Histogram and kernel estimators are usually regarded as the two main classical data-based nonparametric tools to estimate the underlying density functions for some given data sets. In this paper we will integrate them...Histogram and kernel estimators are usually regarded as the two main classical data-based nonparametric tools to estimate the underlying density functions for some given data sets. In this paper we will integrate them and define a histogram-kernel error based on the integrated square error between histogram and binned kernel density estimator, and then exploit its asymptotic properties. 3ust as indicated in this paper, the histogram-kernel error only depends on the choice of bin width and the data for the given prior kernel densities. The asymptotic optimal bin width is derived by minimizing the mean histogram-kernel error. By comparing with Scott＇s optimal bin width formula for a histogram, a new method is proposed to construct the data-based histogram without knowledge of the underlying density function. Monte Carlo study is used to verify the usefulness of our method for different kinds of density functions and sample sizes.展开更多
In digital soil mapping(DSM),a fundamental assumption is that the spatial variability of the target variable can be explained by the predictors or environmental covariates.Strategies to adequately sample the predictor...In digital soil mapping(DSM),a fundamental assumption is that the spatial variability of the target variable can be explained by the predictors or environmental covariates.Strategies to adequately sample the predictors have been well documented,with the conditioned Latin hypercube sampling(cLHS)algorithm receiving the most attention in the DSM community.Despite advances in sampling design,a critical gap remains in determining the number of samples required for DSM projects.We propose a simple workflow and function coded in R language to determine the minimum sample size for the cLHS algorithm based on histograms of the predictor variables using the Freedman-Diaconis rule for determining optimal bin width.Data preprocessing was included to correct for multimodal and non-normally distributed data,as these can affect sample size determination from the histogram.Based on a user-selected quantile range(QR)for the sample plan,the densities of the histogram bins at the upper and lower bounds of the QR were used as a scaling factor to determine minimum sample size.This technique was applied to a field-scale set of environmental covariates for a well-sampled agricultural study site near Guelph,Ontario,Canada,and tested across a range of QRs.The results showed increasing minimum sample size with an increase in the QR selected.Minimum sample size increased from 44 to 83 when the QR increased from 50% to 95% and then increased exponentially to 194 for the 99%QR.This technique provides an estimate of minimum sample size that can be used as an input to the cLHS algorithm.展开更多
炉次计划是炼钢-连铸批量计划的关键计划之一,主要功能是考虑如何充分利用转炉容量及板坯属性使用最少的炉次组织生产,其编制的好坏直接影响后续计划制定及各工序生产节奏.基于目前炉次计划模型存在无法分辨板坯宽度区间相交程度、炉容...炉次计划是炼钢-连铸批量计划的关键计划之一,主要功能是考虑如何充分利用转炉容量及板坯属性使用最少的炉次组织生产,其编制的好坏直接影响后续计划制定及各工序生产节奏.基于目前炉次计划模型存在无法分辨板坯宽度区间相交程度、炉容量利用效率及炉次内板坯间关系的不足及一维装箱理论没有考虑剩余箱子容量及箱子内物品间关系的问题,将炉次计划归结为考虑炉次剩余容量及板坯间关系的一维装箱问题,并建立数学规划模型.基于炉次计划模型解矩阵的特点及迭代局部搜索(iterated local search,ILS)和变邻域搜索(variable neighborhood search,VNS)的优点,提出了将VNS算法作为ILS算法中局部搜索的混合算法.最后利用现场实际数据对模型和算法的有效性进行了对比验证,结果表明炉次计划模型及混合算法是有效的.展开更多
Computation of error in estimation of nonlinearity in ADC using histogram test are reported in this paper. Error determination in estimation of Differential Nonlinearity (DNL) and Integral Nonlinearity (INL) of an ADC...Computation of error in estimation of nonlinearity in ADC using histogram test are reported in this paper. Error determination in estimation of Differential Nonlinearity (DNL) and Integral Nonlinearity (INL) of an ADC is done by taking deviation of estimated value from actual value. Error in estimated INL and DNL is determined to check the usefulness of basic histogram test algorithm. Arbitrary error is introduced in ideal simulated ADC transfer characteristics and full scale simulated sine wave is applied to ADC for computation of error in estimation of transition levels and nonlinearity. Simulation results for 5 and 8 bit ADC are pre-sented which show effectiveness of the proposed method.展开更多
基金Supported by the National Natural Science Foundation of China (No. 70371018, 70572074)
文摘Histogram and kernel estimators are usually regarded as the two main classical data-based nonparametric tools to estimate the underlying density functions for some given data sets. In this paper we will integrate them and define a histogram-kernel error based on the integrated square error between histogram and binned kernel density estimator, and then exploit its asymptotic properties. 3ust as indicated in this paper, the histogram-kernel error only depends on the choice of bin width and the data for the given prior kernel densities. The asymptotic optimal bin width is derived by minimizing the mean histogram-kernel error. By comparing with Scott＇s optimal bin width formula for a histogram, a new method is proposed to construct the data-based histogram without knowledge of the underlying density function. Monte Carlo study is used to verify the usefulness of our method for different kinds of density functions and sample sizes.
