The M-estimate of Local Linear Regression with Variable Window Breadth

In this paper, by using the Brouwer fixed point theorem, we consider the existence and uniqueness of the solution for local linear regression with variable window breadth.

Local Polynomial Regression Estimator of the Finite Population Total under Stratified Random Sampling: A Model-Based Approach

In this paper, auxiliary information is used to determine an estimator of finite population total using nonparametric regression under stratified random sampling. To achieve this, a model-based approach is adopted by making use of the local polynomial regression estimation to predict the nonsampled values of the survey variable y. The performance of the proposed estimator is investigated against some design-based and model-based regression estimators. The simulation experiments show that the resulting estimator exhibits good properties. Generally, good confidence intervals are seen for the nonparametric regression estimators, and use of the proposed estimator leads to relatively smaller values of RE compared to other estimators.

FUNCTIONAL-COEFFICIENT REGRESSION MODEL AND ITS ESTIMATION

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.

Moult intensity constraints along the complete moult sequence of the House Sparrow(Passer domesticus)

Sequence and intensity are two essential components of bird moult.While the moult sequences of remex tracts are highly homogenous across passerines,other tracts apparently show a high variability.Moreover,order of moult activation among tracts are insufficiently known.Likewise,dynamics of moult intensity as moult progresses remains poorly known.Here,we provide detailed quantitative description of moult sequence and intensity in the House Sparrow(Passer domesticus).To understand their role,we tested two hypotheses on the:1) protection function of moult sequence,and 2) aerodynamic and physiological constraints on moult intensity.We scored percentage growth of 313 captured sparrows using the mass of the feathers of each tract(also length for remiges)to monitor moult intensity throughout the complete moult progress,which is defined as the fraction of new and growing feathers in a moulting bird relative to the total plumage.Moult sequence was highly variable both within wing coverts and among feather tracts,with moult sequence differing among all birds to some degree.We only found support for the protection function between greater coverts and both tertials and secondaries.Remex-moult intensity conformed to theoretical predictions,therefore lending support to the aerodynamic-constraint hypothesis.Furthermore,remex-moult speed plateaued during the central stages of moult progress.However,overall plumage-moult speed did not fit predictions of the physiological-constraint hypothesis,showing that the remex moult is only constrained by aerodynamics.Our results indicate that aerodynamic loss is not simply the inevitable effect of moult,but that moult is finely regulated to reduce aerodynamic loss.We propose that the moult of the House Sparrow is controlled through sequence and intensity adjustments in order to:1) avoid body and wing growth peaks;2) fulfil the protection function between some key feather tracts;3) reduce detrimental effects on flight ability;4) keep remex sequence fixed;and 5) relax remex replacement to last the whole moult duration.

Local attribute-similarity weighting regression algorithm for interpolating soil property values

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.

Adaptive Local Linear Quantile Regression

In this paper we propose a new method of local linear adaptive smoothing for nonparametric conditional quantile regression. Some theoretical properties of the procedure are investigated. Then we demonstrate the performance of the method on a simulated example and compare it with other methods. The simulation results demonstrate a reasonable performance of our method proposed especially in situations when the underlying image is piecewise linear or can be approximated by such images. Generally speaking, our method outperforms most other existing methods in the sense of the mean square estimation （MSE） and mean absolute estimation （MAE） criteria. The procedure is very stable with respect to increasing noise level and the algorithm can be easily applied to higher dimensional situations.

Fast magnitude determination using a single seismological station record implementing machine learning techniques

In this work a Support Vector Machine Regression（SVMR） algorithm is used to calculate local magnitude（MI） using only five seconds of signal after the P wave onset of one three component seismic station. This algorithm was trained with 863 records of historical earthquakes, where the input regression parameters were an exponential function of the waveform envelope estimated by least squares and the maximum value of the observed waveform for each component in a single station. Ten-fold cross validation was applied for a normalized polynomial kernel obtaining the mean absolute error for different exponents and complexity parameters. The local magnitude（MI） could be estimated with 0.19 units of mean absolute error. The proposed algorithm is easy to implement in hardware and may be used directly after the field seismological sensor to generate fast decisions at seismological control centers, increasing the possibility of having an effective reaction.

