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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

We consider the problem of estimating a regression function from anonymized data in the framework of local differential privacy. We propose a novel partitioning estimate of the regression function, derive a rate of convergence for the excess prediction risk over H\"older classes, and prove a matching lower bound. In contrast to the existing literature on the problem the so-called strong density assumption on the design distribution is obsolete., Comment: Revised version

Sliced inverse regression (SIR, Li 1991) is a pioneering work and the most recognized method in sufficient dimension reduction. While promising progress has been made in theory and methods of high-dimensional SIR, two remaining challenges are still nagging high-dimensional multivariate applications. First, choosing the number of slices in SIR is a difficult problem, and it depends on the sample size, the distribution of variables, and other practical considerations. Second, the extension of SIR from univariate response to multivariate is not trivial. Targeting at the same dimension reduction subspace as SIR, we propose a new slicing-free method that provides a unified solution to sufficient dimension reduction with high-dimensional covariates and univariate or multivariate response. We achieve this by adopting the recently developed martingale difference divergence matrix (MDDM, Lee & Shao 2018) and penalized eigen-decomposition algorithms. To establish the consistency of our method with a high-dimensional predictor and a multivariate response, we develop a new concentration inequality for sample MDDM around its population counterpart using theories for U-statistics, which may be of independent interest. Simulations and real data analysis demonstrate the favorable finite sample performance of the proposed method.

Directional tests to compare incomplete undirected graphs are developed in the general context of covariance selection for Gaussian graphical models. The exactness of the underlying saddlepoint approximation is proved for chordal graphs and leads to exact control of the size of the tests, given that the only approximation error involved is due to the numerical calculation of two scalar integrals. Although exactness is not guaranteed for non-chordal graphs, the ability of the saddlepoint approximation to control the relative error leads the directional test to overperform its competitors even in these cases. The accuracy of our proposal is verified by simulation experiments under challenging scenarios, where inference via standard asymptotic approximations to the likelihood ratio test and some of its higher-order modifications fails. The directional approach is used to illustrate the assessment of Markovian dependencies in a dataset from a veterinary trial on cattle. A second example with microarray data shows how to select the graph structure related to genetic anomalies due to acute lymphocytic leukemia.

Time series regression models are commonly used in time series analysis. However, in modern real-world applications, serially correlated data with an ultra-high dimension and fat tails are prevalent. This presents a challenge in developing new statistical tools for time series analysis. In this paper, we propose a novel Bernstein-type inequality for high-dimensional linear processes and apply it to investigate two high-dimensional robust estimation problems: (1) time series regression with fat-tailed and correlated covariates and errors, and (2) fat-tailed vector autoregression. Our proposed approach allows for exponential increases in dimension with sample size under mild moment and dependence conditions, while ensuring consistency in the estimation process.

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

Posterior distributions for community structure in sparse planted bi-section models are shown to achieve exact (resp. almost-exact) recovery, with sharp bounds for the sparsity regimes where edge probabilities decrease as $O(\log(n)/n)$ (resp. $O(1/n)$). Assuming posterior recovery, one may interpret credible sets (resp. enlarged credible sets) as asymptotically consistent confidence sets; the diameters of those credible sets are controlled by the rate of posterior concentration. If credible levels are chosen to grow to one quickly enough, corresponding credible sets can be interpreted as frequentist confidence sets without conditions on posterior concentration. In the regimes with $O(1/n)$ edge sparsity, or when within-community and between-community edge probabilities are very close, credible sets may be enlarged to achieve frequentist asymptotic coverage, also without conditions on posterior concentration., 29 pp., 3 fig

We offer a new perspective on risk aggregation with FGM copulas. Along the way, we discover new results and revisit existing ones, providing simpler formulas than one can find in the existing literature. This paper builds on two novel representations of FGM copulas based on symmetric multivariate Bernoulli distributions and order statistics. First, we detail families of multivariate distributions with closed-form solutions for the cumulative distribution function or moments of the aggregate random variables. We order aggregate random variables under the convex order and provide methods to compute the cumulative distribution function of aggregate rvs when the marginals are discrete. Finally, we discuss risk-sharing and capital allocation, providing numerical examples for each.

We extend the theoretical results for any FOU(p) processes for the case in which the Hurst parameter is less than 1/2 and we show theoretically and by simulations that under some conditions on T and the sample size n it is possible to obtain consistent estimators of the parameters when the process is observed in a discretized and equispaced interval [0, T ]. Also we will show that the FOU(p) processes can be used to model a wide range of time series varying from short range dependence to large range dependence with similar results as the ARMA or ARFIMA models, and in several cases outperforms those. Lastly, we give a way to obtain explicit formulas for the auto-covariance function for any FOU(p) and we present an application for FOU(2) and FOU(3).