Guanqun Cao

Simultaneous inference for the mean function based on dense functional data

A polynomial spline estimator is proposed for the mean function of dense functional data together with a simultaneous confidence band which is asymptotically correct. In addition, the spline estimator and its accompanying confidence band enjoy oracle efficiency in the sense that they are asymptotically the same as if all random trajectories are observed entirely and without errors. The confidence band is also extended to the difference of mean functions of two populations of functional data. Simulation experiments provide strong evidence that corroborates the asymptotic theory while computing is efficient. The confidence band procedure is illustrated by analysing the near-infrared spectroscopy data.

Simultaneous confidence bands for derivatives of dependent functional data

Abstract: In this work, consistent estimators and simultaneous confidence bands for the derivatives of mean functions are proposed when curves are repeatedly recorded for each subject. The within-curve correlation of trajectories has been considered while the proposed novel confidence bands still enjoys semiparametric efficiency. The proposed methods lead to a straightforward extension of the two-sample case in which we compare the derivatives of mean functions from two populations. We demonstrate in simulations that the proposed confidence bands are superior to existing approaches which ignore the within-curve dependence. The proposed methods are applied to investigate the derivatives of mortality rates from period lifetables that are repeatedly collected over many years for various countries.

Analysis of solar generation and weather data in smart grid with simultaneous inference of nonlinear time series

Smart Grid is an important component of Smart City, where more renewable power generation and better energy management is required. Forecast on renewable power generation, from sources such as solar and wind, is crucial for better energy management. However, the current forecast methods lack a comprehensive understanding of the natural processes, and are thus limited in precise prediction. In this paper, we introduce simultaneous inference to analyze the solar generation and weather data for better predictions. We first introduce a local linear model for nonlinear time series, and present the construction of the simultaneous confidence bands (SCB) of the time-varying coefficients, which provide more information on the dynamic properties of the model. We then use the simultaneous inference for solar intensity prediction using a real trace, where the superior performance of the proposed scheme is demonstrated over existing approaches.

Statistical Approaches for the Study of Cognitive and Brain Aging.

Neuroimaging studies of cognitive and brain aging often yield massive datasets that create many analytic and statistical challenges. In this paper, we discuss and address several limitations in the existing work. (1) Linear models are often used to model the age effects on neuroimaging markers, which may be inadequate in capturing the potential nonlinear age effects. (2) Marginal correlations are often used in brain network analysis, which are not efficient in characterizing a complex brain network. (3) Due to the challenge of high-dimensionality, only a small subset of the regional neuroimaging markers is considered in a prediction model, which could miss important regional markers. To overcome those obstacles, we introduce several advanced statistical methods for analyzing data from cognitive and brain aging studies. Specifically, we introduce semiparametric models for modeling age effects, graphical models for brain network analysis, and penalized regression methods for selecting the most important markers in predicting cognitive outcomes. We illustrate these methods using the healthy aging data from the Active Brain Study.

A score‐type test for heterogeneity in zero‐inflated models in a stratified population

We propose a score-type statistic to evaluate heterogeneity in zero-inflated models for count data in a stratified population, where heterogeneity is defined as instances in which the zero counts are generated from two sources. Evaluating heterogeneity in this class of models has attracted considerable attention in the literature, but existing testing procedures have primarily relied on the constancy assumption under the alternative hypothesis. In this paper, we extend the literature by describing a score-type test to evaluate homogeneity against general alternatives that do not neglect the stratification information under the alternative hypothesis. The limiting null distribution of the proposed test statistic is a mixture of chi-squared distributions that can be well approximated by a simple parametric bootstrap procedure. Our numerical simulation studies show that the proposed test can greatly improve efficiency over tests of heterogeneity that ignore the stratification information. An empirical application to dental caries data in early childhood further shows the importance and practical utility of the methodology in using the stratification profile to detect heterogeneity in the population.

Efficient estimation for generalized partially linear single-index models

In this paper, we study the estimation for generalized partially linear single-index models, where the systematic component in the model has a flexible semi-parametric form with a general link function. We propose an efficient and practical approach to estimate the single-index link function, single-index coefficients as well as the coefficients in the linear component of the model. The estimation procedure is developed by applying quasi-likelihood and polynomial spline smoothing. We derive large sample properties of the estimators and show the convergence rate of each component of the model. Asymptotic normality and semiparametric efficiency are established for the coefficients in both the single-index and linear components. By making use of spline basis approximation and Fisher score iteration, our approach has numerical advantages in terms of computing efficiency and stability in practice. Both simulated and real data examples are used to illustrate our proposed methodology.

