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.

All Admissible Linear Estimators under Quadratic Loss in Multivariate Model

For multivariate linear model Y=XΘ+ε, ~N(0, σ 2ΣV), this paper is concerned with the admissibility of linear estimators of estimable function SXΘ in the class of all estimators. All admissible linear estimators of SXΘ are given under each of four definitions of admissibility.

THE COMPRESSION LS ESTIMATE OF REGRESSION COEFFICIENT IN MULTIVARIATE LINEAR MODEL

In this paper, compression LS estimate (k) of the regression coefficient B isconsidered when the design matrix present ill-condition in multivariate linear model.The MSE (mean square error)of the estimate(k)=Vec( (k))is less than theMSE of LS estimate β￣* of the regression coefficient β= Vec(B) by choosing the pa-rameter k. Admissibility , numerical stability and relative efficiency of (k)are proved. The method of determining k value for practical use is also suggested

Some Asymptotic Properties for Multivariate Partially Linear Models

The paper considers a multivariate partially linear model under independent errors,and investigates the asymptotic bias and variance-covariance for parametric component βand nonparametric component F（·）by the GJS estimator and Kernel estimation.

Admissibilty for Nonhomogeneous Linear Estimates on Multivariate Random Regression Coefficients and Parameters

In this paper,we consider the admissibility for nonhomogeneous linear estimates on regression coefficients and parameters in multivariate random effect linear model and give eight definitions of different forms for admissibility. We not only prove that they can be divided into three identical subclasses,but also gain three kinds of necessary and sufficient conditions.

Artificial neural network models predicting the leaf area index:a case study in pure even-aged Crimean pine forests from Turkey

Background: Leaf Area Index(LAI) is an important parameter used in monitoring and modeling of forest ecosystems. The aim of this study was to evaluate performance of the artificial neural network(ANN) models to predict the LAI by comparing the regression analysis models as the classical method in these pure and even-aged Crimean pine forest stands.Methods: One hundred eight temporary sample plots were collected from Crimean pine forest stands to estimate stand parameters. Each sample plot was imaged with hemispherical photographs to detect the LAI. The partial correlation analysis was used to assess the relationships between the stand LAI values and stand parameters, and the multivariate linear regression analysis was used to predict the LAI from stand parameters. Different artificial neural network models comprising different number of neuron and transfer functions were trained and used to predict the LAI of forest stands.Results: The correlation coefficients between LAI and stand parameters(stand number of trees, basal area, the quadratic mean diameter, stand density and stand age) were significant at the level of 0.01. The stand age, number of trees, site index, and basal area were independent parameters in the most successful regression model predicted LAI values using stand parameters(R_(adj)~2=0.5431). As corresponding method to predict the interactions between the stand LAI values and stand parameters, the neural network architecture based on the RBF 4-19-1 with Gaussian activation function in hidden layer and the identity activation function in output layer performed better in predicting LAI(SSE(12.1040), MSE(0.1223), RMSE(0.3497), AIC(0.1040), BIC(-77.7310) and R^2(0.6392)) compared to the other studied techniques.Conclusion: The ANN outperformed the multivariate regression techniques in predicting LAI from stand parameters. The ANN models, developed in this study, may aid in making forest management planning in study forest stands.

SELECTING AN ADAPTIVE SEQUENCE FOR COMPUTING RECURSIVE M-ESTIMATORS IN MULTIVARIATE LINEAR REGRESSION MODELS

In this paper, the authors consider an adaptive recursive algorithm by selecting an adaptive sequence for computing M-estimators in multivariate linear regression models. Its asymptotic property is investigated. The recursive algorithm given by Miao and Wu （1996） is modified accordingly. Simu- lation studies of the Mgorithm is also provided. In addition, the Newton-Raphson iterative algorithm is considered for the purpose of comparison.

SOME PROPERTIES OF ROSEN’S MLE FOR GENERAL DISTRIBUTIONS

Von Rosen (1989) proposed the MLE of parameters in multivariate linear normal model MLNM(sumfromn= lto ∞AiBiCi). This paper discusses some properties of Rosen's MLE for general distributions which includs invariant, equivariant, strong consistency and asymptotic normality. Furthermore, we can construct the consistent confidence region for the parameter of experctation in MLNM(sumfromn=1to∞, AiBiCi) and obtain asymptotic distribu- tion and consistent confidence region of the linear discrimination function for canonical correlation by Kahtri (1988).

EMPIRICAL LIKELIHOOD CONFIDENCE REGION FOR PARAMETERS IN LINEAR ERRORS-IN-VARIABLES MODELS WITH MISSING DATA

The multivariate linear errors-in-variables model when the regressors are missing at random in the sense of Rubin （1976） is considered in this paper. A constrained empirical likelihood confidence region for a parameter β0 in this model is proposed, which is constructed by combining the score function corresponding to the weighted squared orthogonal distance based on inverse probability with a constrained region of β0. It is shown that the empirical log-likelihood ratio at the true parameter converges to the standard chi-square distribution. Simulations show that the coverage rate of the proposed confidence region is closer to the nominal level and the length of confidence interval is narrower than those of the normal approximation of inverse probability weighted adjusted least square estimator in most cases. A real example is studied and the result supports the theory and simulation＇s conclusion.