基金the Natural Science and Engineering Research Council(NSERC)of Canada,which supported and funded this project through an NSERC Postgraduate Scholarship—Doctoral(PGS-D)。
文摘In digital soil mapping(DSM),a fundamental assumption is that the spatial variability of the target variable can be explained by the predictors or environmental covariates.Strategies to adequately sample the predictors have been well documented,with the conditioned Latin hypercube sampling(cLHS)algorithm receiving the most attention in the DSM community.Despite advances in sampling design,a critical gap remains in determining the number of samples required for DSM projects.We propose a simple workflow and function coded in R language to determine the minimum sample size for the cLHS algorithm based on histograms of the predictor variables using the Freedman-Diaconis rule for determining optimal bin width.Data preprocessing was included to correct for multimodal and non-normally distributed data,as these can affect sample size determination from the histogram.Based on a user-selected quantile range(QR)for the sample plan,the densities of the histogram bins at the upper and lower bounds of the QR were used as a scaling factor to determine minimum sample size.This technique was applied to a field-scale set of environmental covariates for a well-sampled agricultural study site near Guelph,Ontario,Canada,and tested across a range of QRs.The results showed increasing minimum sample size with an increase in the QR selected.Minimum sample size increased from 44 to 83 when the QR increased from 50% to 95% and then increased exponentially to 194 for the 99%QR.This technique provides an estimate of minimum sample size that can be used as an input to the cLHS algorithm.
文摘炉次计划是炼钢-连铸批量计划的关键计划之一,主要功能是考虑如何充分利用转炉容量及板坯属性使用最少的炉次组织生产,其编制的好坏直接影响后续计划制定及各工序生产节奏.基于目前炉次计划模型存在无法分辨板坯宽度区间相交程度、炉容量利用效率及炉次内板坯间关系的不足及一维装箱理论没有考虑剩余箱子容量及箱子内物品间关系的问题,将炉次计划归结为考虑炉次剩余容量及板坯间关系的一维装箱问题,并建立数学规划模型.基于炉次计划模型解矩阵的特点及迭代局部搜索(iterated local search,ILS)和变邻域搜索(variable neighborhood search,VNS)的优点,提出了将VNS算法作为ILS算法中局部搜索的混合算法.最后利用现场实际数据对模型和算法的有效性进行了对比验证,结果表明炉次计划模型及混合算法是有效的.
文摘Computation of error in estimation of nonlinearity in ADC using histogram test are reported in this paper. Error determination in estimation of Differential Nonlinearity (DNL) and Integral Nonlinearity (INL) of an ADC is done by taking deviation of estimated value from actual value. Error in estimated INL and DNL is determined to check the usefulness of basic histogram test algorithm. Arbitrary error is introduced in ideal simulated ADC transfer characteristics and full scale simulated sine wave is applied to ADC for computation of error in estimation of transition levels and nonlinearity. Simulation results for 5 and 8 bit ADC are pre-sented which show effectiveness of the proposed method.
