Tests for nonparametric parts on partially linear single index models

Tests for nonparametric parts on partially linear single index models are considered in this paper. Based on the estimates obtained by the local linear method, the generalized likelihood ratio tests for the models are established. Under the null hypotheses the normalized tests follow asymptotically the χ2-distribution with the scale constants and the degrees of freedom being independent of the nuisance parameters, which is called the Wilks phenomenon. A simulated example is used to evaluate the performances of the testing procedures empirically.

Estimator of a change point in single index models

This paper considers the problem of change point in single index models.In order to obtain asymptotically valid confidence intervals for the estimation of the change point,the convergence rate and asymptotic distribution of the change point estimate is studied.Some simulation results are presented which show that the numerical performance of our estimator is satisfactory.

Inference of change-point in single index models

Single index models are widely used in medicine, econometrics and some other fields. In this paper, we consider the inference of a change point problem in single index models. Based on density-weighted average derivative estimation (ADE) method, we propose a statistic to test whether a change point exists or not. The null distribution of the test statistic is obtained using a permutation technique. The permuted statistic is rigorously shown to have the same distribution in the limiting sense under both null and alternative hypotheses. After the null hypothesis of no change point is rejected, an ADE-based estimate of the change point is proposed under assumption that the change point is unique. A simulation study confirms the theoretical results.

A Relative Error Estimation Approach for Multiplicative Single Index Model

As an alternative to absolute error methods, such as the least square and least absolute deviation estimations, a product relative error estimation is proposed for a multiplicative single index regression model. Regression coefficients in the model are estimated via a two-stage procedure and their statistical properties such as consistency and normality are studied. Numerical studies including simulation and a body fat example show that the proposed method performs well.

Weighted estimation of single index models with right censored responses

In this paper, the unknown link function, the direction parameter, and the heteroscedastic variance in single index models are estimated by the random weight method under the random censorship, respectively. The central limit theory and the convergence rate of the law of the iterated logarithm for the estimator of the direction parameter are derived, respectively. The optimal convergence rates for the estimators of the link function and the heteroscedastic variance are obtained. Simulation results support the theoretical results of the paper.

Target reliability index for serviceability limit state of single piles

The objective is to develop an approach for the determination of the target reliability index for serviceability limit state(SLS) of single piles. This contributes to conducting the SLS reliability-based design(RBD) of piles. Based on a two-parameter,hyperbolic curve-fitting equation describing the load-settlement relation of piles, the SLS model factor is defined. Then, taking into account the uncertainties of load-settlement model, load and bearing capacity of piles, the formula for computing the SLS reliability index(βsls) is obtained using the mean value first order second moment(MVFOSM) method. Meanwhile, the limit state function for conducting the SLS reliability analysis by the Monte Carlo simulation(MCS) method is established. These two methods are finally applied to determine the SLS target reliability index. Herein, the limiting tolerable settlement(slt) is treated as a random variable. For illustration, four load test databases from South Africa are compiled again to conduct reliability analysis and present the recommended target reliability indices. The results indicate that the MVFOSM method overestimates βsls compared to that computed by the MCS method. Besides, both factor of safety(FS) and slt are key factors influencing βsls, so the combination of FS and βsls is welcome to be used for the SLS reliability analysis of piles when slt is determined. For smaller slt, pile types and soils conditions have significant influence on the SLS target reliability indices; for larger slt, slt is the major factor having influence on the SLS target reliability indices. This proves that slt is the most key parameter for the determination of the SLS target reliability index.

Effect of Si δ-Doping on the Linear and Nonlinear Optical Absorptions and Refractive Index Changes in InAlN/GaN Single Quantum Wells

In the framework of effective mass approximation, we theoretically investigate the electronic structure of the Si δ-doped InAIN/GaN single quantum well by solving numerically the coupled equations Schrodinger-Poisson self-consistently. The linear, nonlinear optical absorption coefficients and relative refractive index changes are calculated as functions of the doping concentration and its thickness. The obtained results show that the position and the amplitude of the linear and total optical absorption coefficients and the refractive index changes can be modified by varying the doping concentration and its thickness. In addition, it is found that the maximum of the optical absorption can be red-shifted or blue-shifted by varying the doping concentration. The obtained results are important for the design of various electronic components such as high-power FETs and infrared photonic devices.

Spatial Analysis on Content Distribution of Soil Heavy Metals Copper (Cu) and Cadmium (Cd) in Duanzhou District of Zhaoqing City

This paper used atomic absorption spectrophotometry to determine the content distribution of Cu and Cd in the soil of Duanzhou District,Zhaoqing City.The single factor index method,Nemerow comprehensive index method,pollution load index method,geoaccumulation index method,and potential ecological hazard index method were used to analyze the content and pollution status of Cu and Cd in the soil of Duanzhou District,providing a basis for understanding the pollution status of Cu and Cd in the soil of Zhaoqing City.

