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Full-Text Articles in Physical Sciences and Mathematics
On Likelihood Ratio Tests When Nuisance Parameters Are Present Only Under The Alternative, Cz Di, K-Y Liang
On Likelihood Ratio Tests When Nuisance Parameters Are Present Only Under The Alternative, Cz Di, K-Y Liang
Chongzhi Di
In parametric models, when one or more parameters disappear under the null hypothesis, the likelihood ratio test statistic does not converge to chi-square distributions. Rather, its limiting distribution is shown to be equivalent to that of the supremum of a squared Gaussian process. However, the limiting distribution is analytically intractable for most of examples, and approximation or simulation based methods must be used to calculate the p values. In this article, we investigate conditions under which the asymptotic distributions have analytically tractable forms, based on the principal component decomposition of Gaussian processes. When these conditions are not satisfied, the principal …
Hypothesis Testing For An Extended Cox Model With Time-Varying Coefficients, Takumi Saegusa, Chongzhi Di, Ying Qing Chen
Hypothesis Testing For An Extended Cox Model With Time-Varying Coefficients, Takumi Saegusa, Chongzhi Di, Ying Qing Chen
Chongzhi Di
In many randomized clinical trials, the log-rank test has routinely been used to detect a treatment effect under the Cox proportional hazards model for censored time-to-event outcomes. However, it may lose power substantially when the proportional hazards assumption does not hold. There are approaches to testing the proportionality, such as the smoothing spline-based score test by Lin, Zhang and Davidian (2006). In this paper, we consider an extended Cox model assuming time-varying treatment effect. We then use smoothing splines to model the time-varying treatment effect, and we propose spline-based score tests for the overall treatment effect. Our proposed tests take …
Multilevel Sparse Functional Principal Component Analysis, Cz Di, C M. Crainiceanu, W Jank
Multilevel Sparse Functional Principal Component Analysis, Cz Di, C M. Crainiceanu, W Jank
Chongzhi Di
We consider analysis of sparsely sampled multilevel functional data, where the basic observational unit is a function and data have a natural hierarchy of basic units. An example is when functions are recorded at multiple visits for each subject. Multilevel functional principal component analysis (MFPCA; Di et al. 2009) was proposed for such data when functions are densely recorded. Here we consider the case when functions are sparsely sampled and may contain only a few observations per function. We exploit the multilevel structure of covariance operators and achieve data reduction by principal component decompositions at both between and within subject …