scholarly journals Goodness-of-fit tests for high dimensional linear models

2017 ◽  
Vol 80 (1) ◽  
pp. 113-135 ◽  
Author(s):  
Rajen D. Shah ◽  
Peter Bühlmann
Keyword(s):  
Goodness Of Fit ◽  
Linear Models ◽  
High Dimensional ◽  
Goodness Of Fit Tests

scholarly journals Goodness-of-fit tests for high-dimensional Gaussian linear models

2010 ◽  
Vol 38 (2) ◽  
pp. 704-752 ◽  
Author(s):  
Nicolas Verzelen ◽  
Fanny Villers
Keyword(s):  
Goodness Of Fit ◽  
Linear Models ◽  
High Dimensional ◽  
Goodness Of Fit Tests ◽  
Gaussian Linear Models

scholarly journals Goodness-of-fit tests in semi-linear models

2011 ◽  
Vol 22 (4) ◽  
pp. 967-979 ◽  
Author(s):  
Simos G. Meintanis ◽  
Jochen Einbeck
Keyword(s):  
Goodness Of Fit ◽  
Linear Models ◽  
Goodness Of Fit Tests

scholarly journals Wald Statistics in high-dimensional PCA

2019 ◽  
Vol 23 ◽  
pp. 662-671
Author(s):  
Matthias Löffler
Keyword(s):  
Goodness Of Fit ◽  
Higher Order ◽  
Model Complexity ◽  
High Dimensional ◽  
Wald Statistic ◽  
Spectral Projector ◽  
Goodness Of Fit Tests ◽  
Effective Rank ◽  
Pertubation Theory ◽  
Confidence Ellipsoids

In this study, we consider PCA for Gaussian observations X1, …, Xn with covariance Σ = ∑iλiPi in the ’effective rank’ setting with model complexity governed by r(Σ) ≔ tr(Σ)∕∥Σ∥. We prove a Berry-Essen type bound for a Wald Statistic of the spectral projector $\hat P_r$. This can be used to construct non-asymptotic goodness of fit tests and confidence ellipsoids for spectral projectors Pr. Using higher order pertubation theory we are able to show that our Theorem remains valid even when $\mathbf{r}(\Sigma) \gg \sqrt{n}$.

scholarly journals Nonparametric independence testing via mutual information

Biometrika ◽  
2019 ◽  
Vol 106 (3) ◽  
pp. 547-566 ◽  
Author(s):  
T B Berrett ◽  
R J Samworth
Keyword(s):  
Mutual Information ◽  
Goodness Of Fit ◽  
Linear Models ◽  
Real Data ◽  
Nearest Neighbour ◽  
Local Power ◽  
Goodness Of Fit Tests ◽  
Numerical Studies ◽  
Independence Testing ◽  
Power Analyses

Summary We propose a test of independence of two multivariate random vectors, given a sample from the underlying population. Our approach is based on the estimation of mutual information, whose decomposition into joint and marginal entropies facilitates the use of recently developed efficient entropy estimators derived from nearest neighbour distances. The proposed critical values may be obtained by simulation in the case where an approximation to one marginal is available or by permuting the data otherwise. This facilitates size guarantees, and we provide local power analyses, uniformly over classes of densities whose mutual information satisfies a lower bound. Our ideas may be extended to provide new goodness-of-fit tests for normal linear models based on assessing the independence of our vector of covariates and an appropriately defined notion of an error vector. The theory is supported by numerical studies on both simulated and real data.

NN goodness-of-fit tests for linear models

1996 ◽  
Vol 53 (1) ◽  
pp. 75-92 ◽  
Author(s):  
W. Stute ◽  
W.González Manteiga
Keyword(s):  
Goodness Of Fit ◽  
Linear Models ◽  
Goodness Of Fit Tests

A Global Test for the Goodness of Fit of Generalized Linear Models : An Estimating Equation Approach

2005 ◽  
Vol 56 (1-4) ◽  
pp. 251-282
Author(s):  
R. Prabhakar Rao ◽  
B.C. Sutradhar
Keyword(s):  
Generalized Linear Models ◽  
Goodness Of Fit ◽  
Exponential Family ◽  
Linear Models ◽  
Estimating Equation ◽  
Goodness Of Fit Test ◽  
Global Test ◽  
Goodness Of Fit Tests ◽  
Exponential Family Of Distributions ◽  
Family Of Distributions

Summary Generalized linear models are used to analyze a wide variety of discrete and continuous data with possible overdispersion under the assumption that the data follow an exponential family of distributions. The violation of this assumption may have adverse effects on the statistical inferences. The existing goodness of fit tests for checking this assumption are valid only for a standard exponential family of distributions with no overdispersion. In this paper, we develop a global goodness of fit test for the general exponential family of distributions which may or may not contain overdispersion. The proposed statistic has asymptotically standard Gaussian distribution which should be easy to implement.

scholarly journals Alternative Goodness-of-Fit Tests for Linear Models

2010 ◽  
Vol 105 (489) ◽  
pp. 291-301 ◽  
Author(s):  
Ronald Christensen ◽  
Siu Kei Sun
Keyword(s):  
Goodness Of Fit ◽  
Linear Models ◽  
Goodness Of Fit Tests

scholarly journals Goodness-of-fit Tests for Functional Linear Models Based on Integrated Projections

2020 ◽  
pp. 107-114
Author(s):  
Eduardo García-Portugués ◽  
Javier álvarez-Liébana ◽  
Gonzalo álvarez-Pérez ◽  
Wenceslao González-Manteiga
Keyword(s):  
Goodness Of Fit ◽  
Linear Models ◽  
Functional Linear Models ◽  
Goodness Of Fit Tests
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