Nonparametric Regression Method Research Articles

Delineation of homogenous regions using hydrological variables predicted by projection pursuit regression

Abstract. This study investigates the utilization of hydrological information in regional flood frequency analysis (RFFA) to enforce desired properties for a group of gauged stations. Neighbourhoods are particular types of regions that are centred on target locations. A challenge for using neighbourhoods in RFFA is that hydrological information is not available at target locations and cannot be completely replaced by the available physiographical information. Instead of using the available physiographic characteristics to define the centre of a target location, this study proposes to introduce estimates of reference hydrological variables to ensure a better homogeneity. These reference variables represent nonlinear relations with the site characteristics obtained by projection pursuit regression, a nonparametric regression method. The resulting neighbourhoods are investigated in combination with commonly used regional models: the index-flood model and regression-based models. The complete approach is illustrated in a real-world case study with gauged sites from the southern part of the province of Québec, Canada, and is compared with the traditional approaches such as region of influence and canonical correlation analysis. The evaluation focuses on the neighbourhood properties as well as prediction performances, with special attention devoted to problematic stations. Results show clear improvements in neighbourhood definitions and quantile estimates.

ESTIMATION OF SUBPIXEL SNOW-COVERED AREA BY NONPARAMETRIC REGRESSION SPLINES

Abstract. Measurement of the areal extent of snow cover with high accuracy plays an important role in hydrological and climate modeling. Remotely-sensed data acquired by earth-observing satellites offer great advantages for timely monitoring of snow cover. However, the main obstacle is the tradeoff between temporal and spatial resolution of satellite imageries. Soft or subpixel classification of low or moderate resolution satellite images is a preferred technique to overcome this problem. The most frequently employed snow cover fraction methods applied on Moderate Resolution Imaging Spectroradiometer (MODIS) data have evolved from spectral unmixing and empirical Normalized Difference Snow Index (NDSI) methods to latest machine learning-based artificial neural networks (ANNs). This study demonstrates the implementation of subpixel snow-covered area estimation based on the state-of-the-art nonparametric spline regression method, namely, Multivariate Adaptive Regression Splines (MARS). MARS models were trained by using MODIS top of atmospheric reflectance values of bands 1-7 as predictor variables. Reference percentage snow cover maps were generated from higher spatial resolution Landsat ETM+ binary snow cover maps. A multilayer feed-forward ANN with one hidden layer trained with backpropagation was also employed to estimate the percentage snow-covered area on the same data set. The results indicated that the developed MARS model performed better than th

FORECASTING HAZARDOUS WASTE GENERATION USING SHORT DATA SETS: CASE STUDY OF LITHUANIA / PAVOJINGŲJŲ ATLIEKŲ SUSIDARYMO PROGNOZAVIMAS NAUDOJANT TRUMPAS DUOMENŲ IMTIS: LIETUVOS ATVEJIS

Due to inefficient waste sorting in primary and secondary waste generation sources Lithuania fails in trying to meet EU requirements for waste management sector regarding the amount of waste flow that reaches landfills. Especially sensitive situation is with hazardous waste, which often are disposed along with municipal solid waste and with it reaches landfills and due to the fact that mechanical and biological treatment plant are only now being established in the biggest cities of Lithuania, landfills becomes a big issue. The main purpose of this research is to find out which mathematical modelling methods could be fitted and if it is possible to forecast annual hazardous waste generation by using automotive, medical and daylight lamps waste generation statistical data. This is part of a research of medical, automotive and daylight lamps waste generation forecasting possibilities. Tests on the performance of artificial neural networks, multiple linear regression, partial least squares, support vector machines and four nonparametric regression methods were conducted on two developed data sets. The best and most promising results in both cases were demonstrated by generalized additives method (R2 = 0.99) and kernel regression (R2 = 0.99). Dėl nepakankamai efektyvaus pirminio ir antrinio atliekų rūšiavimo jų susidarymo šaltiniuose, Lietuva neatitinka ES atliekų tvarkymui keliamų reikalavimų, kurie apibrėžia į sąvartynus patenkančių atliekų srauto procentinę dalį. Pavojingosios atliekos yra ypač daug dėmesio reikalaujantis atliekų tvarkymo sektoriaus aspektas, nes didelė dalis pavojingųjų atliekų kartu su komunalinių atliekų srautu patenka į sąvartynus. Mechaninio ir biologinio apdorojimo įrenginiai, kurie padėtų spręsti šią ir sąvartynų pavojingumo aplinkai problemą, daugelyje didžiųjų šalies miestų tik dabar baigiami įrengti ar pradėti statyti. Pagrindinis šio tyrimo tikslas yra išsiaiškinti, kurie matematinio modeliavimo metodai galėtų būti pritaikyti prognozuojant metinį susidarančių pavojingųjų atliekų kiekį remiantis medicininių, automobilinių ir dienos šviesos lempų atliekų susidarymo duomenimis. Tai yra medicininių, automobilinių ir dienos šviesos lempų atliekų susidarymo prognozavimo galimybių tyrimo dalis. Atliekant tyrimą su dviem duomenų imtimis buvo išbandyti dirbtinių neuronų tinklų, daugialypės tiesinės regresijos, dalinių mažiausių kvadratų, atraminių vektorių, neparametrinės regresijos ir laiko eilučių metodai. Abiejų duomenų imčių atvejais geriausi rezultatai buvo pasiekti taikant bendrųjų adityvų (R2 = 0,99) ir branduolinės regresijos (R2 = 0,99) metodus.

