 , depends on the autocovariance sequence {U n1 , U n2 , .…”

Section: Lemma 1 For the Gamma Functionmentioning

confidence: 99%

“…For instance, Jiang and Yang () and Jiang and Qi () tested mean vectors and covariance matrices of normal distributions using the likelihood ratio test method, under the setting that p is smaller than n but in a way that allows

p / n \to 1

. Zhao and Xu () proposed a generalized high‐dimensional likelihood ratio test for the normal mean vector by a modified union‐intersection method. Städler and Mukherjee () provided a high‐dimensional likelihood ratio test for the two‐sample test based on sample splitting.…”

Section: Introductionmentioning

confidence: 99%

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Diagonal Likelihood Ratio Test for Equality of Mean Vectors in High-Dimensional Data

Tong

Genton

2018

Biometrics

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We propose a likelihood ratio test framework for testing normal mean vectors in high-dimensional data under two common scenarios: the one-sample test and the two-sample test with equal covariance matrices. We derive the test statistics under the assumption that the covariance matrices follow a diagonal matrix structure. In comparison with the diagonal Hotelling's tests, our proposed test statistics display some interesting characteristics. In particular, they are a summation of the log-transformed squared -statistics rather than a direct summation of those components. More importantly, to derive the asymptotic normality of our test statistics under the null and local alternative hypotheses, we do not need the requirement that the covariance matrices follow a diagonal matrix structure. As a consequence, our proposed test methods are very flexible and readily applicable in practice. Simulation studies and a real data analysis are also carried out to demonstrate the advantages of our likelihood ratio test methods.

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Section: =1mentioning

confidence: 99%

Section: Lemma 1 For the Gamma Functionmentioning

confidence: 99%

p / n \to 1

Section: Introductionmentioning

confidence: 99%

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Diagonal Likelihood Ratio Test for Equality of Mean Vectors in High-Dimensional Data

Tong

Genton

2018

Biometrics

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“…Testing hypotheses in high dimension is one of important issues in high dimensional data which has attracted a great deal of attention in recent decades. In two sample testing in high dimension, there have been numerous studies such as Bai and Saranadasa (1996), Srivastava et al (2008Srivastava et al ( , 2009Srivastava et al ( , 2013, Chen and Qin (2010), Aoshima and Yata (2011), Park and Ayyala (2013), Feng et al (2015), Zhou and Kong (2015), Ma et al (2015), Ghosh and Biswas (2016) and Zhao and Xu (2016). For multivariate analysis of variance (MANOVA), see Fujikoshi et al (2004), Schott (2007), Srivastava et al (2007), Cai and Xia (2014) and Cao and Xu (2015).…”

Section: Introductionmentioning

confidence: 99%

A test for the k sample Behrens–Fisher problem in high dimensional data

Cao

Park

2019

Journal of Statistical Planning and Inference

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In this paper, the k sample Behrens-Fisher problem is investigated in high dimensional setting. We propose a new test statistic and demonstrate that the proposed test is expected to have more powers than some existing test especially when sample sizes are unbalanced. We provide theoretical investigation as well as numerical studies on both sizes and powers of the proposed tests and existing test. Both theoretical comparison of the asymptotic power functions and numerical studies show that the proposed test tends to have more powers than existing test in many cases of unbalanced sample sizes.In this section, we give notations and the statistical model for the k sample BF problem. Some assumptions are also illustrated. NotationsThe following notations will be used in subsequent exposition. All vectors are column and M T denotes the transpose of M . All vectors and matrices are bold-faced. For two sequences of real numbers {a n } and {b n }, we write a n = O(b n ) if there exists a constant c such that |a n | ≤ c|b n | holds for all sufficiently large n, and write a n = o(b n ) if lim n→∞ a n /b n = 0. For a random sequence Z n and a random variable Z, Z n pr −→ Z and

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