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Weed scientists are usually interested in the study of the distribution and density functions of the random variable that relates weed emergence with environmental indices like the hydrothermal time (HTT). However, in many situations, experimental data are presented in a grouped way and, therefore, the standard nonparametric kernel estimators cannot be computed.Kernel estimators for the density and distribution functions for interval‐grouped data, as well as bootstrap confidence bands for these functions, have been proposed and implemented in the binnednp package. Analysis with different treatments can also be performed using a bootstrap approach and a Cramér‐von Mises type distance. Several bandwidth selection procedures were also implemented. This package also allows to estimate different emergence indices that measure the shape of the data distribution. The values of these indices are useful for the selection of the soil depth at which HTT should be measured which, in turn, would maximize the predictive power of the proposed methods.This paper presents the functions of the package and provides an example using an emergence data set of Avena sterilis (wild oat).The binnednp package provides investigators with a unique set of tools allowing the weed science research community to analyze interval‐grouped data. [ABSTRACT FROM AUTHOR]

A nonparametric procedure to estimate the conditional probability that a nonstationary geostatistical process exceeds a certain threshold value is proposed. The method consists of a bootstrap algorithm that combines conditional simulation techniques with nonparametric estimations of the trend and the variability. The nonparametric local linear estimator, considering a bandwidth matrix selected by a method that takes the spatial dependence into account, is used to estimate the trend. The variability is modeled estimating the conditional variance and the variogram from corrected residuals to avoid the biasses. The proposed method allows to obtain estimates of the conditional exceedance risk in non-observed spatial locations. The performance of the approach is analyzed by simulation and illustrated with the application to a real data set of precipitations in the USA.Supplementary materials accompanying this paper appear on-line. [ABSTRACT FROM AUTHOR]

This article describes a free, open-source collection of templates for the popular Excel (2013, and later versions) spreadsheet program. These templates are spreadsheet files that allow easy and intuitive learning and the implementation of practical examples concerning descriptive statistics, random variables, confidence intervals, and hypothesis testing. Although they are designed to be used with Excel, they can also be employed with other free spreadsheet programs (changing some particular formulas). Moreover, we exploit some possibilities of the ActiveX controls of the Excel DeveloperMenu to perform interactive Gaussian density charts. Finally, it is important to note that they can be often embedded in a web page, so it is not necessary to employ Excel software for their use. These templates have been designed as a useful tool to teach basic statistics and to carry out data analysis even when the students are not familiar with Excel. Additionally, they can be used as a complement to other analytical software packages. They aim to assist students in learning statistics, within an intuitive working environment. Supplementary materials with the Excel templates are available online. [ABSTRACT FROM AUTHOR]

The aim of this study is to statistically identify and distinguish wood samples corresponding to different areas of annual rings in trees of temperate regions, using the corresponding thermogravimetric (TG) and their first TG derivative (DTG) curves, and specifically to verify whether late and early wood chestnut samples are different with statistical significance, taking into account their TG and DTG curves. These significant differences are sought by applying statistical procedures based on functional data analysis (FDA), such as the functional ANOVA and the FDA classification methods. Each TG curve is firstly smoothed using the local polynomial regression estimator, and its first derivative is estimated. Then, functional ANOVA based on random projections (RP) is used to identify significant differences between TG or DTG curves of early and late wood samples. In order to know the extent of the differences between early and late wood samples, they are discriminated (and the correct classification proportion obtained) by employing a kernel nonparametric functional data analysis technique, based on the Bayes' rule, as well as functional generalized linear models and functional generalized additive models, allowing to classify materials using more than one type of thermal curves simultaneously. The results are compared with those obtained using some classical multivariate supervised classification methods: linear discriminant analysis, naive Bayes (NBC) and quadratic classification (QDA). The partial least squares (PLS) dimension reduction procedure was previously applied to the TG curves in order to employ these multivariate methods. The application of RP ANOVA shows significant differences between late and early wood regarding mass loss and mass loss rate under combustion. The use of PLS multivariate methods or FDA classification approaches applied to the TG and DTG curves allows to distinguish very accurately between late and early wood. The proposed method could be applied to other species to identify thermooxidative differences, combined with other experimental methods to find their chemical and physical causes. [ABSTRACT FROM AUTHOR]