Long-term health care costs for prostate cancer patients on androgen deprivation therapy.

Comparing relative costs for androgen deprivation therapy (adt) protocols in prostate cancer (pca) requires an examination of all health care resources, not only those specific to pca. The objective of the present study was to use administrative data to estimate total health care costs in a population-based cohort of pca patients. Patients in Ontario with pca who started 90 days or more of adt at age 66 years or older during 1995-2005 were selected from cancer registry and health care administrative databases. We classified patients (n = 21,818) by regimen (medical castration, orchiectomy, anti-androgen monotherapy, medical castration with anti-androgen, orchiectomy with anti-androgen) and indication (neoadjuvant, adjuvant, metastatic disease, biochemical recurrence, primary nonmetastatic). Using nonparametric regression methods, with inverse probability weighting to adjust for censoring, and bootstrapping, we computed mean 1-year, 5-year, and 10-year longitudinal total direct medical costs (2009 Canadian dollars). Mean first-year costs were highest for metastatic disease, ranging from $24,400 for orchiectomy to $32,120 for anti-androgen monotherapy. Mean first-year costs for all other indications were less than $20,000. Mean 5-year and 10-year costs were lowest for neoadjuvant treatment: approximately $43,000 and $81,000 respectively, with differences of less than $4,000 between regimens. Annual costs were highest in the first year of adt. Orchiectomy was the least costly regimen for most time periods, but was limited to primary and metastatic indications. Outpatient drugs, including pharmacologic adt, accounted for 17%-65% of total first-year costs. Compared with combined therapies, the adt monotherapies, particularly orchiectomy when clinically feasible, are more economical. Our methods exemplified the use of algorithms to elucidate clinical information from administrative data. Our approach can be adapted for other cancers to expand the range of studies using Canadian administrative data.

Nonparametric Estimation to Reconstruct the Deformation History of an Active Fold in the Caspian Basin

The complete shape of an active fold in the western margin of the South Caspian Basin is established with a seismic section from a post-stacked cube migrated in depth. The structure is an open anticline, which deforms a thick sequence (more than 7 km) of Late Miocene to Pliocene sediments: the productive series (PS 5.9–3.1 Ma). A major erosive unconformity separates the most recent sediments with onlap and draping geometries towards the anticline culmination. Deformation is reconstructed using the complete fit of numerous reflections by the nonparametric regression method. This fold is detached above a weak, shale-rich unit located between 8 and 10 km depth dipping gently towards the E (7 $$^{\circ }$$ ). The fold geometry resembles a detachment fold, although it is reconstructed a long-lived history of basinward tilting accompanying sedimentation and folding, which diminished from 0.61 to 0.34 $$^{\circ }$$ /Ma during deposition of the PS. Fold growth started at 3.5 Ma within the upper PS with a shortening rate of 0.2 mm/year and coinciding with maximum sedimentation rates (3.24 mm/year). Folding continued up-to-Present under lower sedimentation rates (av. 0.66 ± 0.2 mm/year) and a shortening rate that increased slightly from 0.17 mm/year at 3.1 Ma to 0.29 mm/year during the last 1.6 Ma. The balance between sedimentation and shortening rates varies during folding, explaining the contrasting geometries observed in the growth sediments. It is also inferred that the possible occurrence of lateral flow of overpressured mud-rich sediments inflated the fold core during shortening, similarly to the upwelling process commonly described in salt-core anticlines.

