Global statistical techniques often assume homogeneity of relationships between dependent variable and predictors across space. This assumption has been criticized by statistical geographers as a fundamental weakness ...Global statistical techniques often assume homogeneity of relationships between dependent variable and predictors across space. This assumption has been criticized by statistical geographers as a fundamental weakness that may yield misleading result when it is applied to dataset with spatial context. To strengthen this weakness, a new method that accounts for heterogeneity in relationships across geographic space has been presented. This is one of the family of local spatial statistical techniques referred to as geographically weighted regression (GWR). The method captures non-stationarity of relationship in spatial data that the ordinary least square (OLS) regression fails to account for. Thus, the paper is designed to explore and analyze the spatial relationships between cholera occurrence and household sources of water supply using GIS-based GWR, also to compare the modeling fitness of OLS and GWR. Vector dataset (spatial) of the study region by state levels and statistical data (non-spatial) on cholera cases, household sources of water supply and population data were used in this exploratory analysis. The result shows that GWR is a significant improvement on the global model. Comparing both models with the AICc value and the R2 value revealed that for the former, the value is reduced from 698.7 (for OLS model) to 691.5 (for GWR model). For the latter, OLS explained 66.4 percent while GWR explained 86.7 percent. This implies that local model’s fitness is higher than global model. In addition, the empirical analysis revealed that cholera occurrence in the study region is significantly associated with household sources of water supply. This relationship, as detected by GWR, largely varies across the region.展开更多
The magnetic information measured on the smartphone platform has a large fluctuation and the research of indoor localization algorithm based on smart-phone platform is less. Indoor localization algorithm on smartphone...The magnetic information measured on the smartphone platform has a large fluctuation and the research of indoor localization algorithm based on smart-phone platform is less. Indoor localization algorithm on smartphone platform based on particle filter is studied. Robust local weighted regression is used to smooth the original magnetic data in the process of constructing magnetic map. Use moving average filtering model to filter the online magnetic observation data in positioning process. Compare processed online magnetic data with processed magnetic map collected by smartphone platform and the average matching error is 0.3941uT. Average positioning error is 0.229 meter when using processed online and map data.展开更多
This study used spatial autoregression(SAR)model and geographically weighted regression(GWR)model to model the spatial patterns of farmland density and its temporal change in Gucheng County,Hubei Province,China in 199...This study used spatial autoregression(SAR)model and geographically weighted regression(GWR)model to model the spatial patterns of farmland density and its temporal change in Gucheng County,Hubei Province,China in 1999 and 2009,and discussed the difference between global and local spatial autocorrelations in terms of spatial heterogeneity and non-stationarity.Results showed that strong spatial positive correlations existed in the spatial distributions of farmland density,its temporal change and the driving factors,and the coefficients of spatial autocorrelations decreased as the spatial lag distance increased.SAR models revealed the global spatial relations between dependent and independent variables,while the GWR model showed the spatially varying fitting degree and local weighting coefficients of driving factors and farmland indices(i.e.,farmland density and temporal change).The GWR model has smooth process when constructing the farmland spatial model.The coefficients of GWR model can show the accurate influence degrees of different driving factors on the farmland at different geographical locations.The performance indices of GWR model showed that GWR model produced more accurate simulation results than other models at different times,and the improvement precision of GWR model was obvious.The global and local farmland models used in this study showed different characteristics in the spatial distributions of farmland indices at different scales,which may provide the theoretical basis for farmland protection from the influence of different driving factors.展开更多
In this paper,a class of functional-coefficient regression models is proposed and an estimation procedure based on the locally weighted least equares is suggested.This class of models,with the proposed estimation meth...In this paper,a class of functional-coefficient regression models is proposed and an estimation procedure based on the locally weighted least equares is suggested.This class of models,with the proposed estimation method,is a powerful means for exploratory data analysis.展开更多
Focusing on controlling the press-assembly quality of high-precision servo mechanism,an intelligent early warning method based on outlier data detection and linear regression is proposed.Linear regression is used to d...Focusing on controlling the press-assembly quality of high-precision servo mechanism,an intelligent early warning method based on outlier data detection and linear regression is proposed.Linear regression is used to deal with the relationship between assembly quality and press-assembly process,then the mathematical model of displacement-force in press-assembly process is established and a qualified press-assembly force range is defined for assembly quality control.To preprocess the raw dataset of displacement-force in the press-assembly process,an improved local outlier factor based on area density and P weight(LAOPW)is designed to eliminate the outliers which will result in inaccuracy of the mathematical model.A weighted distance based on information entropy is used to measure distance,and the reachable distance is replaced with P weight.Experiments show that the detection efficiency of the algorithm is improved by 5.6 ms compared with the traditional local outlier factor(LOF)algorithm,and the detection accuracy is improved by about 2%compared with the local outlier factor based on area density(LAOF)algorithm.The application of LAOPW algorithm and the linear regression model shows that it can effectively carry out intelligent early warning of press-assembly quality of high precision servo mechanism.展开更多
