Counting data without zero category often occurs in many fields, such as social studies, clinical trials and economic phenomenon analyses. Researchers usually show interest in describing the characteristics of the observed counts and the Poisson distribution is often preferred to model the counted data. Nevertheless, making marginal inference on the population mean is a challenging job when missing zero class occurs and the Poisson mean is considered as an alternative. In this paper, based on a so-called marginalized zero-truncated Poisson (ZTP) regression model, a novel SR-based EM-FS algorithm is proposed to facilitate parameter estimation. To improve the prediction accuracy, this paper proposes a zero-truncated Poisson model averaging prediction that selects the optimal weight combination by minimizing a Kullback–Leibler (KL) divergence criterion. It is shown that the weight criterion is approximately unbiased about the expected KL loss. We further prove that the proposed prediction is asymptotically optimal in the sense that the KL-type loss and prediction risk are asymptotically identical to those of the infeasible best possible averaged prediction. Simulations and two empirical data applications are conducted to illustrate the proposed method.
Spatio-temporal data analysis is an emerging research area due to the development and application of novel computational techniques allowing for the analysis of large spatio-temporal databases. We consider a general class of spatio-temporal linear models, where the number of structural breaks can tend to infinity. A procedure for simultaneously detecting all the change points is developed rigorously via the construction of adaptive group lasso penalty. Consistency of the multiple change point estimation is established under mild technical conditions even when the true number of change points
Feature selection is a changing issue for varying coefficient models when the dimensionality of covariates is ultrahigh. The traditional technology of significantly reducing dimensionality is the marginal correlation screening method based on nonparametric smoothing. However, marginal correlation screening methods may be screen out variables that are jointly correlated to the response. To address this, we propose a novel screener with the name of group screening via nonparametric smoothing high-dimensional ordinary least squares projection, referred to as “Group HOLP” and study its sure screening property. Based on this nice property, we introduce a refined feature selection procedure via employing the extended Bayesian information criteria (EBIC) to select the suitable submodels in varying coefficient models, which is coined as Group HOLP-EBIC method. Under some regularity conditions, we establish the strong consistency of feature selection for the proposed method. The performance of our method is evaluated by simulations and further illustrated by two real examples.
For any minimal system (X, T) and
The theory of tetragonal curves is first applied to the study of discrete integrable systems. Based on the discrete Lenard equation, we derive a hierarchy of extended Volterra lattices associated with the discrete
Federated learning has become a popular tool in the big data era nowadays. It trains a centralized model based on data from different clients while keeping data decentralized. In this paper, we propose a federated sparse sliced inverse regression algorithm for the first time. Our method can simultaneously estimate the central dimension reduction subspace and perform variable selection in a federated setting. We transform this federated high-dimensional sparse sliced inverse regression problem into a convex optimization problem by constructing the covariance matrix safely and losslessly. We then use a linearized alternating direction method of multipliers algorithm to estimate the central subspace. We also give approaches of Bayesian information criterion and holdout validation to ascertain the dimension of the central subspace and the hyper-parameter of the algorithm. We establish an upper bound of the statistical error rate of our estimator under the heterogeneous setting. We demonstrate the effectiveness of our method through simulations and real world applications.
As an important extension of the varying-coefficient model, the partially linear varying-coefficient model has been widely studied in the literature. It is vital that how to simultaneously eliminate the redundant covariates and separate the varying and nonzero constant coefficients for varying-coefficient models. In this paper, we consider the penalized composite quantile regression to explore the model structure of ultra-high-dimensional varying-coefficient models. Under some regularity conditions, we study the convergence rate and asymptotic normality of the oracle estimator and prove that, with probability approaching one, the oracle estimator is a local solution of the nonconvex penalized composite quantile regression. Simulation studies indicate that the novel method as well as the oracle method performs in both low dimension and high dimension cases. An environmental data application is also analyzed by utilizing the proposed procedure.
Backward doubly stochastic integral equations of the Volterra type (BDSIEVs in short) are observed in this paper. Existence of M-solution established under functional Lipschitz assumptions. Duality principle between linear BDSIEVs and (forward) stochastic Volterra integral equations is obtained. Using duality principle, the comparison theorem for the adapted solutions of BDSIEVs is proven.