Strategic management of R&D and marketing integration for multi-dimensional success of new product developments: an empirical investigation in the Korean ICT industry

The purpose of this study is to show the impact of the R&D and marketing integration on new product development (NPD) success without any parametric assumptions on model specification. In the high-tech innovation management context, it has generally been accepted that tight integration between R&D and marketing successfully influences the development of an innovative product by stimulating a mutual understanding between people from different departments. However, a few researchers also pointed out that a too close relationship between R&D personnel and marketing personnel can cause important information to be overlooked, thus reducing NPD success. Our research results, which are based on empirical data and the application of the nonparametric regression method Multivariate Adaptive Regression Splines, show an even more diverse effect of integrating R&D and marketing if different performance criteria are considered. Results demonstrate that the effect of integration between R&D and marketing is nonconstant and nonlinear, a finding that could not be captured with parametric assumptions. Therefore, our research provides an explanation for the opposing observations reported in earlier work.

ANALISIS REGRESI NONPARAMETRIK SPLINE MULTIVARIAT UNTUK PEMODELAN INDIKATOR KEMISKINAN DI INDONESIA

The aim of this study is to obtain statistics models which explain the relationship between variables that influence the poverty indicators in Indonesia using multivariate spline nonparametric regression method. Spline is a nonparametric regression estimation method that is automatically search for its estimation wherever the data pattern move and thus resulting in model which fitted the data. This study, uses data from survey of Social Economy National (Susenas) and survey of Employment National (Sakernas) of 2013 from the publication of the Central Bureau of Statistics (BPS). This study yields two models which are the best model from two used response variables. The criterion uses to select the best model is the minimum Generalized Cross Validation (GCV). The best spline model obtained is cubic spline model with five optimal knots.

Nonparametric Regularized Regression for Phenotype-Associated Taxa Selection and Network Construction with Metagenomic Count Data.

We use a metagenomic approach and network analysis to investigate the relationships between phenotypes across taxa under different environmental conditions. The network structure of taxa can be affected by the disease-associated environmental conditions. In addition, taxa abundance is differentiated under conditions. Therefore, knowing how the correlation or relative abundance changes with these factors would be of great interest to researchers. We develop a nonparametric regularized regression method to construct taxa association networks under different clinical conditions. We let the coefficients be unknown functions of the environmental variable. The varying coefficients are estimated by using regression splines. The proposed method is regularized with concave penalties, and an efficient group descent algorithm is developed for computation. We also apply the varying coefficient model to estimate taxa abundance to see how it changes across different environmental conditions. Moreover, for conducting inference, we propose a bootstrap method to construct the simultaneous confidence bands for the corresponding coefficients. We use different simulated designs and a real data set to demonstrate that our method can identify the network structures successfully under different environmental conditions. As such, the proposed method has potential applications for researchers to construct differential networks and identify taxa.

Revisiting the Distance Duality Relation using a non-parametric regression method

The interdependence of luminosity distance, DL and angular diameter distance, DA given by the distance duality relation (DDR) is very significant in observational cosmology. It is very closely tied with the temperature-redshift relation of Cosmic Microwave Background (CMB) radiation. Any deviation from η(z)≡ DL/DA (1+z)2 =1 indicates a possible emergence of new physics. Our aim in this work is to check the consistency of these relations using a non-parametric regression method namely, LOESS with SIMEX. This technique avoids dependency on the cosmological model and works with a minimal set of assumptions. Further, to analyze the efficiency of the methodology, we simulate a dataset of 020 points of η (z) data based on a phenomenological model η(z)= (1+z)ϵ. The error on the simulated data points is obtained by using the temperature of CMB radiation at various redshifts. For testing the distance duality relation, we use the JLA SNe Ia data for luminosity distances, while the angular diameter distances are obtained from radio galaxies datasets. Since the DDR is linked with CMB temperature-redshift relation, therefore we also use the CMB temperature data to reconstruct η (z). It is important to note that with CMB data, we are able to study the evolution of DDR upto a very high redshift z = 2.418. In this analysis, we find no evidence of deviation from η=1 within a 1σ region in the entire redshift range used in this analysis (0 < z ⩽ 2.418).