Data Fusion about Serviceability Reliability Prediction for the Long-Span Bridge Girder Based on MBDLM and Gaussian Copula Technique

This article presented a new data fusion approach for reasonably predicting dynamic serviceability reliability of the long-span bridge girder.Firstly,multivariate Bayesian dynamic linear model(MBDLM)considering dynamic correlation among the multiple variables is provided to predict dynamic extreme deflections;secondly,with the proposed MBDLM,the dynamic correlation coefficients between any two performance functions can be predicted;finally,based on MBDLM and Gaussian copula technique,a new data fusion method is given to predict the serviceability reliability of the long-span bridge girder,and the monitoring extreme deflection data from an actual bridge is provided to illustrated the feasibility and application of the proposed method.

Some Convergence Properties for Weighted Sums of Martingale Difference Random Vectors

Let{X_(ni),F_(ni);1≤i≤n,n≥1}be an array of R^(d)martingale difference random vectors and{A_(ni),1≤i≤n,n≥1}be an array of m×d matrices of real numbers.In this paper,the Marcinkiewicz-Zygmund type weak law of large numbers for maximal weighted sums of martingale difference random vectors is obtained with not necessarily finite p-th(1<p<2)moments.Moreover,the complete convergence and strong law of large numbers are established under some mild conditions.An application to multivariate simple linear regression model is also provided.

Spatio-temporal variation prediction on Cd content in the rice grains from Northern Zhejiang Plain during 2014–2019 based on high-precision soil geochemical data

In recent years,Cadmium(Cd)pollution has been found in many soil geochemical surveys in Northern Zhejiang Plain,a crucial rice production area in East China,located in the lower Yangtze River.To more scientifically predict the effect of soil Cd on rice safety,data including 348 local rhizosphere soil-rice samples obtained in 2014 were used in this study.Meanwhile,we extracted 90% of random samples as variables based on soil Cd content(Cd_(soil)),soil organic matter(SOM),pH,and other indicators.In addition,a multivariate linear model for rice Cd content(Cd_(rice))prediction based on the indicators including the soil Cd content(Cd_(soil)),the soil organic matter(SOM),and the pH value.The remaining 10%of random samples were used for the significance test.Based on the 2014 soil Cd content(Cd_(soil14))and the 2019 soil Cd content(Cd_(soil19)),this study predicted Cd content in 2019 rice grains(Cd_(p-rice19)).The spatio-temporal variation of Cdrice was contrasted in the five years from 2014 to 2019,and the risk areas of rice safety production were analyzed using the Geographical Information System(GIS).The results indicated that compared with the actual Cd content in 2014 rice grains(Cdrice14),the proportion of Cd_(p-rice19),which exceeded the standard food level in China(GB2762-2017),increased dramatically.Moreover,the high-value areas of Cdrice distributed greatly coincidentally in these two years.By contrast,both Cdrice and Cdsoil show very different spatial scales.The dominant reason is the distribution of the local canal systems,indicating that economic activities and agricultural irrigation may aggravate the risk of soil Cd pollution,thus threatening safe rice production.

The relationship between time to a high COVID-19 response level and timing of peak daily incidence:an analysis of governments’Stringency Index from 148 countries

Background The transmission dynamics and severity of coronavirus disease 2019(COVID-19)pandemic is different across countries or regions.Differences in governments’policy responses may explain some of these differences.We aimed to compare worldwide government responses to the spread of COVID-19,to examine the relationship between response level,response timing and the epidemic trajectory.Methods Free publicly-accessible data collected by the Coronavirus Government Response Tracker(OxCGRT)were used.Nine sub-indicators reflecting government response from 148 countries were collected systematically from January 1 to May 1,2020.The sub-indicators were scored and were aggregated into a common Stringency Index(SI,a value between 0 and 100)that reflects the overall stringency of the government’s response in a daily basis.Group-based trajectory modelling method was used to identify trajectories of SI.Multivariable linear regression models were used to analyse the association between time to reach a high-level SI and time to the peak number of daily new cases.Results Our results identified four trajectories of response in the spread of COVID-19 based on when the response was initiated:before January 13,from January 13 to February 12,from February 12 to March 11,and the last stage—from March 11(the day WHO declared a pandemic of COVID-19)on going.Governments’responses were upgraded with further spread of COVID-19 but varied substantially across countries.After the adjustment of SI level,geographical region and initiation stages,each day earlier to a high SI level(SI>80)from the start of response was associated with 0.44(standard error:0.08,P<0.001,R2=0.65)days earlier to the peak number of daily new case.Also,each day earlier to a high SI level from the date of first reported case was associated with 0.65(standard error:0.08,P<0.001,R2=0.42)days earlier to the peak number of daily new case.Conclusions Early start of a high-level response to COVID-19 is associated with early arrival of the peak number of daily new cases.This may help to reduce the delays in flattening the epidemic curve to the low spread level.

THE APPLICATION OF COBB-DOUGLAS FUNCTION IN FORECASTING THE DURATION OF INTERNET PUBLIC OPINIONS CAUSED BY THE FAILURE OF PUBLIC POLICIES

Gushes of Internet public opinions may trigger unexpected incidents that significantly affectsocial security and stability, especially for ones caused by the failure of public policies. Therefore,forecasting this kind of Interact public opinions is of great significance. The duration could be citedas one of the most direct indicators that can reflect the severity of a specific Internet public opinioncase. Based on this background, this paper aims to find the factors that may affect the duration of Internet public opinions, and accordingly proposes a model that can accurately predict the durationbefore the release of public policies. Specifically, an index system including 8 factors by consideringfour dimensions, namely, object, environment, reality （offline）, and the network （online）, isestablished. In addition, based on the dataset containing 23 typical Internet public opinion casescaused by the failure of public policies, 9 prediction models are gained by applying the multivariatelinear regression model, multivariate nonlinear regression model, and the Cobb-Douglas function.