THE SUPERIORITY OF EMPIRICAL BAYES ESTIMATION OF PARAMETERS IN PARTITIONED NORMAL LINEAR MODEL

In this article,the empirical Bayes（EB）estimators are constructed for the estimable functions of the parameters in partitioned normal linear model.The superiorities of the EB estimators over ordinary least-squares（LS）estimator are investigated under mean square error matrix（MSEM）criterion.

Analysis of forest cover change at Khadimnagar National Park, Sylhet,Bangladesh, using Landsat TM and GIS data

We mapped the forest cover of Khadimnagar National Park （KNP） of Sylhet Forest Division and estimated forest change over a period of 22 years （1988-2010） using Landsat TM images and other GIS data. Supervised classification and Normalized Difference Vegetation Index （NDVI） image classification approaches were applied to the images to produce three cover classes, viz. dense forest, medium dense forest, and bare land. The change map was produced by differencing classified imageries of 1988 and 2010 as before image and after image, respectively, in ERDAS IMAGINE. Error matrix and kappa statistics were used to assess the accuracy of the produced maps. Overall map accuracies resulting from supervised classification of 1988 and 2010 imageries were 84.6% （Kappa 0.75） and 87.5% （Kappa 0.80）, respec- tively. Forest cover statistics resulting from supervised classification showed that dense forest and bare land declined from 526 ha （67%） to 417 ha （59%） and 105 ha （13%） to 8 ha （1%）, respectively, whereas medium dense forest increased from 155 ha （20%） to 317 ha （40%）. Forest cover change statistics derived from NDVI classification showed that dense forest declined from 525 ha （67%） to 421 ha （54%） while medium dense forest increased from 253 ha （32%） to 356 ha （45%）. Both supervised and NDVI classification approaches showed similar trends of forest change, i.e. decrease of dense forest and increase of medium dense forest, which indicates dense forest has been converted to medium dense forest. Area of bare land was unchanged. Illicit felling, encroachment, and settlement near forests caused the dense forest decline while short and long rotation plantations raised in various years caused the increase in area of medium dense forest. Protective measures should be undertaken to check further degradation of forest at KNP.

Land Use/Land Cover Change Detection in Pokhara Metropolitan, Nepal Using Remote Sensing

Land use and land cover are essential for maintaining and managing the natural resources on the earth surface. A complex set of economic, demographic, social, cultural, technological, and environmental processes usually result in the change in the land use/land cover change (LULC). Pokhara Metropolitan is influenced mainly by the combination of various driving forces: geographical location, high rate of population growth, economic opportunity, globalization, tourism activities, and political activities. In addition to this, geographically steep slope, rugged terrain, and fragile geomorphic conditions and the frequency of earthquakes, floods, and landslides make the Pokhara Metropolitan region a disaster-prone area. The increment of the population along with infrastructure development of a given territory leads towards the urbanization. It has been rapidly changing due to urbanization, industrialization and internal migration since the 1970s. The landscapes and ground patterns are frequently changing on time and prone to disaster. Here a study has been carried to study on LULC for the last 18 years (2000-2018). The supervised classification on Landsat Imagery was performed and verified the classification through computing the error matrix. Besides, the water bodies and vegetation area were extracted through the Normalized Difference Water Index (NDWI) and Normalized Difference Vegetation Index (NDWI) respectively. This research shows that during the last 18 years the agricultural areas diminishing by 15.66% while urban area is increasing by 13.2%. This research is beneficial for preparing the plan and policy in the sustainable development of Pokhara Metropolitan.

D-Optimal Designs for Hierarchical Linear Models with Heteroscedastic Errors

This paper investigates the optimal design problem for the prediction of the individual parameters in hierarchical linear models with heteroscedastic errors.An equivalence theorem is established to characterize D-optimality of designs for the prediction based on the mean squared error matrix.The admissibility of designs is also considered and a sufficient condition to simplify the design problem is obtained.The results obtained are illustrated in terms of a simple linear model with random slope and heteroscedastic errors.