Fusion of LiDAR Orthowaveforms and Hyperspectral Imagery for Shallow River Bathymetry and Turbidity Estimation

We propose an approach to voxelize bathymetric full-waveform LiDAR (Light Detection and Ranging) to generate orthowaveforms and use them to estimate shallow water bathymetry and turbidity with a nonparametric support vector regression (SVR) method. Two distinct shallow rivers were investigated ranging from clear to turbid water; hyperspectral imagery and traditional full-waveform LiDAR processing were also investigated as a baseline for comparison with the proposed orthowaveform strategy. The orthowaveform showed significant correlation to water depth in both scenarios and outperformed hyperspectral imagery for water depth estimation in more turbid water. The orthowaveforms showed similar performance to full-waveform LiDAR point observations for bathymetry estimation in clear water and outperformed the bathymetry performance of full-waveform processing in turbid water. The orthowaveforms also showed similar performance to hyperspectral imagery for predicting water turbidity in turbid water, with a root mean square error (RMSE) of 1.32 NTU. The fusion of both hyperspectral imagery and orthowaveforms was also investigated and gave superior performance to using either data set alone. The fused data set was able to estimate depth in clear and turbid water with an RMSE of 10 and 21 cm, respectively, and turbidity with an RMSE of 1.16 NTU.

Improving the Accuracy of K-Nearest Neighbour Method in Long Lead Hydrological Forecasting

The non-parametric regression method of K-nearest neighbour (K-NN) has been used in a variety of eco-hydrological issues. In this study, some techniques are presented to improve the accuracy of the K-NN method in forecasting the accumulated 9-month inflow of Zayandeh-rud dam in Iran, from winter to the end of the following summer. The improving techniques considered at current study include: 1) selection of the best data pre-processing functions, 2) selecting the best number of neighbour, 3) selecting the best distance functions, 4) specifying the best weights of predictors at distance functions, and 5) Adding the ability of extrapolation to K-NN using a simple method. Final results show that the use of mentioned techniques can improve the accuracy of K-NN’s forecast meaningfully. The results of goodness-of-fit criteria for the optimized K-NN in comparison with a regular K-NN can present an increase of 31% at correlation coefficient (from 65% to 96%), a decrease from 31 to 8 at volume error, and finally a drop from 54 to 25 at root mean square error.

An Improved Double-layer K-nearest Neighbor Nonparametric Regression Method for Short-time Traffic Flow Prediction

In combination with the repeatability of the traffic flow state patterns, this article improved the k-nearest neighbor non-parametric regression method. To be specific, the neighbors were screened twice and the function based on state pattern recognition was introduced; moreover, the traffic flows in the past time and the traffic flows towards the related directions at both upstream and downstream crossroads were taken into account, so that the predictive ability of the proposed k-nearest neighbor non-parametric regression method can be improved. In addition, the final prediction results were output using the weighted average method of the reciprocal of the state pattern vector matching distance, so as to enhance the accuracy and real-time performance of the short-term traffic flow prediction.

Estimating the expected value of partial perfect information in health economic evaluations using integrated nested Laplace approximation.

The Expected Value of Perfect Partial Information (EVPPI) is a decision‐theoretic measure of the ‘cost’ of parametric uncertainty in decision making used principally in health economic decision making. Despite this decision‐theoretic grounding, the uptake of EVPPI calculations in practice has been slow. This is in part due to the prohibitive computational time required to estimate the EVPPI via Monte Carlo simulations. However, recent developments have demonstrated that the EVPPI can be estimated by non‐parametric regression methods, which have significantly decreased the computation time required to approximate the EVPPI. Under certain circumstances, high‐dimensional Gaussian Process (GP) regression is suggested, but this can still be prohibitively expensive. Applying fast computation methods developed in spatial statistics using Integrated Nested Laplace Approximations (INLA) and projecting from a high‐dimensional into a low‐dimensional input space allows us to decrease the computation time for fitting these high‐dimensional GP, often substantially. We demonstrate that the EVPPI calculated using our method for GP regression is in line with the standard GP regression method and that despite the apparent methodological complexity of this new method, R functions are available in the package BCEA to implement it simply and efficiently. © 2016 The Authors. Statistics in Medicine Published by John Wiley & Sons Ltd.

