Robust modal estimation and variable selection for single-index varying-coefficient models

In this article, we present a new efficient iteration estimation approach based on local modal regression for single-index varying-coefficient models. The resulted estimators are shown to be robust with regardless of outliers and error distributions. The asymptotic properties of the estimators are established under some regularity conditions and a practical modified EM algorithm is proposed for the new method. Moreover, to achieve sparse estimator when there exists irrelevant variables in the index parameters, a variable selection procedure based on SCAD penalty is developed to select significant parametric covariates and the well-known oracle properties are also derived. Finally, some numerical examples with various distributed errors and a real data analysis are conducted to illustrate the validity and feasibility of our proposed method.     

A note on efficient simulation of multidimensional spatial autoregressive processes

In applications of spatial statistics, it is necessary to compute the product of some matrix W of spatial weights and a vector y of observations. The weighting matrix often needs to be adapted to the specific problems, such that the computation of Wy cannot necessarily be done with available R-packages. Hence, this article suggests one possibility treating such issues. The proposed technique avoids the computation of the matrix product by calculating each entry of Wy separately. Initially, a specific spatial autoregressive process is introduced. The performance of the proposed program is briefly compared to a basic program using the matrix multiplication.     

Variable selection for semiparametric proportional hazards model under progressive Type-II censoring

Variable selection is an effective methodology for dealing with models with numerous covariates. We consider the methods of variable selection for semiparametric Cox proportional hazards model under the progressive Type-II censoring scheme. The Cox proportional hazards model is used to model the influence coefficients of the environmental covariates. By applying Breslow’s “least information” idea, we obtain a profile likelihood function to estimate the coefficients. Lasso-type penalized profile likelihood estimation as well as stepwise variable selection method are explored as means to find the important covariates. Numerical simulations are conducted and Veteran’s Administration Lung Cancer data are exploited to evaluate the performance of the proposed method.     

Bayesian parameter inference for stochastic SIR epidemic model with hyperbolic diffusion

This paper is concerned with the Bayesian estimation parameters of the stochastic SIR (Susceptible-Infective-Removed) epidemic model from the trajectory data. Specifically, the data from the count of both infectives and susceptibles is assumed to be available on some time grid as the epidemic progresses. The diffusion approximation of the appropriate jump process is then used to estimate missing data between every pair of observation times. If the time step of imputations is small enough, we derive the posterior distributions of the infection and recovery rates using the Milstein scheme. The paper also presents Markov-chain Monte Carlo (MCMC) simulation that demonstrates that the method provides accurate estimates, as illustrated by the synthetic data from SIR epidemic model and the real data.     

t-Type corrected-loss estimation for error-in-variable model

In this article, we consider a linear model in which the covariates are measured with errors. We propose a t-type corrected-loss estimation of the covariate effect, when the measurement error follows the Laplace distribution. The proposed estimator is asymptotically normal. In practical studies, some outliers that diminish the robustness of the estimation occur. Simulation studies show that the estimators are resistant to vertical outliers and an application of 6-minute walk test is presented to show that the proposed method performs well.     

Bootstrap forecast intervals for asymmetric volatilities via EGARCH model

Bootstrap forecast intervals are developed for volatilities having asymmetric features, which are accounted for by fitting EGARCH models. A Monte-Carlo simulation compares the proposed forecast intervals with those based on GARCH fittings which ignore asymmetry. The comparison reveals substantial advantage of addressing asymmetry through EGARCH fitting over ignoring it as the conventional GARCH forecast. The EGARCH forecast intervals have empirical coverage probabilities closer to the nominal level and/or have shorter average lengths than the GARCH forecast intervals. The finding is also supported by real dataset analysis of Dow–Jones index and financial times stock exchange (FTSE) 100 index.