Inner envelopes: efficient estimation in multivariate linear regression

Su, Zhihua; Cook, R. Dennis

doi:10.1093/biomet/ass024

Cited by 49 publications

(50 citation statements)

References 8 publications

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“…The multivariate linear regression model is y i = B T x i + ϵ i for i = 1, ..., n. This paper suggests some plots and reviews some recent results by Kakizawa (2009) and Su and Cook (2012) …”

Section: Introductionmentioning

confidence: 81%

“…1;2015 linearity can be quickly assessed and influential cases can often be quickly detected. The plots can also be used for competing methods such as the envelopes estimators of Su and Cook (2012 Cramér (1946, pp. 414-415) shows that when the e i are iid N(0, σ 2 ) and none of the p − 1 nontrivial predictors are needed in the multiple linear regression model, then E(R 2 ) = (p − 1)/(n − 1) where R 2 is the coefficient of multiple determination.…”

Section: Discussionmentioning

confidence: 99%

“…This subsection reviews useful results from Kakizawa (2009) and Su and Cook (2012). These results will show that the Hotelling Lawley test statistic is an extension of the partial F test statistic.…”

Section: Testing Hypothesesmentioning

confidence: 96%

“…This model has m ≥ 2 response variables. Results by Kakizawa (2009) and Su and Cook (2012) can be used to explain the large sample theory of the least squares estimator and of the widely used Wilks' Λ, Pillai's trace, and Hotelling Lawley trace test statistics. Kakizawa (2009) shows that these statistics have the same limiting distribution.…”

mentioning

confidence: 99%

See 3 more Smart Citations

Visualizing and Testing the Multivariate Linear Regression Model

Olive¹,

Watagoda²,

Don³

2015

IJSP

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Recent results make the multivariate linear regression model much easier to use. This model has m ≥ 2 response variables. Results by Kakizawa (2009) and Su and Cook (2012) can be used to explain the large sample theory of the least squares estimator and of the widely used Wilks' Λ, Pillai's trace, and Hotelling Lawley trace test statistics. Kakizawa (2009) shows that these statistics have the same limiting distribution. This paper reviews these results and gives two theorems to show that the Hotelling Lawley test generalizes the usual partial F test for m = 1 response variable to m ≥ 1 response variables. Plots for visualizing the model are also given, and can be used to check goodness and lack of fit, to check for outliers and influential cases, and to check whether the error distribution is multivariate normal or from some other elliptically contoured distribution.

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Section: Introductionmentioning

confidence: 81%

Section: Discussionmentioning

confidence: 99%

Section: Testing Hypothesesmentioning

confidence: 96%

mentioning

confidence: 99%

See 2 more Smart Citations

Visualizing and Testing the Multivariate Linear Regression Model

Olive¹,

Watagoda²,

Don³

2015

IJSP

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show abstract

“…Recent developments of envelopes under other settings may be found in, for example, Su and Cook (), Cook et al . () and Cook and Zhang ().…”

Section: Review Of Envelopesmentioning

confidence: 99%

Matrix Variate Regressions and Envelope Models

Ding

Cook

2017

Journal of the Royal Statistical Society Series B: Statistical Methodology

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Summary Modern technology often generates data with complex structures in which both response and explanatory variables are matrix valued. Existing methods in the literature can tackle matrix‐valued predictors but are rather limited for matrix‐valued responses. We study matrix variate regressions for such data, where the response Y on each experimental unit is a random matrix and the predictor X can be either a scalar, a vector or a matrix, treated as non‐stochastic in terms of the conditional distribution Y|X. We propose models for matrix variate regressions and then develop envelope extensions of these models. Under the envelope framework, redundant variation can be eliminated in estimation and the number of parameters can be notably reduced when the matrix variate dimension is large, possibly resulting in significant gains in efficiency. The methods proposed are applicable to high dimensional settings.

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Bibliography

2018

An Introduction to Envelopes

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Inner envelopes: efficient estimation in multivariate linear regression

Cited by 49 publications

References 8 publications

Visualizing and Testing the Multivariate Linear Regression Model

Visualizing and Testing the Multivariate Linear Regression Model

Matrix Variate Regressions and Envelope Models

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