Asymptotically distribution free tests in heteroscedastic unbalanced high dimensional ANOVA

Wang, Haiyan; Akritas, Michaël G.

doi:10.5705/ss.2009.061

Cited by 8 publications

(16 citation statements)

References 24 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The results in Theorem 3.1 are of similar form as the corresponding results in [8], except that the present results hold without any moment conditions. Thus, the present results are of wider applicability in addition to the fact that rank statistics converge faster to their limiting distributions.…”

Section: Remarksupporting

confidence: 64%

“…When both a and b are large, regardless of whether c is small or large, the test statistic is √ ab(F R (AB) − 1), where F R (AB) is given in Equation (8). The asymptotic distribution of the test statistics above are given below.…”

Section: Testing For No Two-way Interaction Effectsmentioning

confidence: 97%

“…(3) When both a and b are large, let F R (AB) be the statistic given in Equation (8). Then under H 0 (AB), as a, b → ∞, regardless of whether c and n ij k ≥ 2 tend to ∞ or stay fixed,…”

Section: Testing For No Two-way Interaction Effectsmentioning

confidence: 99%

“…The rank test statistics are obtained by replacing the original observations by their overall (mid-)ranks in the test statistics given in [8]. Since the aforementioned paper yields the distribution of corresponding expressions where the original observations are substituted by the asymptotic rank transformation [21], the asymptotic distribution of the rank statistics will be established by establishing their asymptotic equivalence to the corresponding expressions with the asymptotic rank transformation.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Rank tests in heteroscedastic multi-way HANOVA

Wang

Akritas

2009

Journal of Nonparametric Statistics

Self Cite

View full text Add to dashboard Cite

This article develops rank tests for the nonparametric main factor effects and interactions in multi-way high-dimensional analysis of variance when the cell distributions are completely unspecified. The design can be balanced or unbalanced with the cell sample sizes fixed or tending to infinity. An arbitrary number of factors and all types of ordinal data are allowed. This extends the use of rank methods to the NeymannScott and triangular array problems. The asymptotic distribution of the rank statistics is obtained by showing their asymptotic equivalence to corresponding expressions based on the asymptotic rank transform. Compared with test procedures based on the original observations, the proposed rank procedures are free of moment conditions, converge to their limiting distribution faster, and have better power when the underlying distributions are heavy tailed or skewed. These advantages are demonstrated by simulations and an application to a real data set.

show abstract

Section: Remarksupporting

confidence: 64%

Section: Testing For No Two-way Interaction Effectsmentioning

confidence: 97%

Section: Testing For No Two-way Interaction Effectsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Rank tests in heteroscedastic multi-way HANOVA

Wang

Akritas

2009

Journal of Nonparametric Statistics

Self Cite

View full text Add to dashboard Cite

show abstract

“…The following Theorem provides such an estimator. A similar estimator has been used in a univariate setting in Wang and Akritas (2009).…”

Section: Consistent Estimator Of τ 2 ψ ( )mentioning

confidence: 95%

A modified two-factor multivariate analysis of variance: asymptotics and small sample approximations

Harrar

Bathke

2010

Ann Inst Stat Math

View full text Add to dashboard Cite

In this paper, we present results for testing main, simple and interaction effects in heteroscedastic two factor MANOVA models. In particular, we suggest modifications to the MANOVA sum of squares and cross product matrices to account for heteroscedasticity. Based on these modified matrices, we define some multivariate test statistics and derive their asymptotic distributions under non-normality for the null as well as non-null cases. Derivation of these results relies on the perturbation method and limit theorems for independently distributed random matrices. Based on the asymptotic distributions, we devise small sample approximations for the quantiles of the null distributions. The numerical accuracy of the large sample as well as small sample approximations are favorable. A real data set from a Smoking Cessation Trial is analyzed to illustrate the application of the methods.

show abstract

A new distribution‐free k‐sample test: Analysis of kernel density functionals

Chen

2019

Can J Statistics

View full text Add to dashboard Cite

A novel distribution‐free k‐sample test of differences in location shifts based on the analysis of kernel density functional estimation is introduced and studied. The proposed test parallels one‐way analysis of variance and the Kruskal–Wallis (KW) test aiming at testing locations of unknown distributions. In contrast to the rank (score)‐transformed non‐parametric approach, such as the KW test, the proposed F‐test uses the measurement responses along with well‐known kernel density estimation (KDE) to estimate the locations and construct the test statistic. A practical optimal bandwidth selection procedure is also provided. Our simulation studies and real data example indicate that the proposed analysis of kernel density functional estimate (ANDFE) test is superior to existing competitors for fat‐tailed or heavy‐tailed distributions when the k groups differ mainly in location rather than shape, especially with unbalanced data. ANDFE is also highly recommended when it is unclear whether test groups differ mainly in shape or location. The Canadian Journal of Statistics 48: 167–186; 2020 © 2019 Statistical Society of Canada

show abstract

Asymptotically distribution free tests in heteroscedastic unbalanced high dimensional ANOVA

Cited by 8 publications

References 24 publications

Rank tests in heteroscedastic multi-way HANOVA

Rank tests in heteroscedastic multi-way HANOVA

A modified two-factor multivariate analysis of variance: asymptotics and small sample approximations

A new distribution‐free k‐sample test: Analysis of kernel density functionals

Contact Info

Product

Resources

About