The Application and Property of Elastic Net Procedure for Partially Linear Models

Variable selection plays an important role in high-dimensional data analysis.But the high-dimensional data often induces the strongly correlated variables problem,which should be properly handled.In this paper,we propose Elastic Net procedure for partially linear models and prove the group effect of its estimate.A simulation study shows that the Elastic Net procedure deals with the strongly correlated variables problem better than the Lasso,ALasso and the Ridge do.Based on the real world data study,we can get that the Elastic Net procedure is particularly useful when the number of predictors pffis much bigger than the sample size n.

A TOBIN-TYPE ESTIMATE OF CENSORED LINEAR MODELS

The paper presents a two-stage method for estimating the parameters in the censored linear model Y-i = max(0, alpha(o) + X-i'beta(o)), 1 less than or equal to i less than or equal to n. In the first stage the data are grouped in some groups and then some adjustments are made, the results are used in the latter stage to form a Tobin-type estimate. The asymptotic normality of the estimate is proved and some simulations are made.

The 3-Hour-Interval Prediction of Ground-Level Temperature in South Korea Using Dynamic Linear Models

The 3-hour-interval prediction of ground-level temperature from +00 h out to +45 h in South Korea (38 stations) is performed using the DLM (dynamic linear model) in order to eliminate the systematic error of numerical model forecasts. Numerical model forecasts and observations are used as input values of the DLM. According to the comparison of the DLM forecasts to the KFM (Kalman filter model) forecasts with RMSE and bias, the DLM is useful to improve the accuracy of prediction.

EMPIRICAL LIKELIHOOD FOR LINEAR MODELS UNDER m-DEPENDENT ERRORS

In this paper,the empirical likelihood confidence regions for the regression coefficient in a linear model are constructed under m-dependent errors.It is shown that the blockwise empirical likelihood is a good way to deal with dependent samples.

STRONG CONVERGENCE RATES OF SEVERAL ESTIMATORS IN SEMIPARAMETRIC VARYING-COEFFICIENT PARTIALLY LINEAR MODELS

This article is concerned with the estimating problem of semiparametric varyingcoefficient partially linear regression models. By combining the local polynomial and least squares procedures Fan and Huang （2005） proposed a profile least squares estimator for the parametric component and established its asymptotic normality. We further show that the profile least squares estimator can achieve the law of iterated logarithm. Moreover, we study the estimators of the functions characterizing the non-linear part as well as the error variance. The strong convergence rate and the law of iterated logarithm are derived for them, respectively.

EMPIRICAL LIKELIHOOD-BASED INFERENCE IN LINEAR MODELS WITH INTERVAL CENSORED DATA

An empirical likelihood approach to estimate the coefficients in linear model with interval censored responses is developed in this paper. By constructing unbiased transformation of interval censored data,an empirical log-likelihood function with asymptotic X^2 is derived. The confidence regions for the coefficients are constructed. Some simulation results indicate that the method performs better than the normal approximation method in term of coverage accuracies.

THE RELATIVE EFFICIENCIES OF LEAST SQUARES IN LINEAR MODELS

The present paper daisses the relative efficiencies of the least square estimates in linear models. For Gauss-Markoff model: Y=Xe + e E(e)= 0, Cov(e)=V, an new efficiencyo f least square estimate for linearly estimable function c'r is proposed and its lower bound is giv-en. For variance component model: Y=X + e, E(e)=0, Cov(e)=, an new efficiency of least square estimate for linearly estimable function C'r is introduced for the first timeand its lower bound, which is independent of unknown parameters, is also obtained.

Prediction of Typhoon Tracks Using Dynamic Linear Models

This paper presents a study on the statistical forecasts of typhoon tracks. Numerical models have their own systematic errors, like a bias. In order to improve the accuracy of track forecasting, a statistical model called DLM (dynamic linear model) is applied to remove the systematic error. In the analysis of typhoons occurring over the western North Pacific in 1997 and 2000, DLM is useful as an adaptive model for the prediction of typhoon tracks.