Heavy metal distribution patterns and environmental quality assessment of the mariculture areas in Nanao,Shantou

The Fe, Zn, Mn and Pb concentrations in the seawater dissolved phase were investigated in the sea-surface microlayer （SML）, subsurface water （SSW） and bottom water （BW） samples collected at of three mariculture areas of the Nanao Island ocean zone. The results showed that the SML and the BW were important compartments for these heavy metals in the mariculture areas and the concentrations varied from 23.0 μg/L to 268.0 μg/L（Fe）, 11.0 μg/L to 82.2 μg/L（Zn）, 1.5 μg/L to 11.0 μg/L（Mn） and 6.0 μg/L to 40.5 μg/L（Pb） in SSW, while a clear enrichment is observed in the SML, where these ranged from 27.5 μg/L to 286.5 μg/L（Fe）, 13.5/lg/L to 89.0μg/L（Zn）, 3.0μg/L to 12.0 μg/L（Mn） and 7.0 μg/L to 46.0μg/L（Pb）. The enrichment factors were in the range of 1.07 - 1.39 which showed a slight enrichment. The average enrichment factors of Fe, Zn, Pb and Mn were 1.18, 1.13, 1.12 and 1.30, respectively. The average enrichment factors in shellfish, fish and gracilaria lemaneaformis farming areas were 1.26, 1.19 and 1.11, respectively, which showed that the surface activity was highest in the shellfish farming area. Furthermore, the heavy metals concentrations were lowest in the gracUaria lemaneaformis farming area. The results of single factor contamination index showed that the investigated areas were slightly contaminated with Zn, while the partial farming areas were seriously contaminated with Pd during a certain period of time.

Adsorption of Fe on GaAs（100）Surface

The adsorption of one monolayer Fe atoms on an ideal GaAs (100) surface is studied by using the self-consistent tight-binding linear muffin-tin orbital method. The Fe adatom chemisorption on Ga- and As-terminatedsurface are considered separately. A monolayer of S atoms is used to saturate the dangling bonds on one of the supercellsurfaces. Energies of adsorption systems of an Fe atom on different sites are calculated, and the charge transfers areinvestigated. It is found that Fe-As interaction is stronger than Fe-Ga interaction and Fe atoms prefer to be adsorbed onthe As-terminated surface. It is possible for the adsorbed Fe atoms to sit below the As-terminated surface resulting inan Fe-Ga-As mixed layer. The layer projected density states are calculated and compared with that of the clean surface.

Analysis of Total Antimony in Fresh Fruit and Pollution Evaluation in Hunan Province

[ Objective] The content of total antimony （Sb） in fresh fruit was investigated and its pollution was evaluated, to provide the basic data for diet exposure evaluation. [ Method] The content of total Sb in 194 samples was detected by hydride generation-atomic fluorescence spectrometry （HG-AFS）, and the Sb pollution in several fruits was evaluated by the method of single factor pollution index. [ Result ] The mean of total Sb was 0. 005 6 mg/kg, and the median was 0.003 8 mg/kg. The minimum value was not detected while the maximum value was O. 21 mg/kg, and the confidence interval was ND-O. 019 mg/kg （PS-P95）. The medi- ans of total Sb content in different fruits successively were dragon fruit （0.011 0 mg/kg） 〉 kiwi fruit （0.008 0 mg/kg） 〉 peach （0.006 0 mg/kg）. According to the method of single factor pollution index, the index from all samples was less than 0.2, suggesting that the samples involved were under the normal background value. [ Conclusion ] The Sb was detected in all samples but under the background value, and it was concluded that there was no Sb pollution in fresh fruit in Hunan Province.

Actuality research on base of non-pollution agricultural products in Yilan county

The base of non-pollution agricultural products is a prerequisite for the non-pollution agricultural production. Based on two factors, i.e., irrigation water and soil, the environmental quality of Yilan county＇s base of non-pollution agricultural products was evaluated by single pollution index. The main monitoring items included the content of Hg, Se, Cr, Pb, fluoride, and so on, and the evaluating results showed Pi〈1 which indicated that this area was fit for developing not only non-pollution products but also greenfood of A level.

Asymptotic properties of a nonparametric conditional density estimator in the local linear estimation for functional data via a functional single-index model

This paper deals with the conditional density estimator of a real response variable given a functional random variable(i.e.,takes values in an infinite-dimensional space).Specifically,we focus on the functional index model,and this approach represents a good compromise between nonparametric and parametric models.Then we give under general conditions and when the variables are independent,the quadratic error and asymptotic normality of estimator by local linear method,based on the single-index structure.Finally,wecomplete these theoretical advances by some simulation studies showing both the practical result of the local linear method and the good behaviour for finite sample sizes of the estimator and of the Monte Carlo methods to create functional pseudo-confidence area.

Water Quality Assessment of Dachangshan ArtificialHabitat Development Demonstration Area

[Objective] The paper was to evaluate the water quality environment in Dachangshan artificial habitat development demonstration area.[Method] From 2013 to 2015, an environmental survey was conducted for eight voyages in Dachangshan artificial habitat development demonstration area of Changhai County, Dalian City, and 20 hydrochemical indexes including salinity, pH, and COD were monitored. The water quality of thesea area was analyzed by principal component analysis and single factor index method. [Result] Except for that the control area of the August 2014voyage belonged to IIclass sea water standard, the water quality in other stations of all voyages conformed toIclass sea water standard. Totally 20water quality indicators were synthesized into six principal components using principal component analysis, which explained 79.165% of the results;the principal component score was ranged from -1.536 to 3.706; the score in August 2014 was the highest, and the evaluation results were basicallyconsistent with the results of single factor index analysis. [Conclusion] The overall water quality is good in Dachangshan artificial habitat development demonstration area.

