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 A note on Asymptotical Efficiency of the Goodness of Fit Tests Based on disjoint k-spacings Statistic

2018 ◽  
pp. 839-851
Author(s):  
Muhammad Naeem
Keyword(s):  
General Result ◽  
Goodness Of Fit ◽  
Higher Order ◽  
Goodness Of Fit Tests ◽  
Type Statistic

In this paper Pitman's asymptotic efficiencies (AE) as well as Kallenberg's intermediate AE of the goodness-of-fit tests based on higher-order non-overlapping spacings is considered. We study log statistic as well as entropy type statistic based on k-spacings when k may tend to infinity as n approaches infinity. It certainly compliments the available results for fixed k and provides more general result. We show that both types of statistics based on higher ordered spacings have higher efficiencies in Pitman's sense compared to their counterparts based on simple spacings. It is also shown that the Kallenberg's intermediate AE of such test coincides with its Pitman's AE, the power of the tests are also discussed.

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 Dependence Modeling in Energy Markets using Sibuya-type Copulas

2017 ◽  
Vol 6 (3) ◽  
pp. 43
Author(s):  
Nikolai Kolev ◽  
Jayme Pinto
Keyword(s):  
Goodness Of Fit ◽  
Basic Assumption ◽  
Energy Markets ◽  
Dependence Structure ◽  
Dependence Function ◽  
Dependence Modeling ◽  
Goodness Of Fit Tests ◽  
Oil And Natural Gas ◽  
Error Terms ◽  
Time Invariant

The dependence structure between 756 prices for futures on crude oil and natural gas traded on NYMEX is analyzed  using  a combination of novel time-series and copula tools.  We model the log-returns on each commodity individually by Generalized Autoregressive Score models and account for dependence between them by fitting various copulas to corresponding  error terms. Our basic assumption is that the dependence structure may vary over time, but the ratio between the joint distribution of error terms and the product of marginal distributions (e.g., Sibuya's dependence function) remains the same, being time-invariant.  By performing conventional goodness-of-fit tests, we select the best copula, being member of the currently  introduced class of  Sibuya-type copulas.

scholarly journals Goodness-of-Fit Tests for Bivariate Time Series of Counts

Econometrics ◽  
2021 ◽  
Vol 9 (1) ◽  
pp. 10
Author(s):  
Šárka Hudecová ◽  
Marie Hušková ◽  
Simos G. Meintanis
Keyword(s):  
Goodness Of Fit ◽  
Probability Generating Function ◽  
Parametric Bootstrap ◽  
Real Data ◽  
Data Sets ◽  
Test Statistics ◽  
Finite Sample ◽  
Generalized Poisson ◽  
Goodness Of Fit Tests ◽  
Monte Carlo Experiments

This article considers goodness-of-fit tests for bivariate INAR and bivariate Poisson autoregression models. The test statistics are based on an L2-type distance between two estimators of the probability generating function of the observations: one being entirely nonparametric and the second one being semiparametric computed under the corresponding null hypothesis. The asymptotic distribution of the proposed tests statistics both under the null hypotheses as well as under alternatives is derived and consistency is proved. The case of testing bivariate generalized Poisson autoregression and extension of the methods to dimension higher than two are also discussed. The finite-sample performance of a parametric bootstrap version of the tests is illustrated via a series of Monte Carlo experiments. The article concludes with applications on real data sets and discussion.

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