Local Linear Regression for Data with AR Errors

In many statistical applications, data are collected over time, and they are likely correlated. In this paper, we investigate how to incorporate the correlation information into the local linear regression. Under the assumption that the error process is an auto-regressive process, a new estimation procedure is proposed for the nonparametric regression by using local linear regression method and the profile least squares techniques. We further propose the SCAD penalized profile least squares method to determine the order of auto-regressive process. Extensive Monte Carlo simulation studies are conducted to examine the finite sample performance of the proposed procedure, and to compare the performance of the proposed procedures with the existing one. From our empirical studies, the newly proposed procedures can dramatically improve the accuracy of naive local linear regression with working-independent error structure. We illustrate the proposed methodology by an analysis of real data set.

Novel algorithm for pose-invariant face recognition

By combining the AdaBoost modular locality preserving projection （AMLPP） algorithm and the locally linear regression （LLR） algorithm, a novel pose-invariant algorithm is proposed to realize high-accuracy face recognition under different poses. In the training stage of this algorithm, the AMLPP is employed to select the crucial frontal blocks and construct effective strong classifier. According to the selected frontal blocks and the corresponding non-frontal blocks, LLR is then applied to learn the linear mappings which will be used to convert the non-frontal blocks to visual frontal blocks. During the testing of the learned linear mappings, when a non-frontal face image is inputted, the non-frontal blocks corresponding to the selected frontal blocks are extracted and converted to the visual frontal blocks. The generated virtual frontal blocks are finally fed into the strong classifier constructed by AMLPP to realize accurate and efficient face recognition. Our algorithm is experimentally compared with other pose-invariant face recognition algorithms based on the Bosphorus database. The results show a significant improvement with our proposed algorithm.

Discharge estimation based on machine learning

To overcome the limitations of the traditional stage-discharge models in describing the dynamic characteristics of a river, a machine learning method of non-parametric regression, the locally weighted regression method was used to estimate discharge. With the purpose of improving the precision and efficiency of river discharge estimation, a novel machine learning method is proposed： the clustering-tree weighted regression method. First, the training instances are clustered. Second, the k-nearest neighbor method is used to cluster new stage samples into the best-fit cluster. Finally, the daily discharge is estimated. In the estimation process, the interference of irrelevant information can be avoided, so that the precision and efficiency of daily discharge estimation are improved. Observed data from the Luding Hydrological Station were used for testing. The simulation results demonstrate that the precision of this method is high. This provides a new effective method for discharge estimation.

Concentration Prediction of Total Flavonoids in Aurantii Fructus Extraction Process:Locally Weighted Regression versus Kinetic Model Equation Based on Fick's Law

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.

A credit scoring model based on the Myers–Briggs type indicator in online peer-to-peer lending

Although psychometric features have been considered for alternative credit scoring,they have not yet been applied to peer-to-peer(P2P)lending because such information is not available on platforms.This study proposed an alternative credit scoring model for P2P lending by extracting typical personality types inferred from the borrowers’job category.We projected a virtual space of borrowers by using the affinity matrix based on the Myers–Briggs type indicator(MBTI)that fits each job category.Applying the distance in this space to Lending Club data,we used locally weighted logistic regression to vary the coefficients of the variables,which affect loan repayments,with each MBTI type for predicting the default probability.We found that each MBTI type’s credit scoring model has different significant variables.This study provides insights into breakthroughs in developing alternative credit scoring for P2P lending.

Adaptive Locally Weighted Projection Regression Method for Uncertainty Quantification

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.

Prediction of flyrock induced by mine blasting using a novel kernel-based extreme learning machine

Blasting is a common method of breaking rock in surface mines.Although the fragmentation with proper size is the main purpose,other undesirable effects such as flyrock are inevitable.This study is carried out to evaluate the capability of a novel kernel-based extreme learning machine algorithm,called kernel extreme learning machine(KELM),by which the flyrock distance(FRD) is predicted.Furthermore,the other three data-driven models including local weighted linear regression(LWLR),response surface methodology(RSM) and boosted regression tree(BRT) are also developed to validate the main model.A database gathered from three quarry sites in Malaysia is employed to construct the proposed models using 73 sets of spacing,burden,stemming length and powder factor data as inputs and FRD as target.Afterwards,the validity of the models is evaluated by comparing the corresponding values of some statistical metrics and validation tools.Finally,the results verify that the proposed KELM model on account of highest correlation coefficient(R) and lowest root mean square error(RMSE) is more computationally efficient,leading to better predictive capability compared to LWLR,RSM and BRT models for all data sets.