Determination of Harmful Elements and Analysis of Pollution Level in Lysimachia christinae

[Objectives]To detect content of Pb,Cd,Hg,As,Cu,Zn,and Cr in Lysimachia christinae,and to analyze the pollution level.[Methods]Seven kinds of elements in L.christinae were determined by Inductively coupled plasma mass spectrometry and analyzed by single index and comprehensive index.[Results]The seven heavy metal elements showed good linearity in their respective concentration ranges.The recoveries of the samples were 84.5%-109.5%,and the RSD values were 2.30%-5.10%.Comparing the measured results of heavy metal elements with the limit values stipulated in the 2020 edition of the Chinese Pharmacopoeia and other standards,the Cr element in 19 batches of samples exceeded the standard,and the Zn element in 7 batches of samples exceeded the standard.The exceeding rates were 100.0%and 36.8%,respectively;the content of other heavy metal elements did not exceed the standard.The order of individual index from large to small was Cr,Zn,Cd,Hg,Cu,As,and Pb,and the average comprehensive pollution level was mild pollution and above.[Conclusions]L.christinae was mainly polluted by Cr,followed by Zn;this study can provide basic data for drafting of the limit standard for heavy metal elements in L.christinae.

Heavy Metal Dispersion in Stream Sediments in River Iyiudene, Abakaliki South-Eastern Nigeria: Source, Distribution Pattern, and Contamination Assessment

River Iyiudene is a vital distributary resource in Abakaliki, southeastern Nigeria and conveys an abundant amount of sediments to provincial and residual ecosystems. Although the importance of the river cannot be overemphasized, the geochemistry of its stream sediments is less investigated. Twenty (20) stream sediment samples were taken at the centre of the river channels to represent the entire drainage area well and avoid collapsed bank materials. The stream sediment samples were used to determine the dispersion, contamination status and sources of heavy metal concentrations. Total elemental digestion accompanied this with the use of aqua regia, an admixture of Hydrochloric acid (HCl) and Nitric acid (HNO3) in the ratio of 3:1 using the atomic absorption spectrometer (AAS). The heavy metal concentration levels in River Iyiudene were low compared with sediments from Imo River, Gulf of California, Upper continental crust, Average shale and surface horizons, excluding Cd, which showed high concentration levels than the other reference studies. The results delineated a wide contrast in the concentration levels of the heavy metals, with the mean contents in the order Zn > Cu > Pb > Cd > Ni > As. The pollution evaluation utilizing the Effect range low (ERL), Effect range median (ERM), single pollution index, and geo-accumulation index revealed Cd contamination. This study indicates that the heavy metals were sourced from the natural geological background of the river basin and possibly from agricultural runoff and atmospheric pollutants.

Distribution and assessment of heavy metals in the surface sediment of Yellow River, China

Large amounts of heavy metals discharged by industrial cities that are located along the middle reach of Yellow River, China have detrimental impacts on both the ecological environment and human health. In this study, fourteen surface sediment samples were taken in the middle reach of the Yellow River. Contents of Zn, Pb, Ni, Cu, Cr, Cd, As were measured, and the pollution status was assessed using three widely used pollution assessment methods, including the single factor index method, Nemerow pollution index method and potential ecological risk index. The concentrations of the studied heavy metals followed the order： Zn 〉 Cr 〉 Cu 〉 Ni 〉 Pb 〉 As 〉 Cd. Nearly 50% of sites had Cu and Cr accumulation. The concentration of Cu at the Yiluo River exceeded the secondary standard value of the Environmental quality standard for soils. Comparison of heavy metal concentrations between this study and other selected rivers indicated that Cu and Cr may be the major pollutants in our case. The single factor index indicated that many samples were at high levels of pollution for Cu and Cd; the Nemerow pollution index indicated that the Yihe River, Luohe River, Yiluo River and Huayuankou were polluted. According to the results of potential ecological risk assessment, Cd in the tributaries of Luo River, Yihe River,and Yiluo River showed high risk toward the ecosystem and human health, Cd in Huanyuankou and Cu in Yiluo River showed a middle level of risk and other samples were at a low level of risk.

The chemisorption of Mg on the Si(100)-(2×1) surface

The adsorption of a half monolayer of Mg atoms on the Si（100）-（2×1） surface is studied by using the self-consistent tight binding linear muffin-tin orbital method.Energies of the adsorption systems of Mg atoms on the different sites are calculated.It has been found that the adsorbed Mg atoms are more favorable on the cave site above the surface than any other sites on the Si（100）-（2×1） surface and a metastable shallow site also exists above the surface.This is in agreement with the experimental results.The charge transfer and the layer projected density of states are also studied.