Interval-grouped data are defined, in general, when the event of interest cannot be directly observed and it is only known to have been occurred within an interval. In this framework, a nonparametric kernel density estimator is proposed and studied. The approach is based on the classical Parzen–Rosenblatt estimator and on the generalisation of the binned kernel density estimator. The asymptotic bias and variance of the proposed estimator are derived under usual assumptions, and the effect of using non-equally spaced grouped data is analysed. Additionally, a plug-in bandwidth selector is proposed. Through a comprehensive simulation study, the behaviour of both the estimator and the plug-in bandwidth selector considering different scenarios of data grouping is shown. An application to real data confirms the simulation results, revealing the good performance of the estimator whenever data are not heavily grouped. [ABSTRACT FROM AUTHOR]

Distribution function estimation of the random variable of river flow is an important problem in hydrology. This issue is directly related to quantile estimation, and consequently to return level prediction. The estimation process can be complemented with the construction of confidence intervals (CIs) to perform a probabilistic assessment of the different variables and/or estimated functions. In this work, several methods for constructing CIs using bootstrap techniques, and parametric and nonparametric procedures in the estimation process are studied and compared. In the case that the target is the joint estimation of a vector of values, some new corrections to obtain joint coverage probabilities closer to the corresponding nominal values are also presented. A comprehensive simulation study compares the different approaches, and the application of the different procedures to real data sets from four rivers in the United States and one in Spain complete the paper. [ABSTRACT FROM AUTHOR]

The aim of this study is to propose an alternative methodology to classify wood species using the first (DTG), second (2DTG), and third (3DTG) derivatives of the thermogravimetric curves (TG). Accordingly, the main contribution of this new procedure consists on classifying materials (wood) taking into account the mass loss rate and acceleration with respect to temperature. In our research, each TG curve is firstly smoothed using the local polynomial regression estimator, and the first, second, and third derivatives are estimated. The application of the local polynomial regression estimator provides a reliable way to obtain the TG derivatives, overcoming the noise problem in the TG derivative estimation. Then, using these estimated curves, the different wood classes are discriminated employing a nonparametric functional data analysis (NPFDA) technique, based on the Bayes rule and the Nadaraya-Watson regression estimator, and also novel functional generalized additive models (GAM). The latter allows to classify materials using simultaneously more than one type of thermal curves. The results are compared with those obtained using classical and machine learning multivariate supervised classification methods, such as Linear discriminant analysis, Quadratic classification, Naïve Bayes, Logistic regression, $$k$$ Nearest neighbors, Neural networks, and Support vector machines. A regression model consisting of the mixture of the first derivatives of four generalized logistic components, one per principal wood constituent (water, hemicellulose, cellulose, and lignin), is applied to fit the DTG curves. The resulting 16 parameters from this fit characterize each curve and are used as datasets to apply the multivariate supervised classification methods. The use of the TG derivatives jointly with the TG curves has proved to be an optimal discriminating feature, when the new functional GAM techniques are employed. [ABSTRACT FROM AUTHOR]

In geostatistics, the approximation of the spatial dependence structure of a process, through the estimation of the variogram or the covariogram of the variable under consideration, is an important issue. In this work, under a general spatial model, including a mean or trend function, and without assuming any parametric model for this function and for the dependence structure of the process, a general nonparametric estimator of the variogram is proposed. The new approach consists in applying an iterative algorithm, using the residuals obtained from a nonparametric local linear estimation of the trend function, jointly with a correction of the bias due to the use of these residuals. A simulation study checks the validity of the presented approaches in practice. The broad applicability of the procedures is demonstrated on a real data set. [ABSTRACT FROM AUTHOR]