Objective To predict the total flavonoids concentration of Aurantii Fructus fried with bran in its extraction process. Methods Ultraviolet spectrophotometry was used to determine the concentration of total flavonoids ...Objective To predict the total flavonoids concentration of Aurantii Fructus fried with bran in its extraction process. Methods Ultraviolet spectrophotometry was used to determine the concentration of total flavonoids in different extraction time （t） and solvent load （M）. Then the predicted procedure was carried out using the following data： 1 ） based on Ficks second law, the parameters of the kinetic model could be deduced and the equation was established; 2） Locally weighted regression （LWR） code was developed in the WEKA software environment to predict the concentration. And then we used both methods to predict the concentration of total flavonoids in new experiments. Results After comparing the predicted results with the experimental data, the LWR model had better accuracy and performance in the prediction. Conclusion LWR is applied to analyze the extraction process of Chinese herb for the first time, and it is totally fit for the extraction. LWR-based system is a more simple and accurate way to predict than the established equation. It is a good choice especially for a process which exists no clear rules, and can be used in the real-time control during the process.展开更多
We develop an efficient,adaptive locally weighted projection regression(ALWPR)framework for uncertainty quantification(UQ)of systems governed by ordinary and partial differential equations.The algorithm adaptively sel...We develop an efficient,adaptive locally weighted projection regression(ALWPR)framework for uncertainty quantification(UQ)of systems governed by ordinary and partial differential equations.The algorithm adaptively selects the new input points with the largest predictive variance and decides when and where to add new localmodels.It effectively learns the local features and accurately quantifies the uncertainty in the prediction of the statistics.The developed methodology provides predictions and confidence intervals at any query input and can dealwithmulti-output cases.Numerical examples are presented to show the accuracy and efficiency of the ALWPR framework including problems with non-smooth local features such as discontinuities in the stochastic space.展开更多
Some fundamental issues on statistical inferences relating to varying-coefficient regression models are addressed and studied. An exact testing procedure is proposed for checking the goodness of fit of a varying-coeff...Some fundamental issues on statistical inferences relating to varying-coefficient regression models are addressed and studied. An exact testing procedure is proposed for checking the goodness of fit of a varying-coefficient model fited by the locally weighted regression technique versus an ordinary linear regression model. Also, an appropriate statistic for testing variation of model parameters over the locations where the observations are collected is constructed and a formal testing approach which is essential to exploring spatial non-stationarity in geography science is suggested.展开更多
Existing spatial interpolation methods estimate the property values of an unmeasured point with observations of its closest points based on spatial distance(SD).However,considering that properties of the neighbors spa...Existing spatial interpolation methods estimate the property values of an unmeasured point with observations of its closest points based on spatial distance(SD).However,considering that properties of the neighbors spatially close to the unmeasured point may not be similar,the estimation of properties at the unmeasured one may not be accurate.The present study proposed a local attribute-similarity weighted regression(LASWR)algorithm,which characterized the similarity among spatial points based on non-spatial attributes(NSA)better than on SD.The real soil datasets were used in the validation.Mean absolute error(MAE)and root mean square error(RMSE)were used to compare the performance of LASWR with inverse distance weighting(IDW),ordinary kriging(OK)and geographically weighted regression(GWR).Cross-validation showed that LASWR generally resulted in more accurate predictions than IDW and OK and produced a finer-grained characterization of the spatial relationships between SOC and environmental variables relative to GWR.The present research results suggest that LASWR can play a vital role in improving prediction accuracy and characterizing the influence patterns of environmental variables on response variable.展开更多
Censored regression ("Tobit") models have been in common use, and their linear hypothesis testings have been widely studied. However, the critical values of these tests are usually related to quantities of a...Censored regression ("Tobit") models have been in common use, and their linear hypothesis testings have been widely studied. However, the critical values of these tests are usually related to quantities of an unknown error distribution and estimators of nuisance parameters. In this paper, we propose a randomly weighting test statistic and take its conditional distribution as an approximation to null distribution of the test statistic. It is shown that, under both the null and local alternative hypotheses, conditionally asymptotic distribution of the randomly weighting test statistic is the same as the null distribution of the test statistic. Therefore, the critical values of the test statistic can be obtained by randomly weighting method without estimating the nuisance parameters. At the same time, we also achieve the weak consistency and asymptotic normality of the randomly weighting least absolute deviation estimate in censored regression model. Simulation studies illustrate that the per-formance of our proposed resampling test method is better than that of central chi-square distribution under the null hypothesis.展开更多
