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Blockwise missing data occurs frequently when we integrate multisource or multimodality data where different sources or modalities contain complementary information. In this paper, we consider a high-dimensional linear regression model with blockwise missing covariates and a partially observed response variable. Under this framework, we propose a computationally efficient estimator for the regression coefficient vector based on carefully constructed unbiased estimating equations and a blockwise imputation procedure, and obtain its rate of convergence. Furthermore, building upon an innovative projected estimating equation technique that intrinsically achieves bias-correction of the initial estimator, we propose a nearly unbiased estimator for each individual regression coefficient, which is asymptotically normally distributed under mild conditions. Based on these debiased estimators, asymptotically valid confidence intervals and statistical tests about each regression coefficient are constructed. Numerical studies and application analysis of the Alzheimer's Disease Neuroimaging Initiative data show that the proposed method performs better and benefits more from unsupervised samples than existing methods., Comment: V2: 40 pages, 2 figures. Accepted at Statistica Sinica

The distribution of the incubation period of the novel coronavirus disease that emerged in 2019 (COVID-19) has crucial clinical implications for understanding this disease and devising effective disease-control measures. Qin et al. (2020) designed a cross-sectional and forward follow-up study to collect the duration times between a specific observation time and the onset of COVID-19 symptoms for a number of individuals. They further proposed a mixture forward-incubation-time epidemic model, which is a mixture of an incubation-period distribution and a forward time distribution, to model the collected duration times and to estimate the incubation-period distribution of COVID-19. In this paper, we provide sufficient conditions for the identifiability of the unknown parameters in the mixture forward-incubation-time epidemic model when the incubation period follows a two-parameter distribution. Under the same setup, we propose a likelihood ratio test (LRT) for testing the null hypothesis that the mixture forward-incubation-time epidemic model is a homogeneous exponential distribution. The testing problem is non-regular because a nuisance parameter is present only under the alternative. We establish the limiting distribution of the LRT and identify an explicit representation for it. The limiting distribution of the LRT under a sequence of local alternatives is also obtained. Our simulation results indicate that the LRT has desirable type I errors and powers, and we analyze a COVID-19 outbreak dataset from China to illustrate the usefulness of the LRT., 34 pages, 2 figures, 2 tables