Simultaneous inference for the mean of repeated functional data

Abstract Motivated by recent works studying the longitudinal diffusion tensor imaging (DTI) studies, we develop a novel procedure to construct simultaneous confidence bands for mean functions of repeatedly observed functional data. A fully nonparametric method is proposed to estimate the mean function and variance–covariance function of the repeated trajectories via polynomial spline smoothing. The proposed confidence bands are shown to be asymptotically correct by taking into account the correlation of trajectories within subjects. The procedure is also extended to the two-sample case in which we focus on comparing the mean functions from two populations of functional data. We show the finite-sample properties of the proposed confidence bands by simulation studies, and compare the performance of our approach with the “naive” method that assumes the independence within the repeatedly observed trajectories. The proposed method is applied to the DTI study.

M-based simultaneous inference for the mean function of functional data

Estimating and constructing a simultaneous confidence band for the mean function in the presence of outliers is an important problem in the framework of functional data analysis. In this paper, we propose a robust estimator and a robust simultaneous confidence band for the mean function of functional data using M-estimation and B-splines. The robust simultaneous confidence band is also extended to the difference of mean functions of two populations. Further, the asymptotic properties of the M-based mean function estimator, such as the asymptotic consistency and asymptotic normality, are studied. The performance of the proposed robust methods and their robustness are demonstrated with an extensive simulation study and two real data examples.

Multivariate semiparametric spatial methods for imaging data

Univariate semiparametric methods are often used in modeling nonlinear age trajectories for imaging data, which may result in efficiency loss and lower power for identifying important age-related effects that exist in the data. As observed in multiple neuroimaging studies, age trajectories show similar nonlinear patterns for the left and right corresponding regions and for the different parts of a big organ such as the corpus callosum. To incorporate the spatial similarity information without assuming spatial smoothness, we propose a multivariate semiparametric regression model with a spatial similarity penalty, which constrains the variation of the age trajectories among similar regions. The proposed method is applicable to both cross-sectional and longitudinal region-level imaging data. We show the asymptotic rates for the bias and covariance functions of the proposed estimator and its asymptotic normality. Our simulation studies demonstrate that by borrowing information from similar regions, the proposed spatial similarity method improves the efficiency remarkably. We apply the proposed method to two neuroimaging data examples. The results reveal that accounting for the spatial similarity leads to more accurate estimators and better functional clustering results for visualizing brain atrophy pattern.Functional clustering; Longitudinal magnetic resonance imaging (MRI); Penalized B-splines; Region of interest (ROI); Spatial penalty.

Abstract A6: A global sensitivity test for evaluating hypotheses with non- and weakly identifiable statistical models: An application to breast cancer outcomes

Background and objectives: Motivated from a study on breast cancer, we consider the problem of evaluating a statistical hypothesis when some model characteristics are potentially non or weakly identifiable from observed data. Such scenarios are common in longitudinal studies for evaluating a covariate effect when dropouts may be informative. The hypothesis related to treatment effects may not be testable nonparametrically, with untestable model restrictions necessary for inference. A popular approach is to assume a finite dimensional model and to fix a minimal set of parameters, called sensitivity parameters, conditional upon which hypothesized parameters are assumed identifiable. These profile models, viewed as a functional of the secondary or sensitivity parameters, form the basis of sensitivity analysis. In the current literature, however, inference regarding significance of the covariates is ad hoc, ignoring that multiple tests are conducted and that the working model may be misspecified. Methods and results: In this paper, we propose conservatively testing the null hypothesis of interest across the support of the sensitivity parameters using an infimum test statistic. The test must account for the facts that inferences are carried out simultaneously across the entire range of the sensitivity parameters and that the model may be misspecified under certain values of the sensitivity parameters, as might occur if a nonignorable model is fit, when, in reality, missingness is ignorable. We characterize the limiting distribution of the statistic as a functional of processes in the sensitivity parameters, which involves a careful theoretical analysis of its behavior under model misspecification. In practice, we suggest a simple yet flexible resampling procedure to implement the infimum test as well as to construct confidence bands for simultaneous pointwise tests across all values of the sensitivity parameters. The methodology9s practical utility is illustrated in simulations and an analysis of quality-of-life outcomes from a longitudinal study on breast cancer. Interestingly in this example, a covariate effect on cancer outcomes is detected over a wide range of the sensitivity parameter when a Wald test that assumes identifiability fails. Implications and next steps: The key implication of this work is that the hypothesis of interest can be conservatively evaluated across the support of the sensitivity parameters using an infimum test statistic over the space of these parameters. A key assumption of this paper is that the working model is finite dimensional although the full specification of distribution of the data is not required. The methodology should be broadly applicable to infinite dimensional models, such as survival models for censored data. This extension is the focus of current research work. Citation Information: Cancer Epidemiol Biomarkers Prev 2011;20(10 Suppl):A6.