Asymptotic Normality of Multi-Dimension Quasi Maximum Likelihood Estimate in Generalized Linear Models withAdaptive Design

We study the quasi likelihood equation in Generalized Linear Models（GLM） with adaptive design ∑（i=1）^n xi（yi-h（x＇iβ））=0, where yi is a q=vector, and xi is a p×q random matrix. Under some assumptions, it is shown that the Quasi- Likelihood equation for the GLM has a solution which is asymptotic normal.

Sieve MLE for Generalized Partial Linear Models with Type Ⅱ Interval-censored Data

This article concerded with a semiparametric generalized partial linear model （GPLM） with the type Ⅱ censored data. A sieve maximum likelihood estimator （MLE） is proposed to estimate the parameter component, allowing exploration of the nonlinear relationship between a certain covariate and the response function. Asymptotic properties of the proposed sieve MLEs are discussed. Under some mild conditions, the estimators are shown to be strongly consistent. Moreover, the estimators of the unknown parameters are asymptotically normal and efficient, and the estimator of the nonparametric function has an optimal convergence rate.

Testing Equality of Nonparametric Functions in Two Partially Linear Models

We propose the test statistic to check whether the nonpararnetric functions in two partially linear models are equality or not in this paper. We estimate the nonparametric function both in null hypothesis and the alternative by the local linear method, where we ignore the parametric components, and then estimate the parameters by the two stage method. The test statistic is derived, and it is shown to be asymptotically normal under the null hypothesis.

Testing Linearity in Functional Partially Linear Models

For the functional partially linear models including flexible nonparametric part and functional linear part,the estimators of the nonlinear function and the slope function have been studied in existing literature.How to test the correlation between response and explanatory variables,however,still seems to be missing.Therefore,a test procedure for testing the linearity in the functional partially linear models will be proposed in this paper.A test statistic is constructed based on the existing estimators of the nonlinear and the slope functions.Further,we prove that the approximately asymptotic distribution of the proposed statistic is a chi-squared distribution under some regularity conditions.Finally,some simulation studies and a real data application are presented to demonstrate the performance of the proposed test statistic.

D-optimal Designs for Multiresponse Linear Models with a Qualitative Factor Under General Covariance Structure

This paper considers a linear regression model involving both quantitative and qualitative factors and an m-dimensional response variable y. The main purpose of this paper is to investigate D-optimal designs when the levels of the qualitative factors interact with the levels of the quantitative factors. Under a general covariance structure of the response vector y, here we establish that the determinant of the information matrix of a product design can be separated into two parts corresponding to the two marginal designs. Moreover, it is also proved that D-optimal designs do not depend on the covariance structure if we assume hierarchically ordered system of regression models.

Testing for Error Correlation in Semi-Functional Linear Models

Existing methods for analyzing semi-functional linear models usually assumed that random errors are not serially correlated or serially correlated with the known order.However,in some applications,these assumptions on random errors may be unreasonable or questionable.To this end,this paper aims at testing error correlation in a semi-functional linear model(SFLM).Based on the empirical likelihood approach,the authors construct an empirical likelihood ratio statistic to test the serial correlation of random errors and identify the order of autocorrelation if the serial correlation holds.The proposed test statistic does not need to estimate the variance as it is data adaptive and possesses the nonparametric version of Wilks'theorem.Simulation studies are conducted to investigate the performance of the proposed test procedure.Two real examples are illustrated by the proposed test method.

Empirical Likelihood for Generalized Linear Models with Longitudinal Data

Generalized linear models are usually adopted to model the discrete or nonnegative responses.In this paper,empirical likelihood inference for fixed design generalized linear models with longitudinal data is investigated.Under some mild conditions,the consistency and asymptotic normality of the maximum empirical likelihood estimator are established,and the asymptotic χ^(2) distribution of the empirical log-likelihood ratio is also obtained.Compared with the existing results,the new conditions are more weak and easy to verify.Some simulations are presented to illustrate these asymptotic properties.