This work addresses the problem of supervised classification of industrial wood species (seven different types in the present study) through their thermo-oxidative stability. This is evaluated by pressure differential scanning calorimetry (PDSC) using the ASTM E2009. The maximization of the ratio of correct classification and the reduction of the costs of this activity are intended. This supervised classification problem was carried out using two different proposals: applying novel nonparametric functional data analysis techniques, based on kernel estimation, to the original PDSC curves, and using machine learning classification approaches applied to different multivariate data sets. The multivariate data sets were obtained, on the one hand, by estimating the fractal (Hausdorff) dimension of the PDSC curves by several methods, jointly with selecting the parameters from fitting a nonlinear model to the PDSC curves and, on the other hand, applying principal component analysis or partial linear squares to the thermograms. The results obtained show that the PDSC curves can be used to discriminate wood samples when these innovative and traditional statistical techniques are applied. In the best of the cases, a probability of correct classification that equals to 0.92 was obtained. PDSC represents a new alternative to the use of images, spectra, and other thermal signals as thermogravimetric analysis for classification purposes.Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, nonparametric curve estimation methods are applied to analyze time series of wind speeds, focusing on the extreme events exceeding a chosen threshold. Classical parametric statistical approaches in this context consist in fitting a generalized Pareto distribution (GPD) to the tail of the empirical cumulative distribution, using maximum likelihood or the method of the moments to estimate the parameters of this distribution. Additionally, confidence intervals are usually computed to assess the uncertainty of the estimates. Nonparametric methods to estimate directly some quantities of interest, such as the probability of exceedance, the quantiles or return levels, or the return periods, are proposed. Moreover, bootstrap techniques are used to develop pointwise and simultaneous confidence intervals for these functions. The proposed models are applied to wind speed data in the Gulf Coast of US, comparing the results with those using the GPD approach, by means of a split-sample test. Results show that nonparametric methods are competitive with respect to the standard GPD approximations. The study is completed generating synthetic data sets and comparing the behavior of the parametric and the nonparametric estimates in this framework. [ABSTRACT FROM AUTHOR]

. Systematic sampling is frequently used in surveys, because of its ease of implementation and its design efficiency. An important drawback of systematic sampling, however, is that no direct estimator of the design variance is available. We describe a new estimator of the model-based expectation of the design variance, under a non-parametric model for the population. The non-parametric model is sufficiently flexible that it can be expected to hold at least approximately in many situations with continuous auxiliary variables observed at the population level. We prove the model consistency of the estimator for both the anticipated variance and the design variance under a non-parametric model with a univariate covariate. The broad applicability of the approach is demonstrated on a dataset from a forestry survey. [ABSTRACT FROM AUTHOR]

Abstract: Wood is one of the most complicated materials to be classified in different classes or species. In this paper, the thermogravimetric (TG) curves of 49 wood samples are used to classify them in 7 predetermined species. Different functional and multivariate statistical supervised classification methods are used for this task: a nonparametric Nadaraya–Watson kernel functional estimator (K-NFDA), using the complete TG curves, and multivariate supervised classification approaches, such as linear discriminant analysis (LDA), k Nearest Neighbors (k-NN), Naïve Bayes (NBC), Neural Networks (NN), and Support Vector Machines (SVM). Before applying the multivariate techniques, the TG curves are discretized using principal component analysis (PCA) or fitting a four-component generalized logistic model. The results show that the classical method of LDA using the logistic parameters had the best performance, although high correct classification percentages were also obtained with the rest of the approaches. The work is completed with a comprehensive simulation study, comparing the classification techniques in different scenarios. Artificial TG curves are generated using the logistic model and additional conclusions on wood classification are established. Due to the heterogeneity of wood, this simulation study is very useful to describe worst-case scenarios and to assess more accurately the proposed classification methodologies. [Copyright &y& Elsevier]

Abstract: Nonparametric techniques are frequently used in seismology studies to fit statistical models to earthquake data, as an alternative to classical parametric methods. In this paper, we apply nonparametric techniques to study some area-characteristic seismic hazard parameters (such as the mean return period or the expected number of earthquakes) in the northwest of the Iberian Peninsula, using a complete data catalog. Moreover, bootstrap techniques are used to develop simultaneous confidence bands for these functions. The previous nonparametric approaches are adapted to a spatial framework, obtaining maps of the probabilities of exceedance of the annual maximum magnitude in the zone of study. This procedure suitably describes the features of the area studied, being consistent with previous geological researches. [Copyright &y& Elsevier]

Abstract: Controlling emissions of air pollutants and establishing air quality objectives to improve and protect ambient air quality are very important tasks of Governments. Ozone (O3), one of those pollutants of concern, is not emitted directly into the atmosphere, but is a secondary pollutant produced by reaction between nitrogen dioxide (NO2), hydrocarbons and sunlight. High levels of ozone can produce harmful effects on human health and the environment in general. Therefore, the study of extreme values of ozone represents an important topic of research in environmental problems. Classical extreme value theory has been usually used in air-pollution studies. It consists of fitting a parametric generalized extreme value (GEV) distribution to a data set of extreme values and using the estimated distribution to compute quantities like the probability of exceedance, the quantiles, the return levels or the mean return periods. In this paper, we propose nonparametric methods to estimate those quantities. Additionally, nonparametric estimators of the trends of very high values of ozone are proposed. The nonparametric estimators are applied to real samples of maximum ozone values obtained from several monitoring stations belonging to the Automatic Urban and Rural Network (AURN) from the UK. Results show that nonparametric estimators work satisfactorily, generally outperforming the behaviour of classical parametric estimators. [ABSTRACT FROM AUTHOR]