STATISTICAL INFERENCES FOR VARYING-COEFFICINT MODELS BASED ON LOCALLY WEIGHTED REGRESSION TECHNIQUE

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.

ClimateAP: an application for dynamic local downscaling of historical and future climate data in Asia Pacific

While low-to-moderate resolution gridded climate data are suitable for climate-impact modeling at global and ecosystems levels, spatial analyses conducted at local scales require climate data with increased spatial accuracy. This is particularly true for research focused on the evaluation of adaptive forest management strategies. In this study, we developed an application, Climate AP, to generate scale-free(i.e., specific to point locations) climate data for historical(1901–2015) and future(2011–2100)years and periods. Climate AP uses the best available interpolated climate data for the reference period 1961–1990 as baseline data. It downscales the baseline data from a moderate spatial resolution to scale-free point data through dynamic local elevation adjustments. It also integrates and downscales the historical and future climate data using a delta approach. In the case of future climate data, two greenhouse gas representative concentration pathways(RCP 4.5 and 8.5) and 15 general circulation models are included to allow for the assessment of alternative climate scenarios. In addition, Climate AP generates a large number of biologically relevant climate variables derived from primary monthly variables. The effectiveness of the local downscaling was determined based on the strength of the local linear regression for the estimate of lapse rate. The accuracy of the Climate AP output was evaluated through comparisons of Climate AP output against observations from 1805 weather stations in the Asia Pacific region. The local linear regression explained 70%–80% and 0%–50% of the total variation in monthly temperatures and precipitation, respectively, in most cases. Climate AP reduced prediction error by up to27% and 60% for monthly temperature and precipitation,respectively, relative to the original baselines data. The improvements for baseline portions of historical and futurewere more substantial. Applications and limitations of the software are discussed.

Two-stage Local Walsh Average Estimation of Generalized Varying Coefficient Models

In this paper we investigate the robust estimation of generalized varying coefficient models in which the unknown regression coefficients may change with different explanatory variables. Based on the B-spline series approximation and Walsh-average technique we develop an initial estimator for the unknown regression coefficient functions. By virtue of the initial estimator, the generalized varying coefficient model is reduced to a univariate nonparametric regression model. Then combining the local linear smooth and Walsh average technique we further propose a two-stage local linear Walsh-average estimator for the unknown regression coefficient functions. Under mild assumptions, we establish the large sample theory of the proposed estimators by utilizing the results of U-statistics and shows that the two-stage local linear Walsh-average estimator own an oracle property, namely the asymptotic normality of the two-stage local linear Walsh-average estimator of each coefficient function is not affected by other unknown coefficient functions. Extensive simulation studies are conducted to assess the finite sample performance, and a real example is analyzed to illustrate the proposed method.

Partially Linear Single-Index Model in the Presence of Measurement Error

The partially linear single-index model(PLSIM) is a flexible and powerful model for analyzing the relationship between the response and the multivariate covariates. This paper considers the PLSIM with measurement error possibly in all the variables. The authors propose a new efficient estimation procedure based on the local linear smoothing and the simulation-extrapolation method,and further establish the asymptotic normality of the proposed estimators for both the index parameter and nonparametric link function. The authors also carry out extensive Monte Carlo simulation studies to evaluate the finite sample performance of the new method, and apply it to analyze the osteoporosis prevention data.

Testing for Change Points in Partially Linear Models

In this paper we provide a method to test the existence of the change points in the nonparametric regression function of partially linear models with conditional heteroscedastic variance. We propose the test statistic and establish its asymptotic properties under some regular conditions. Some simulation studies are given to investigate the performance of the proposed method in finite samples. Finally, the proposed method is applied to a real data for illustration.

Approximating Conditional Density Functions Using Dimension Reduction

We propose to approximate the conditional density function of a random variable Y given a dependent random d-vector X by that of Y given θ^τX, where the unit vector θ is selected such that the average Kullback-Leibler discrepancy distance between the two conditional density functions obtains the minimum. Our approach is nonparametric as far as the estimation of the conditional density functions is concerned. We have shown that this nonparametric estimator is asymptotically adaptive to the unknown index θ in the sense that the first order asymptotic mean squared error of the estimator is the same as that when θ was known. The proposed method is illustrated using both simulated and real-data examples.