文摘Global statistical techniques often assume homogeneity of relationships between dependent variable and predictors across space. This assumption has been criticized by statistical geographers as a fundamental weakness that may yield misleading result when it is applied to dataset with spatial context. To strengthen this weakness, a new method that accounts for heterogeneity in relationships across geographic space has been presented. This is one of the family of local spatial statistical techniques referred to as geographically weighted regression (GWR). The method captures non-stationarity of relationship in spatial data that the ordinary least square (OLS) regression fails to account for. Thus, the paper is designed to explore and analyze the spatial relationships between cholera occurrence and household sources of water supply using GIS-based GWR, also to compare the modeling fitness of OLS and GWR. Vector dataset (spatial) of the study region by state levels and statistical data (non-spatial) on cholera cases, household sources of water supply and population data were used in this exploratory analysis. The result shows that GWR is a significant improvement on the global model. Comparing both models with the AICc value and the R2 value revealed that for the former, the value is reduced from 698.7 (for OLS model) to 691.5 (for GWR model). For the latter, OLS explained 66.4 percent while GWR explained 86.7 percent. This implies that local model’s fitness is higher than global model. In addition, the empirical analysis revealed that cholera occurrence in the study region is significantly associated with household sources of water supply. This relationship, as detected by GWR, largely varies across the region.
文摘The magnetic information measured on the smartphone platform has a large fluctuation and the research of indoor localization algorithm based on smart-phone platform is less. Indoor localization algorithm on smartphone platform based on particle filter is studied. Robust local weighted regression is used to smooth the original magnetic data in the process of constructing magnetic map. Use moving average filtering model to filter the online magnetic observation data in positioning process. Compare processed online magnetic data with processed magnetic map collected by smartphone platform and the average matching error is 0.3941uT. Average positioning error is 0.229 meter when using processed online and map data.
基金Under the auspices of National Natural Science Foundation of China(No.40601073,41101192,41201571)Fundamental Research Funds for the Central Universities(No.2011PY112,2011QC041,2011QC091)Huazhong Agricultural University Scientific&Technological Self-innovation Foundation(No.2011SC21)
文摘This study used spatial autoregression(SAR)model and geographically weighted regression(GWR)model to model the spatial patterns of farmland density and its temporal change in Gucheng County,Hubei Province,China in 1999 and 2009,and discussed the difference between global and local spatial autocorrelations in terms of spatial heterogeneity and non-stationarity.Results showed that strong spatial positive correlations existed in the spatial distributions of farmland density,its temporal change and the driving factors,and the coefficients of spatial autocorrelations decreased as the spatial lag distance increased.SAR models revealed the global spatial relations between dependent and independent variables,while the GWR model showed the spatially varying fitting degree and local weighting coefficients of driving factors and farmland indices(i.e.,farmland density and temporal change).The GWR model has smooth process when constructing the farmland spatial model.The coefficients of GWR model can show the accurate influence degrees of different driving factors on the farmland at different geographical locations.The performance indices of GWR model showed that GWR model produced more accurate simulation results than other models at different times,and the improvement precision of GWR model was obvious.The global and local farmland models used in this study showed different characteristics in the spatial distributions of farmland indices at different scales,which may provide the theoretical basis for farmland protection from the influence of different driving factors.
文摘In this paper,a class of functional-coefficient regression models is proposed and an estimation procedure based on the locally weighted least equares is suggested.This class of models,with the proposed estimation method,is a powerful means for exploratory data analysis.
文摘Focusing on controlling the press-assembly quality of high-precision servo mechanism,an intelligent early warning method based on outlier data detection and linear regression is proposed.Linear regression is used to deal with the relationship between assembly quality and press-assembly process,then the mathematical model of displacement-force in press-assembly process is established and a qualified press-assembly force range is defined for assembly quality control.To preprocess the raw dataset of displacement-force in the press-assembly process,an improved local outlier factor based on area density and P weight(LAOPW)is designed to eliminate the outliers which will result in inaccuracy of the mathematical model.A weighted distance based on information entropy is used to measure distance,and the reachable distance is replaced with P weight.Experiments show that the detection efficiency of the algorithm is improved by 5.6 ms compared with the traditional local outlier factor(LOF)algorithm,and the detection accuracy is improved by about 2%compared with the local outlier factor based on area density(LAOF)algorithm.The application of LAOPW algorithm and the linear regression model shows that it can effectively carry out intelligent early warning of press-assembly quality of high precision servo mechanism.