Abstract: The study of extreme values and prediction of ozone data is an important topic of research when dealing with environmental problems. Classical extreme value theory is usually used in air-pollution studies. It consists in fitting a parametric generalised extreme value (GEV) distribution to a data set of extreme values, and using the estimated distribution to compute return levels and other quantities of interest. Here, we propose to estimate these values using nonparametric functional data methods. Functional data analysis is a relatively new statistical methodology that generally deals with data consisting of curves or multi-dimensional variables. In this paper, we use this technique, jointly with nonparametric curve estimation, to provide alternatives to the usual parametric statistical tools. The nonparametric estimators are applied to real samples of maximum ozone values obtained from several monitoring stations belonging to the Automatic Urban and Rural Network (AURN) in the UK. The results show that nonparametric estimators work satisfactorily, outperforming the behaviour of classical parametric estimators. Functional data analysis is also used to predict stratospheric ozone concentrations. We show an application, using the data set of mean monthly ozone concentrations in Arosa, Switzerland, and the results are compared with those obtained by classical time series (ARIMA) analysis. [ABSTRACT FROM AUTHOR]

Background: Predictive microbiology develops mathematical models that can predict the growth rate of a microorganism population under a set of environmental conditions. Many primary growth models have been proposed. However, when primary models are applied to bacterial growth curves, the biological variability is reduced to a single curve defined by some kinetic parameters (lag time and growth rate), and sometimes the models give poor fits in some regions of the curve. The development of a prediction band (from a set of bacterial growth curves) using non-parametric and bootstrap methods permits to overcome that problem and include the biological variability of the microorganism into the modelling process. Results: Absorbance data from Listeria monocytogenes cultured at 22, 26, 38, and 42°C were selected under different environmental conditions of pH (4.5, 5.5, 6.5, and 7.4) and percentage of NaCl (2.5, 3.5, 4.5, and 5.5). Transformation of absorbance data to viable count data was carried out. A random effect multiplicative heteroscedastic model was considered to explain the dynamics of bacterial growth. The concept of a prediction band for microbial growth is proposed. The bootstrap method was used to obtain resamples from this model. An iterative procedure is proposed to overcome the computer intensive task of calculating simultaneous prediction intervals, along time, for bacterial growth. The bands were narrower below the inflection point (0-8 h at 22°C, and 0-5.5 h at 42°C), and wider to the right of it (from 9 h onwards at 22°C, and from 7 h onwards at 42°C). A wider band was observed at 42°C than at 22°C when the curves reach their upper asymptote. Similar bands have been obtained for 26 and 38°C. Conclusions: The combination of nonparametric models and bootstrap techniques results in a good procedure to obtain reliable prediction bands in this context. Moreover, the new iterative algorithm proposed in this paper allows one to achieve exactly the prefixed coverage probability for the prediction band. The microbial growth bands reflect the influence of the different environmental conditions on the microorganism behaviour, helping in the interpretation of the biological meaning of the growth curves obtained experimentally. [ABSTRACT FROM AUTHOR]

In this paper, we consider a fixed regression model where the errors are a strictly stationary process and in which both functions, the conditional mean and the conditional variance (volatility), are unknown. Two nonparametric estimators of the volatility function based on local polynomial fitting are studied. Expressions of the asymptotic bias and variance are given and the asymptotic normality is shown for both estimators. The influence of the dependence of the data is observed in the expressions of the variance. A simulation study and an analysis with real economic data illustrate the behavior of the proposed nonparametric estimators. [ABSTRACT FROM AUTHOR]

