LIMITING BEHAVIOR OF RECURSIVE M-ESTIMATORS IN MULTIVARIATE LINEAR REGRESSION MODELS AND THEIR ASYMPTOTIC EFFICIENCIES

Recursive algorithms are very useful for computing M-estimators of regression coefficients and scatter parameters. In this article, it is shown that for a nondecreasing ul （t）, under some mild conditions the recursive M-estimators of regression coefficients and scatter parameters are strongly consistent and the recursive M-estimator of the regression coefficients is also asymptotically normal distributed. Furthermore, optimal recursive M-estimators, asymptotic efficiencies of recursive M-estimators and asymptotic relative efficiencies between recursive M-estimators of regression coefficients are studied.

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.

Threshold Signature Scheme with Threshold Verification Based on Multivariate Linear Polynomial

Secret sharing schemes are multi-party protocols related to key establishment. They also facilitate distributed trust or shared control for critical activities (e.g., signing corporate cheques and opening bank vaults), by gating the critical action on cooperation from t(t ∈Z+) of n(n ∈Z+) users. A (t, n) threshold scheme (t < n) is a method by which a trusted party computes secret shares Γi(1 i n) from an initial secret Γ0 and securely distributes Γi to user. Any t or more users who pool their shares may easily recover Γ0, but any group knowing only t-1 or fewer shares may not. By the ElGamal public key cryptophytes and the Schnorr's signature scheme, this paper proposes a new (t,n) threshold signature scheme with (k,m) (k,m ∈Z+) threshold verification based on the multivariate linear polynomial.

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

A matrix Padé-type-Routh model reduction method for multivariable linear systems

In the present paper, the formulae for matrix Padé-type approximation were improved. The mixed model reduction method of matrix Padé-type-Routh for the multivariable linear systems was presented. A well-known example was given to illustrate that the mixed method is efficient.

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.

Statistical approach to determination of overhaul and maintenance cost of loading equipment in surface mining

The purpose of this research was to develop a new approach in determination of overhaul and maintenance cost of loading equipment in surface mining. Two statistical models including univariate exponential regression (UER) and multivariate linear regression (MLR) were used in this study. Loading equipment parameters such as bucket capacity, machine weight, engine power, boom length, digging depth, and dumping height were considered as variables. The results obtained by models and mean absolute error rate indicate that these models can be applied as the useful tool in determination of overhaul and maintenance cost of loading equipment. The results of this study can be used by the decision-makers for the specific surface mining operations.

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).

Patterns of species diversity and its determinants in a temperate deciduous broad-leaved forest

Biodiversity conservation has long been a subject of extreme interest to community ecologists,with a particular focus on exploring the underlying causes of species diversity based on niche and neutral theories.This study aims to identify the potential determinants of species diversity in a deciduous broad-leaved forest in the transitional region from subtropical to temperate climate in China.We collected woody plant data and environmental variables in a fully mapped 25-ha permanent forest plot,partitioned the beta-diversity into local contributions(LCBD)and species contributions(SCBD),and then applied multivariate linear regression analysis to test the effects of biotic and abiotic factors on alpha-diversity,LCBD,and SCBD.We used variation partitioning in combination with environmental variables and spatial distance to determine the contribution of environment-related variations versus spatial variations.Our results showed that the indices of alpha-diversity(i.e.,species abundance and richness)were positively correlated with soil available phosphorus(P)and negatively with slope.For the betadiversity,environment and space together explained nearly half of the variations in community composition.Approximately 60%of the variation of LCBD in the understory layer,40%in the substory layer,and 29%in the canopy layer were jointly explained by topographic,soil and biological variables,with biotic factors playing a dominant role in determining the beta-diversity.Species abundance accounted for a large proportion of the variations in SCBD in each vertical stratum,and niche position(NP)was the ecological trait that significantly affected the variations in SCBD in the substory and canopy layers.Our findings help to gain better understanding on how species diversity in forest ecosystem responds to environmental conditions and how it is influenced by biotic factors and ecological traits of species.

The Time and Cost Prediction of Tunnel Boring Machine in Tunnelling

Making use of microsoft visual studio. net platform, the assistant decision-making system of tunnel boring machine in tunnelling has been built to predict the time and cost. Computation methods of the performance parameters have been discussed. New time and cost prediction models have been depicted. The multivariate linear regression has been used to make the parameters more precise, which are the key factor to affect the prediction near to the reality.

NUMERICAL SIMULATION AND EXPERIMENTAL STUDY OF A KIND OF LOCAL EXHAUST VENTILATION HOOD

A new local exhaust ventilation hood is presented. First, the test system inlaboratory room is established. Secondly a mathematical model is developed in terms of the stokesstream function, and the governing equation is solved using finite-difference techniques. Theinjection flow of the exhaust hood is treated as a boundary condition of the main flow. Experimentsresults well agree with the solution of theoretical prediction. The model can, therefore, be used todesign this kind of Aaberg hood. Thirdly the important parameters affecting the performance ofAaberg exhaust hood are taken into account. In the mean time the connection of these parameters isdeduced by multivariate linear regression based on the experimental results. The work is usefulwhether in designing this kind of local ventilation Aaberg exhaust hood or in predicting the hood'swork performance.