New analysis methods to push the boundaries of diagnostic techniques in the environmental sciences

In the last years, new and more sophisticated measurements have been at the basis of the major progress in various disciplines related to the environment, such as remote sensing and thermonuclear fusion. To maximize the effectiveness of the measurements, new data analysis techniques are required. First data processing tasks, such as filtering and fitting, are of primary importance, since they can have a strong influence on the rest of the analysis. Even if Support Vector Regression is a method devised and refined at the end of the 90s, a systematic comparison with more traditional non parametric regression methods has never been reported. In this paper, a series of systematic tests is described, which indicates how SVR is a very competitive method of non-parametric regression that can usefully complement and often outperform more consolidated approaches. The performance of Support Vector Regression as a method of filtering is investigated first, comparing it with the most popular alternative techniques. Then Support Vector Regression is applied to the problem of non-parametric regression to analyse Lidar surveys for the environments measurement of particulate matter due to wildfires. The proposed approach has given very positive results and provides new perspectives to the interpretation of the data.

Bayesian manifold regression

There is increasing interest in the problem of nonparametric regression with high-dimensional predictors. When the number of predictors $D$ is large, one encounters a daunting problem in attempting to estimate a $D$-dimensional surface based on limited data. Fortunately, in many applications, the support of the data is concentrated on a $d$-dimensional subspace with $d \ll D$. Manifold learning attempts to estimate this subspace. Our focus is on developing computationally tractable and theoretically supported Bayesian nonparametric regression methods in this context. When the subspace corresponds to a locally-Euclidean compact Riemannian manifold, we show that a Gaussian process regression approach can be applied that leads to the minimax optimal adaptive rate in estimating the regression function under some conditions. The proposed model bypasses the need to estimate the manifold, and can be implemented using standard algorithms for posterior computation in Gaussian processes. Finite sample performance is illustrated in an example data analysis.

Association of CYP2C19*2 and associated haplotypes with lower norendoxifen concentrations in tamoxifen-treated Asian breast cancer patients.

The aim was to examine the influence of CYP2C19 variants and associated haplotypes on the disposition of tamoxifen and its metabolites, particularly norendoxifen (NorEND), in Asian patients with breast cancer. Sixty-six CYP2C19 polymorphisms were identified in healthy Asians (n = 240), of which 14 were found to be tightly linked with CYP2C19*2, CYP2C19*3 and CYP2C19*17. These 17 SNPs were further genotyped in Asian breast cancer patients receiving tamoxifen (n = 201). Steady-state concentrations of tamoxifen and its metabolites were quantified using liquid chromatography–mass spectrometry. Non-parametric tests and regression methods were implemented to evaluate genotypic–phenotypic associations and haplotypic effects of the SNPs. CYP2C19 functional polymorphisms and their linked SNPs were not significantly associated with plasma concentrations of tamoxifen and its main metabolites N-desmethyltamoxifen, (Z)-4-hydroxytamoxifen and (Z)-Endoxifen. However, CYP2C19*2 and its seven linked SNPs were significantly associated with lower NorEND concentrations, MRNorEND/NDDM and MRNorEND/(Z)-END. Specifically, patients carrying the CYP2C19*2 variant allele A had significantly lower NorEND concentrations [median (range), GG vs. GA vs. AA: 1.51 (0.38–3.28) vs. 1.28 (0.30–3.36) vs. 1.15 ng ml−1 (0.26–2.45, P = 0.010)] as well as significantly lower MRNorEND/(Z)-END [GG vs. GA vs. AA: 9.40 (3.27–28.35) vs. 8.15 (2.67–18.9) vs. 6.06 (4.47–14.6), P < 0.0001] and MRNorEND/NDDM [GG vs. GA vs. AA: 2.75 (0.62–6.26) vs. 2.43 (0.96–4.18) vs. 1.75 (1.10–2.49), P < 0.00001]. CYP2C19 H2 haplotype, which included CYP2C19*2, was also significantly associated with lower NorEND concentrations (P = 0.0020), MRNorEND/NDDM (P < 0.0001) and MRNorEND/(Z)-END (P < 0.0001), indicating significantly lower formation rates of NorEND. These data highlight the potential relevance of CYP2C19 pharmacogenetics in influencing NorEND concentrations in tamoxifen-treated patients, which may influence treatment outcomes.