Consider the fixed regression model where the error random variables are coming from a strictly stationary, non-white noise stochastic process. In a situation like this, automated bandwidth selection methods for non-parametric regression break down. We present a plug-in method for choosing the smoothing parameter for local least squares estimators of the regression function. The method takes the presence of correlated errors explicitly into account through a parametric correlation function specification. The theoretical performance for the local linear estimator of the regression function is obtained in the case of an AR(1) correlation function. These results can readily be extended to other settings, such as different parametric specifications of the correlation function, derivative estimation and multiple non-parametric regression. Estimators of regression functionals and the error correlation based on local least squares ideas are developed in this article. A simulation study and an analysis with real economic data illustrate the selection method proposed. [ABSTRACT FROM AUTHOR]

In oceanography, modeling wave fields requires the use of statistical tools capable of handling the circular nature of the data measurements. An important issue in ocean wave analysis is the study of height and direction waves, being direction values recorded as angles or, equivalently, as points on a unit circle. Hence, reconstruction of a wave direction field on the sea surface can be approached by the use of a linear–circular regression model, viewing wave directions as a realization of a circular spatial process whose trend should be estimated. In this paper, we consider a spatial regression model with a circular response and several real-valued predictors. Nonparametric estimators of the circular trend surface are proposed, accounting for the (unknown) spatial correlation. Some asymptotic results about these estimators as well as some guidelines for their practical implementation are also given. The performance of the proposed estimators is investigated in a simulation study. An application to wave directions in the Adriatic Sea is provided for illustration. [ABSTRACT FROM AUTHOR]

A crankshaft is a mechanical component of an engine that performs a conversion of an alternative movement of a piston in a rotational motion of a shaft. It is a critical part and one of the most expensive of an engine. Defects in crankshafts may imply serious failures and, consequently, possible injuries and high costs. Therefore, the manufacture quality is of primordial importance for security and economic reasons. Nowadays, the quality control of crankshafts manufactured by forging in the automotive industry consists, among others, in inspecting them at the final process, using a magnetic particle procedure. This slow and highly stressful technique depends on operators and consumes many human resources, time, and space. This paper presents a methodology to automatically detect defective crankshafts. The proposed procedure is based on digital image analysis techniques, to extract a set of representative features from crankshaft images. Statistical techniques for supervised classification are used to classify the images into defective or not. The experimental results demonstrated the good performance of the proposed method with a classification accuracy over 99%, a 10% higher than the one obtained by manual inspection. Therefore, working time and personnel required for this task can be reduced when using this automated procedure. [ABSTRACT FROM AUTHOR]

In this work, a fully nonparametric geostatistical approach to estimate threshold exceeding probabilities is proposed. To estimate the large-scale variability (spatial trend) of the process, the nonparametric local linear regression estimator, with the bandwidth selected by a method that takes the spatial dependence into account, is used. A bias-corrected nonparametric estimator of the variogram, obtained from the nonparametric residuals, is proposed to estimate the small-scale variability. Finally, a bootstrap algorithm is designed to estimate the unconditional probabilities of exceeding a threshold value at any location. The behavior of this approach is evaluated through simulation and with an application to a real data set. [ABSTRACT FROM AUTHOR]

This article consists of two parts. The first one contains a brief review of global and local dependence measures, including the local Gaussian correlation. For this, the local correlation at a point x is obtained by approximating the given bivariate density f at x by a bivariate Gaussian and then taking the correlation of that bivariate Gaussian as the definition of local Gaussian correlation. The second part consists in a bias study of the local Gaussian correlation. A small simulation experiment is performed. In the Appendix, the possibility of a neighbourhood-free definition of local Gaussian correlation is explored. [ABSTRACT FROM AUTHOR]

Abstract: The principal aim of this study is to classify wood species using scanning electron microscopy (SEM) micrographs obtained with 1500× magnification and processed by image segmentation. The results show that it is possible to observe differences among species in the wood texture at this magnification. The micrographs have been processed in a simple way using segmentation and object recognition to identify the cross-section tracheids belonging to earlywood of 7 different timber species: Fagus sylvatica, Castanea sativa, Juglans regia, Eucalyptus globulus, Hymenaea courbaril, Pinus silvestris and Pinus radiata. We have analyzed the shape, number and distribution of the tracheids using 5 features: circularity, rectangularity, number of tracheids, distance between tracheids and average area. The extracted features are classified using different statistical methods: Linear Discriminant Analysis (LDA), Quadratic classification, Logistic regression, K Nearest Neighbors (KNN), Naïve Bayes, Support Vector Machines (SVM) and Neural Networks. A comparative study using gray level co-occurrence based features is also presented, with the improvement of using the segmentation method. Moreover, some additional results showing the possibility of using fractal analysis in this framework complete the research. [Copyright &y& Elsevier]