Ability to detect and locate gross errors on DEM matching algorithm

Digital elevation model(DEM)matching techniques have been extended to DEM deformation detection by substituting a robust estimator for the least squares estimator,in which terrain changes are treated as gross errors.However,all existing methods only emphasise their deformation detecting ability,and neglect another important aspect:only when the gross error can be detected and located,can this system be useful.This paper employs the gross error judgement matrix as a tool to make an in-depth analysis of this problem.The theoretical analyses and experimental results show that observations in the DEM matching algorithm in real applications have the ability to detect and locate gross errors.Therefore,treating the terrain changes as gross errors is theoretically feasible,allowing real DEM deformations to be detected by employing a surface matching technique.

Modified Almost Unbiased Liu Estimator in Linear Regression Model

In this paper,we propose a new biased estimator namely modified almost unbiased Liu estimator by combining almost unbiased Liu estimator(AULE)andridge estimator(RE)in a linear regression model when multicollinearity presents amongthe independent variables.Necessary and sufficient conditions for the proposed estimator over the ordinary least square estimator,RE,AULE and Liu estimator(LE)in the mean squared error matrix sense are derived,and the optimal biasing parameters are obtained.To illustrate the theoretical findings,a Monte Carlo simulation study is carried out and a numerical example is used.

A Numerical Error Modeling Method for Parallel Kinematic Machines and Its Applications

Error model is the basis for accuracy-related computations and analyses for parallel kinematic machines（PKMs）.Traditional error modeling methods are usually based on differentiation of kinematic solutions,but the solving process is often complex and has limitations for certain specialized PKMs.A concise numerical error modeling method with the inverse kinematic solution as its only requirement is presented in this paper.To avoid complex Jacobian matrix computations,the difference matrix that can be quickly calculated by kinematic solutions was used to replace the differential matrix.The quasi-Newton method,which has high speed and high precision,was introduced to solve the numerical forward kinematic problem.To verify the efficiency of this numerical error modeling method,three applications in error transformation matrix（ETM） modeling,error analysis,and kinematic calibration were simulated on a 4RRR PKM.A comparison with the results obtained by the traditional method shows that the numerical method is accurate,convenient,and has lower requirements and wider applicability,especially for certain specialized and manufactured PKMs.

On the Stochastic Restricted Modified Almost Unbiased Liu Estimator in Linear Regression Model

In this article,we propose a new biased estimator,namely stochastic restricted modified almost unbiased Liu estimator by combining modified almost unbiased Liu estimator(MAULE)and mixed estimator(ME)when the stochastic restrictions are available and the multicollinearity presents.The conditions of supe-riority of the proposed estimator over the ordinary least square estimator,ME,ridge estimator,Liu estimator,almost unbiased Liu estimator,stochastic restricted Liu esti-mator and MAULE in the mean squared error matrix sense are obtained.Finally,a numerical example and a Monte Carlo simulation are given to illustrate the theoretical findings.

Ensemble unit and Al techniques for prediction of rock strain

The behavior of rock masses is influenced by a variety of forces,with measurement of stress and strain playing the most critical roles in assessing deformation.The laboratory test for determining strain at each location within rock samples is expensive and difficult but rock strain data are important for predicting failure of rock material.Many researchers employ AI technology in order to solve these difficulties.AI algorithms such as gradient boosting machine(GBM),support vector regression(SVR),random forest(RF),and group method of data handling(GMDH)are used to efficiently estimate the strain at every point within a rock sample.Additionally,the ensemble unit(EnU)may be utilized to evaluate rock strain.In this study,3000 experimental data are used for the purpose of prediction.The obtained strain values are then evaluated using various statistical parameters and compared to each other using EnU.Ranking analysis,stress-strain curve,Young’s modulus,Poisson’s ratio,actual vs.predicted curve,error matrix and the Akaike’s information criterion(AIC)values are used for comparing models.The GBM model achieved 98.16%and 99.98%prediction accuracy(in terms of values of R2)in the longitudinal and lateral dimensions,respectively,during the testing phase.The GBM model,based on the experimental data,has the potential to be a new option for engineers to use when assessing rock strain.