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doi: 10.1111/stan.12259pmid: N/A
Based on periodogram‐ratios of two univariate time series at different frequency points, two tests are proposed for comparing their spectra. One is an Anderson–Darling‐like statistic for testing the equality of two time‐invariant spectra. The other is the maximum of Anderson–Darling‐like statistics for testing the equality of two time‐varying spectra. Both of two tests are applicable for independent or dependent time series. Several simulation examples show that the proposed statistics outperform those that are also based on periodogram‐ratios but constructed by the Pearson‐like statistics.
Menssen, Max; Schaarschmidt, Frank
doi: 10.1111/stan.12260pmid: N/A
In many pharmaceutical and biomedical applications such as assay validation, assessment of historical control data, or the detection of anti‐drug antibodies, the calculation and interpretation of prediction intervals (PI) is of interest. The present study provides two novel methods for the calculation of prediction intervals based on linear random effects models and restricted maximum likelihood (REML) estimation. Unlike other REML‐based PI found in the literature, both intervals reflect the uncertainty related with the estimation of the prediction variance. The first PI is based on Satterthwaite approximation. For the other PI, a bootstrap calibration approach that we will call quantile‐calibration was used. Due to the calibration process this PI can be easily computed for more than one future observation and based on balanced and unbalanced data as well. In order to compare the coverage probabilities of the proposed PI with those of four intervals found in the literature, Monte Carlo simulations were run for two relatively complex random effects models and a broad range of parameter settings. The quantile‐calibrated PI was implemented in the statistical software R and is available in the predint package.
Hunsberger, Sally; Long, Lori; Reese, Sarah E.; Hong, Gloria H.; Myles, Ian A.; Zerbe, Christa S.; Chetchotisakd, Pleonchan; Shih, Joanna H.
doi: 10.1111/stan.12261pmid: 35936973
This paper develops methods to test for associations between two variables with clustered data using a U‐Statistic approach with a second‐order approximation to the variance of the parameter estimate for the test statistic. The tests that are presented are for clustered versions of: Pearsons χ2 test, the Spearman rank correlation and Kendall's τ for continuous data or ordinal data and for alternative measures of Kendall's τ that allow for ties in the data. Shih and Fay use the U‐Statistic approach but only consider a first‐order approximation. The first‐order approximation has inflated significance level in scenarios with small sample sizes. We derive the test statistics using the second‐order approximations aiming to improve the type I error rates. The method applies to data where clusters have the same number of measurements for each variable or where one of the variables may be measured once per cluster while the other variable may be measured multiple times. We evaluate the performance of the test statistics through simulation with small sample sizes. The methods are all available in the R package cluscor.
Etiévant, Lola; Viallon, Vivian
doi: 10.1111/stan.12262pmid: N/A
Partial least squares (PLS) refer to a class of dimension‐reduction techniques aiming at the identification of two sets of components with maximal covariance, to model the relationship between two sets of observed variables x∈ℝp and y∈ℝq, with p≥1,q≥1. Probabilistic formulations have recently been proposed for several versions of the PLS. Focusing first on the probabilistic formulation of the PLS‐SVD proposed by el Bouhaddani et al., we establish that the constraints on their model parameters are too restrictive and define particular distributions for (x,y), under which components with maximal covariance (solutions of PLS‐SVD) are also necessarily of respective maximal variances (solutions of principal components analyses of x and y, respectively). We propose an alternative probabilistic formulation of PLS‐SVD, no longer restricted to these particular distributions. We then present numerical illustrations of the limitation of the original model of el Bouhaddani et al. We also briefly discuss similar limitations in another latent variable model for dimension‐reduction.
Wang, Wei; Li, Linjian; Li, Sheng; Yin, Fei; Liao, Fang; Zhang, Tao; Li, Xiaosong; Xiao, Xiong; Ma, Yue
doi: 10.1111/stan.12263pmid: N/A
We developed a novel method to address multicollinearity in linear models called average ordinary least squares (OLS)‐centered penalized regression (AOPR). AOPR penalizes the cost function to shrink the estimators toward the weighted‐average OLS estimator. The commonly used ridge regression (RR) shrinks the estimators toward zero, that is, employs penalization prior β∼N(0,1/k) in the Bayesian view, which contradicts the common real prior β≠0. Therefore, RR selects small penalization coefficients to relieve such a contradiction and thus makes the penalizations inadequate. Mathematical derivations remind us that AOPR could increase the performance of RR and OLS regression. A simulation study shows that AOPR obtains more accurate estimators than OLS regression in most situations and more accurate estimators than RR when the signs of the true βs are identical and is slightly less accurate than RR when the signs of the true βs are different. Additionally, a case study shows that AOPR obtains more stable estimators and stronger statistical power and predictive ability than RR and OLS regression. Through these results, we recommend using AOPR to address multicollinearity more efficiently than RR and OLS regression, especially when the true βs have identical signs.
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