In this study, thermogravimetric (TG) and differential scanning calorimetry (DSC) curves, obtained by means of a simultaneous TG/DSC analyzer, and statistical functional nonparametric methods are used to classify different wood species. The temperature ranges, where the highest probability of correct classification is reached, are also computed. As each observation is a curve, a nonparametric functional discriminant technique based on the Bayes rule and the Nadaraya-Watson regression estimator is used. It assigns a future observation to the highest probability predefined class (supervised classification). The smoothing parameter needed in this nonparametric method is selected according to the cross-validation technique. The method proposed is applied to a sample of 49 wood items (7 per wood class) and also to classify between hardwoods and softwoods. In all the cases, the samples have been successfully classified, obtaining better results with the TG curves. The results are compared with those obtained with other nonparametric methods based on boosting algorithm. A discussion about the relation of the obtained results with the referenced wood component degradation temperature ranks is presented. [ABSTRACT FROM AUTHOR]

Abstract: The main purpose of this work is to use a new technique that combines functional data analysis and design of experiments, functional ANOVA for a one way treatment, to measure the influence of adding fumed silica on the thermal degradation of an epoxy resin. To achieve this, a design of experiments with a treatment factor (the amount of fumed silica) at three different levels (0, 10 and 20wt.%) is performed. The data are obtained through the use of Thermogravimetric Analysis (TG), resulting in five degradation curves per level. The functional ANOVA uses all the information of each curve or functional data. The results obtained using this methodology with the TG rescaled data and their derivatives (DTG) indicate that the amount of fumed silica significantly affects the thermal stability of the compound. These facts may be indicative of the interaction between the organic phase and the inorganic particles. In addition, pairwise comparisons using the functional ANOVA method and a bootstrap distance based test are carried out to discern which factor levels provide different ways of degradation. [Copyright &y& Elsevier]

The principal aim of the present study is to describe, analyze, and compare from a statistical standpoint the generalized logistic model with some well-known models used in the solid-state kinetics: power law, Avrami-Erofeev, and reaction order. For this purpose, synthetic conversion curves that simulate the kinetic processes were generated using the power law, Avrami-Erofeev, and reaction order models, where the Arrhenius equation was assumed in all the cases. This comprehensive simulation study allows to describe the relationship between the parameters belonging to the proposed generalized logistic model and the pointed traditional models' parameters, and also to validate the performance of the generalized logistic model in a wide variety of cases where other methods can be applied. Performing this analysis has been necessary to employ some new statistical techniques in thermal analysis modeling as the generalized additive models, and to perform global optimization evolutionary algorithms as the differential evolution for solving the non-linear regression problem. In order to implement these techniques, R statistical software routines were developed and applied. [ABSTRACT FROM AUTHOR]

A new statistical functional data analysis (FDA) approach to perform interlaboratory tests is proposed and successfully applied to thermogravimetry (TG) and differential scanning calorimetry (DSC). This functional approach prevents the typical losses of information associated to the dimension reduction processes. It allows the location and variability of the thermal curves obtained by the application of a particular test procedure. The intra- and inter-laboratory variability and location have been estimated using a FDA approach as well as the traditional reproducibility and repeatability studies. To evaluate the new approach, 105 TG curves and 90 calorimetric curves were obtained from calcium oxalate monohydrate. The obtained curves correspond to seven simulated laboratories, 15 curves per laboratory. Functional mean and variance were estimated. From a functional point of view, these descriptive statistics consider each datum as a curve or function of infinite dimension. Confidence bands were computed using smooth bootstrap resampling. A laboratory consistency study is performed in a functional context. The functional depth approach based on bootstrap resampling is a useful tool to identify outliers among the laboratories. The new FDA approach permits to identify as outliers the thermal curves obtained with old or wrong calibrations. Functional analysis of variance test based on random projections and the false discovery rate procedure (FDR) provides which laboratories obtain significant different thermal curves. This approach can be applied to perform interlaboratory test programs where the response of the test result is functional, as, for example, DSC and TG tests, without having to assume that data follow a Gaussian distribution. [ABSTRACT FROM AUTHOR]