Probability method for cryptanalysis of general multivariate modular linear equation

Finding the solution to a general multivariate modular linear equation plays an important role in cryptanalysis field. Earlier results show that obtaining a relatively short solution is possible in polynomial time. However, one problem arises here that if the equation has a short solution in given bounded range, the results outputted by earlier algorithms are often not the ones we are interested in. In this paper, we present a probability method based on lattice basis reduction to solve the problem. For a general multivariate modular linear equation with short solution in the given bounded range, the new method outputs this short solution in polynomial time, with a high probability. When the number of unknowns is not too large （smaller than 68）, the probability is approximating 1. Experimental results show that Knapsack systems and Lu-Lee type systems are easily broken in polynomial time with this new method.

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.

Southern and Tropical Indian Ocean SST: A Possible Predictor of Winter Monsoon Rainfall over South India

The complexities in the relationship between winter monsoon rainfall (WMR) over South India and Sea Surface temperature (SST) variability in the southern and tropical Indian Ocean (STIO) are evaluated statistically. The data of the time period of our study (1950-2003) have been divided exactly in two halves to identify predictors. Correlation analysis is done to see the effect of STIO SST variability on winter monsoon rainfall index (WMRI) for South India with a lead-lag of 8 seasons (two years). The significant positive correlation is found between Southern Indian Ocean (SIO) SST and WMRI in July-August-September season having a lag of one season. The SST of the SIO, Bay of Bengal and North Equatorial Indian Ocean are negatively correlated with WMRI at five, six and seven seasons before the onset of winter monsoon. The maximum positive correlation of 0.61 is found from the region south of 500 S having a lag of one season and the negative correlations of 0.60, 0.53 and 0.57 are found with the SST of the regions SIO, Bay of Bengal and North Equatorial Ocean having lags of five, six and seven seasons respectively and these correlation coefficients have confidence level of 99%. Based on the correlation analysis, we defined Antarctic Circumpolar Current Index A and B (ACCIA (A) & ACCIB (B)), Bay of Bengal index (BOBI (C)) and North Equatorial Index (NEI (D)) by averageing SST for the regions having maximum correlation (positive or negative) with WMRI index. These SST indices are used to predict the WMRI using linear and multivariate linear regression models. In addition, we also attempted to detect a dynamic link for the predictability of WMRI using Nino 3.4 index. The predictive skill of these indices is tested by error analysis and Willmott’s index.

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.

Efficient Algorithms for Generating Truncated Multivariate Normal Distributions

Sampling from a truncated multivariate normal distribution （TMVND） constitutes the core computational module in fitting many statistical and econometric models. We propose two efficient methods, an iterative data augmentation （DA） algorithm and a non-iterative inverse Bayes formulae （IBF） sampler, to simulate TMVND and generalize them to multivariate normal distributions with linear inequality constraints. By creating a Bayesian incomplete-data structure, the posterior step of the DA Mgorithm directly generates random vector draws as opposed to single element draws, resulting obvious computational advantage and easy coding with common statistical software packages such as S-PLUS, MATLAB and GAUSS. Furthermore, the DA provides a ready structure for implementing a fast EM algorithm to identify the mode of TMVND, which has many potential applications in statistical inference of constrained parameter problems. In addition, utilizing this mode as an intermediate result, the IBF sampling provides a novel alternative to Gibbs sampling and elimi- nares problems with convergence and possible slow convergence due to the high correlation between components of a TMVND. The DA algorithm is applied to a linear regression model with constrained parameters and is illustrated with a published data set. Numerical comparisons show that the proposed DA algorithm and IBF sampler are more efficient than the Gibbs sampler and the accept-reject algorithm.

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.

A Hybrid Dynamical-Statistical Approach for Predicting Winter Precipitation over Eastern China

Correlation analysis revealed that winter precipitation in six regions of eastern China is closely related not only to preceding climate signals but also to synchronous atmospheric general circulation fields. It is therefore necessary to use a method that combines both dynamical and statistical predictions of winter precipitation over eastern China （hereinafter called the hybrid approach）, in this connection, seasonal real-time prediction models for winter precipitation were established for the six regions. The models use both the preceding observations and synchronous numerical predictions through a multivariate linear regression analysis. To improve the prediction accuracy, the systematic error between the original regression model result and the corresponding observation was corrected. Cross-validation analysis and real-time prediction experiments indicate that the prediction models using the hybrid approach can reliably predict the trend, sign, and interannual variation of regionally averaged winter precipitation in the six regions of concern. Averaged over the six target regions, the anomaly correlation coefficient and the rate with the same sign of anomaly between the cross-validation analysis and observation during 1982-2008 are 0.69 and 78%, respectively. This indicates that the hybrid prediction approach adopted in this study is applicable in operational practice.

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.