基金National Nature Science Foundation of China(surface project)(81173563)
文摘Objective To predict the total flavonoids concentration of Aurantii Fructus fried with bran in its extraction process. Methods Ultraviolet spectrophotometry was used to determine the concentration of total flavonoids in different extraction time （t） and solvent load （M）. Then the predicted procedure was carried out using the following data： 1 ） based on Ficks second law, the parameters of the kinetic model could be deduced and the equation was established; 2） Locally weighted regression （LWR） code was developed in the WEKA software environment to predict the concentration. And then we used both methods to predict the concentration of total flavonoids in new experiments. Results After comparing the predicted results with the experimental data, the LWR model had better accuracy and performance in the prediction. Conclusion LWR is applied to analyze the extraction process of Chinese herb for the first time, and it is totally fit for the extraction. LWR-based system is a more simple and accurate way to predict than the established equation. It is a good choice especially for a process which exists no clear rules, and can be used in the real-time control during the process.
文摘We develop an efficient,adaptive locally weighted projection regression(ALWPR)framework for uncertainty quantification(UQ)of systems governed by ordinary and partial differential equations.The algorithm adaptively selects the new input points with the largest predictive variance and decides when and where to add new localmodels.It effectively learns the local features and accurately quantifies the uncertainty in the prediction of the statistics.The developed methodology provides predictions and confidence intervals at any query input and can dealwithmulti-output cases.Numerical examples are presented to show the accuracy and efficiency of the ALWPR framework including problems with non-smooth local features such as discontinuities in the stochastic space.
基金the National Natural Science Foundation of China (No.60075001) and Xi'anJiaotong University Natural Science Foundation.
文摘Some fundamental issues on statistical inferences relating to varying-coefficient regression models are addressed and studied. An exact testing procedure is proposed for checking the goodness of fit of a varying-coefficient model fited by the locally weighted regression technique versus an ordinary linear regression model. Also, an appropriate statistic for testing variation of model parameters over the locations where the observations are collected is constructed and a formal testing approach which is essential to exploring spatial non-stationarity in geography science is suggested.
基金supported by National Natural Science Foundation(41201299)the Ministry of Water Resources Public Welfare Industry Scientific Research Special(201501055).
文摘Existing spatial interpolation methods estimate the property values of an unmeasured point with observations of its closest points based on spatial distance(SD).However,considering that properties of the neighbors spatially close to the unmeasured point may not be similar,the estimation of properties at the unmeasured one may not be accurate.The present study proposed a local attribute-similarity weighted regression(LASWR)algorithm,which characterized the similarity among spatial points based on non-spatial attributes(NSA)better than on SD.The real soil datasets were used in the validation.Mean absolute error(MAE)and root mean square error(RMSE)were used to compare the performance of LASWR with inverse distance weighting(IDW),ordinary kriging(OK)and geographically weighted regression(GWR).Cross-validation showed that LASWR generally resulted in more accurate predictions than IDW and OK and produced a finer-grained characterization of the spatial relationships between SOC and environmental variables relative to GWR.The present research results suggest that LASWR can play a vital role in improving prediction accuracy and characterizing the influence patterns of environmental variables on response variable.
基金supported by National Natural Science Foundation of China (Grant No. 10471136)PhD Program Foundation of the Ministry of Education of ChinaSpecial Foundations of the Chinese Academy of Sciences and University of Science and Technology of China
文摘Censored regression ("Tobit") models have been in common use, and their linear hypothesis testings have been widely studied. However, the critical values of these tests are usually related to quantities of an unknown error distribution and estimators of nuisance parameters. In this paper, we propose a randomly weighting test statistic and take its conditional distribution as an approximation to null distribution of the test statistic. It is shown that, under both the null and local alternative hypotheses, conditionally asymptotic distribution of the randomly weighting test statistic is the same as the null distribution of the test statistic. Therefore, the critical values of the test statistic can be obtained by randomly weighting method without estimating the nuisance parameters. At the same time, we also achieve the weak consistency and asymptotic normality of the randomly weighting least absolute deviation estimate in censored regression model. Simulation studies illustrate that the per-formance of our proposed resampling test method is better than that of central chi-square distribution under the null hypothesis.