Integrating Multiple Linear Regression and Infectious Disease Models for Predicting Information Dissemination in Social Networks

Social network is the mainstream medium of current information dissemination,and it is particularly important to accurately predict its propagation law.In this paper,we introduce a social network propagation model integrating multiple linear regression and infectious disease model.Firstly,we proposed the features that affect social network communication from three dimensions.Then,we predicted the node influence via multiple linear regression.Lastly,we used the node influence as the state transition of the infectious disease model to predict the trend of information dissemination in social networks.The experimental results on a real social network dataset showed that the prediction results of the model are consistent with the actual information dissemination trends.

Estimation of Daily Global Solar Radiation with Different Sunshine-Based Models for Some Burundian Stations

Sunshine duration (S) based empirical equations have been employed in this study to estimate the daily global solar radiation on a horizontal surface (G) for six meteorological stations in Burundi. Those equations include the Ångström-Prescott linear model and four amongst its derivatives, i.e. logarithmic, exponential, power and quadratic functions. Monthly mean values of daily global solar radiation and sunshine duration data for a period of 20 to 23 years, from the Geographical Institute of Burundi (IGEBU), have been used. For any of the six stations, ten single or double linear regressions have been developed from the above-said five functions, to relate in terms of monthly mean values, the daily clearness index () to each of the next two kinds of relative sunshine duration (RSD): and . In those ratios, G0, S0 and stand for the extraterrestrial daily solar radiation on a horizontal surface, the day length and the modified day length taking into account the natural site’s horizon, respectively. According to the calculated mean values of the clearness index and the RSD, each station experiences a high number of fairly clear (or partially cloudy) days. Estimated values of the dependent variable (y) in each developed linear regression, have been compared to measured values in terms of the coefficients of correlation (R) and of determination (R2), the mean bias error (MBE), the root mean square error (RMSE) and the t-statistics. Mean values of these statistical indicators have been used to rank, according to decreasing performance level, firstly the ten developed equations per station on account of the overall six stations, secondly the six stations on account of the overall ten equations. Nevertheless, the obtained values of those indicators lay in the next ranges for all the developed sixty equations:;;;, with . These results lead to assert that any of the sixty developed linear regressions (and thus equations in terms of and ), fits very adequately measured data, and should be used to estimate monthly average daily global solar radiation with sunshine duration for the relevant station. It is also found that using as RSD, is slightly more advantageous than using for estimating the monthly average daily clearness index, . Moreover, values of statistical indicators of this study match adequately data from other works on the same kinds of empirical equations.

Asymptotic Properties of the Maximum Likelihood Estimate in Generalized Linear Models with Stochastic Regressors

For generalized linear models （GLM）, in case the regressors are stochastic and have different distributions, the asymptotic properties of the maximum likelihood estimate （MLE） β^n of the parameters are studied. Under reasonable conditions, we prove the weak, strong consistency and asymptotic normality of β^n

Semiparametric Empirical Likelihood Estimation for Two-stage Outcome-dependent Sampling under the Frame of Generalized Linear Models

Epidemiologic studies use outcome-dependent sampling （ODS） schemes where, in addition to a simple random sample, there are also a number of supplement samples that are collected based on outcome variable. ODS scheme is a cost-effective way to improve study efficiency. We develop a maximum semiparametric empirical likelihood estimation （MSELE） for data from a two-stage ODS scheme under the assumption that given covariate, the outcome follows a general linear model. The information of both validation samples and nonvalidation samples are used. What is more, we prove the asymptotic properties of the proposed MSELE.

The Superiorities of Bayes Linear Unbiased Estimator in Multivariate Linear Models

In this article, the Bayes linear unbiased estimator （BALUE） of parameters is derived for the multivariate linear models. The superiorities of the BALUE over the least square estimator （LSE） is studied in terms of the mean square error matrix （MSEM） criterion and Bayesian Pitman closeness （PC） criterion.