Inference on the Order of a Normal Mixture

Chen, Jiahua; Li, Pengfei; Fu, Yuejiao

doi:10.1080/01621459.2012.695668

Cited by 52 publications

(47 citation statements)

References 29 publications

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“…Then, ω 12 is defined as the average of ω 1|2 and ω 2|1 , and ω 23 is defined as the average of ω 2|3 and ω 3|2 . The empirical formula in (23) is obtained through computer experiments that are similar to those in Chen and Li (2009) and Chen et al (2012).…”

Section: Choice Of Penalty Functionmentioning

confidence: 99%

“…Based on our experience, we recommend T = {0.5} and K = 2 or 3; following the recommendation given by Chen et al (2012), we set and 6 if a n = o p (n 1/4 ). In models with a regressor, we use an additional restriction σ j ≥ 0.01σ j , which does not change the theoretical results but improves finite sample performance.…”

Section: Choice Of Penalty Functionmentioning

confidence: 99%

“…In normal mixtures with heteroscedastic components, however, the asymptotic distribution of the LRT statistic remains an open question because, as discussed in Chen et al (2012), normal mixtures have an additional undesirable mathematical property that inval-idates key assumptions in these works. In particular, the normal density with mean µ and variance σ 2 , f (y; µ, σ 2 ), has the property ∂ 2 ∂µ∂µ f (y; µ, σ 2 ) = 2 ∂ ∂σ 2 f (y; µ, σ 2 ).…”

Section: Introductionmentioning

confidence: 99%

“…As discussed in Chen et al (2012), while model selection procedures seek to find a parsimonious model that adequately describes the observed data, the number of components is often linked to scientific propositions, and a hypothesis test can be used to check their validity.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Testing the Number of Components in Normal Mixture Regression Models

Kasahara

Shimotsu

2015

Journal of the American Statistical Association

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Testing the number of components in finite normal mixture models is a longstanding challenge because of its non-regularity. This paper studies likelihood-based testing of the number of components in normal mixture regression models with heteroscedastic components. We construct a likelihood-based test of the null hypothesis of m 0 components against the alternative hypothesis of m 0 + 1 components for any m 0 . The null asymptotic distribution of the proposed modified EM test statistic is the maximum of m 0 random variables that can be easily simulated. The simulations show that the proposed test has very good finite sample size and power properties.

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Section: Choice Of Penalty Functionmentioning

confidence: 99%

Section: Choice Of Penalty Functionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Testing the Number of Components in Normal Mixture Regression Models

Kasahara

Shimotsu

2015

Journal of the American Statistical Association

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“…Simulations indicate that our algorithm using k-deleted log-likelihood criterion is successful to search appropriate subspaces and estimate converges to true parameter values. It is possible to extend likelihood ratio tests and EM tests for GMM (Chen et al, 2012;Jeffries, 2003;Lo, 2005;Lo et al, 2001) and apply it sequentially when selecting the number of groups and total number of components. In addition, we may also try several possible combinations of groups and components and select the best model by cross validation or comparing log-likelihood values.…”

Section: Discussionmentioning

confidence: 99%

Model-based inverse regression for mixture data

Choi

Park

2017

CSAM

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This paper proposes a method for sufficient dimension reduction (SDR) of mixture data. We consider mixture data containing more than one component that have distinct central subspaces. We adopt an approach of a modelbased sliced inverse regression (MSIR) to the mixture data in a simple and intuitive manner. We employed mixture probabilistic principal component analysis (MPPCA) to estimate each central subspaces and cluster the data points. The results from simulation studies and a real data set show that our method is satisfactory to catch appropriate central spaces and is also robust regardless of the number of slices chosen. Discussions about root selection, estimation accuracy, and classification with initial value issues of MPPCA and its related simulation results are also provided.

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The joy of proofs in statistical research

Chen

2015

Can J Statistics

Self Cite

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Without exception, great statisticians have penetrating statistical insight. Technical strength is likely secondary in their research, although it never hurts. In contrast, mathematical skill has been pivotal in my work, particularly in combination with my proximity to many great statistical minds. In the occasion of receiving the Gold Medal of the Statistical Society of Canada, I wish to attribute part of my success to the joy of proofs. Proofs are an indispensable ingredient in my research achievements. I hasten to add that proofs are delightful only if they help to develop innovative statistical methods: proving theorems solely for the sake of publication can be boring and a waste of time. With this preamble, I selectively present some research achievements and encourage other researchers to proudly maximize the benefits of their technical strength. The Canadian Journal of Statistics 43: 481–497; 2015 © 2015 Statistical Society of Canada

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Inference on the Order of a Normal Mixture

Cited by 52 publications

References 29 publications

Testing the Number of Components in Normal Mixture Regression Models

Testing the Number of Components in Normal Mixture Regression Models

Model-based inverse regression for mixture data

The joy of proofs in statistical research

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