A New Hybrid-Multiscale SSA Prediction of Non-Stationary Time Series

Singular spectral analysis (SSA) is a non-parametric method used in the prediction of non-stationary time series. It has two parameters, which are difficult to determine and very sensitive to their values. Since, SSA is a deterministic-based method, it does not give good results when the time series is contaminated with a high noise level and correlated noise. Therefore, we introduce a novel method to handle these problems. It is based on the prediction of non-decimated wavelet (NDW) signals by SSA and then, prediction of residuals by wavelet regression. The advantages of our method are the automatic determination of parameters and taking account of the stochastic structure of time series. As shown through the simulated and real data, we obtain better results than SSA, a non-parametric wavelet regression method and Holt–Winters method.

Forecasting medical waste generation using short and extra short datasets: Case study of Lithuania.

The aim of the study is to evaluate the performance of various mathematical modelling methods, while forecasting medical waste generation using Lithuania's annual medical waste data. Only recently has a hazardous waste collection system that includes medical waste been created and therefore the study access to gain large sets of relevant data for its research has been somewhat limited. According to data that was managed to be obtained, it was decided to develop three short and extra short datasets with 20, 10 and 6 observations. Spearman's correlation calculation showed that the influence of independent variables, such as visits at hospitals and other medical institutions, number of children in the region, number of beds in hospital and other medical institutions, average life expectancy and doctor's visits in that region are the most consistent and common in all three datasets. Tests on the performance of artificial neural networks, multiple linear regression, partial least squares, support vector machines and four non-parametric regression methods were conducted on the collected datasets. The best and most promising results were demonstrated by generalised additive (R(2) = 0.90455) in the regional data case, smoothing splines models (R(2) = 0.98584) in the long annual data case and multilayer feedforward artificial neural networks in the short annual data case (R(2) = 0.61103).

Modeling lightcurves for improved classification of astronomical objects

Many synoptic surveys are observing large parts of the sky multiple times. The resulting time series of light measurements, called lightcurves, provide a wonderful window to the dynamic nature of the Universe. However, there are many significant challenges in analyzing these lightcurves. We describe a modeling‐based approach using Gaussian process regression for generating critical measures for the classification of such lightcurves. This method has key advantages over other popular nonparametric regression methods in its ability to deal with censoring, a mixture of sparsely and densely sampled curves, the presence of annual gaps caused by objects not being visible throughout the year from a given position on Earth and known but variable measurement errors. We demonstrate that our approach performs better by showing it has a higher correct classification rate than past methods popular in astronomy. Finally, we provide future directions for use in sky‐surveys that are getting even bigger by the day. © 2016 Wiley Periodicals, Inc. Statistical Analysis and Data Mining: The ASA Data Science Journal, 2016

Exploratory Methods for the Study of Incomplete and Intersecting Shape Boundaries from Landmark Data

Structured spatial point patterns appear in many applications within the natural sciences. The points often record the location of key features, called landmarks, on continuous object boundaries, such as anatomical features on a human face. In other situations, the points may simply be arbitrarily spaced marks along a smooth curve, such as on handwritten numbers. This paper proposes novel exploratory methods for the identification of structure within point datasets. In particular, points are linked together to form curves which estimate the original shape from which the points are the only recorded information. Nonparametric regression methods are applied to polar coordinate variables obtained from the point locations and periodic modelling allows closed curves to be fitted even when data are available on only part of the boundary. Further, the model allows discontinuities to be identified to describe rapid changes in the curves. These generalizations are particularly important when the points represent shapes which are occluded or are intersecting. A range of real-data examples is used to motivate the modelling and to illustrate the flexibility of the approach. The method successfully identifies the underlying structure and its output could also be used as the basis for further analysis.