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This paper provides a new perspective for robust estimation and inference methods based on Huber regression. An efficient distributed learning with sparsity is proposed, in which the observations are randomly divided among different machines. We modify the proximal alternating direction method of multiplies (ADMM) algorithm to calculate the sparse penalized Huber regression. The convergence property of the algorithm is established. Computationally, our proposed approach requires only a central machine to solve a SCAD or adaptive lasso penalized M-estimation problem, and other node machines to calculate gradients based on local datasets. In terms of communication, the estimation error of our method decreases to that of the centralized method in several rounds of communication. Simulation studies are conducted to evaluate the finite-sample performance of our proposed method. The empirical study shows that our method has good practicability in the practice of a Communities and Crime analysis. [ABSTRACT FROM AUTHOR]

Calibration estimation is a popular method for making inference from probability samples and dealing with nonresponse problems. Calibration estimation, specially model-assisted calibration estimation, has been extensively explored for inference from non-probability samples in recent years. When there are rich covariates, the variable selection method such as Adaptive LASSO can be used to select important covariates and estimate model parameters for establishing appropriate models in model-assisted calibration estimation. In addition to the established model, distance functions also have an impact on calibration estimation. Different distance functions may produce different calibration estimators. In this paper, traditional calibration estimators, estimated-control model-assisted calibration estimators and estimated-control model-assisted calibration estimators with Adaptive LASSO under the chi-square distance and the modified backward Kullback-Leibler distance are proposed when the population information of covariates is unknown. The calibrated weights based on traditional calibration, model-assisted calibration and model-assisted calibration with Adaptive LASSO under the two distance functions are also derived. Results from a simulation study are presented to compare different calibration estimators. A real data set is also adopted to confirm the performance of the proposed estimators. [ABSTRACT FROM AUTHOR]

To reduce the cost and improve the efficiency of cohort studies, case-cohort design is a widely used biased-sampling scheme for time-to-event data. In modeling process, we may encounter the situation that actual covariates are not directly observed, but are contaminated with a multiplicative factor which is determined by a smooth unknown function of an observed covariate. In this paper, we study the inference methods for case-cohort data under the additive hazards model with covariate adjustment. We propose to estimate the distorting function by nonparametric regressing the contaminated covariates on the distorting factor. The estimators for the parameters can then be obtained based on the estimated covariates. A series of simulation studies are conducted to assess the finite-sample performance of the proposed estimator. An application to a pulmonary exacerbation study demonstrates the practicability of the proposed methods. [ABSTRACT FROM AUTHOR]

Ladder type disc acoustic radiator is widely used in high power ultrasonic field. The frequency equation of stepped thickness disk in free boundary condition are derived based on Mindlin theory from the acoustic point of application and The frequency equation was numerically solved,At the same time,the effects of geometric parameters on the frequency is analyzed. The results show that when the other parameters are constant,the frequency increases with the increase of the disk and the base ring thickness,and decreases with the diameter increases,increases with the increasing diameter. The test results of the calculated frequencies and finite element simulation and experiment is consistent with the basic. Design of bending vibration radiator the conclusion of the thick disc provides the theory reference and the frequency of debugging basis.

The case-cohort design is used in large cohort study to improve the efficiency and reduce the cost. In modeling process, we meet the situation that some covariates in a regression model are distorted by an unknown function of an observable confounding variable in a multiplicative form. In this paper, we consider fitting covariate-adjusted proportional hazards model for case-cohort studies. We propose to estimate the distorted function by non parametrically regressing the observed covariates on the distorted confounder, and then an estimator for the regression parameter is obtained by using the estimated covariates. Under some mild assumptions, we establish the asymptotic properties of the proposed estimator. The results from both artificial and real data demonstrate good performance and practicality of the proposed method. [ABSTRACT FROM AUTHOR]

When covariate information is collected through opinion surveys, experimental science, medical research and so on, incomplete records may result in missing information. Expectile regression is used in many fields; however, many fewer developments have been made with expectile regression for data with missing information. In this paper, we develop a weighted expectile regression approach for estimating the conditional expectile when covariates are missing at random (MAR). The asymptotic normality of the proposed weighted estimators is established. A proximal alternating direction method of multipliers (pADMM) algorithm is developed for the calculation of the weighted estimator. Simulation studies are conducted to assess the finite-sample performance of the proposed method. We illustrate the application of the method by analyzing a real data set from Beijing Olympic sports center monitoring stations. [ABSTRACT FROM AUTHOR]

With the extensive application of high-dimensional heterogeneous data in various disciplines, sparse expectile regression is increasingly favoured by people. In this paper, we make use of the graphical structure among predictors node-by-node to improve the performance of parameter estimation, model selection and prediction in sparse expectile regression. A modified alternating direction method of multipliers (ADMM) algorithm with a linearization trick is proposed to implement the proposed method numerically, and the convergence of the algorithm is proved. Simulation studies are conducted to evaluate the finite-sample performance of the proposed method. We demonstrate the practicability of the proposed approach with a dataset of the expression quantitative trait locus mapping (eQTL) experiment in Rattus norvegicus. [ABSTRACT FROM AUTHOR]

To reduce the cost and improve the efficiency of studies, the generalized case-cohort design, in which the risk-factors include the subcohort members sampled by simple random sample from the full cohort, augmented with another subset sampled from the failure of interest outside the subcohort, has been widely used in many prevention trials and epidemiological cohort studies. In modeling process, including prior information about the parameters into consideration can further improve the study efficiency. In this article, regression analysis of Cox's model with parameter constraints under the generalized case-cohort design is studied. A working likelihood function is constructed for the estimation of the model parameters. The asymptotic properties of the constrained estimation are derived by using the Karush-Kuhn-Tucker conditions. A constrained minorization-maximization algorithm is developed for the calculation of the constrained estimator. Simulation studies are conducted to evaluate the finite-sample performance of our proposed estimator. We demonstrate the practicability of the proposed approach with a data set from a Wilms tumor study. [ABSTRACT FROM AUTHOR]