Geometrical bounding of data space and nonlinear classification of chemical data using MPGA algorithm

This paper develops a multi-parturition genetic algorithm (MPGA) to be used in geometrical bounding of the overlapped clusters in a data set for the classification of chemical data. Two new operators have been introduced to modify the conventional genetic algorithm, namely, multi-parturition and decimation and orientated creation to improve the linear classification results and diminish the computational time. To circumvent the difficulty commonly encountered in the treatment of linearly inseparable chemical data sets, the optimized linear classifier is further modified to provide a complementary nonlinear classifier. For this reason the space regions of the overlapped clusters have been bounded by erection of half-hyperellipsoids over the linearly misclassified patterns. The proposed MPGA was applied to classify a number of chemical and other data sets with a dimension from 4 to 14. Experimental results have indicated that the proposed MPGA could classify seriously overlapped data sets with an acceptable error rate.     

Using mesh-based methods to solve nonlinear problems of statics for thin shells

The paper outlines a numerical procedure for solving physically and geometrically nonlinear problems of statics for thin shells based on three mesh-based methods: finite-difference, variational difference, and finite-element methods. The methodological, algorithmic, and analytical aspects of implementing the Kirchhoff–Love hypotheses are analyzed. The algorithmic approach employs Lagrangian multipliers. The advantages and disadvantages of these methods are evaluated Translated from Prikladnaya Mekhanika, Vol. 45, No. 1, pp. 41–70, January 2009.     

EMPIRICAL LIKELIHOOD RATIO CONFIDENCE INTERVALS FOR VARIOUS DIFFERENCES OF TWO POPULATIONS

Recently the empirical likelihood has been shown to be very useful in nonparametric models. Qin combined the empirical likelihood thought and the parametric likelihood method to construct confidence intervals for the difference of two population means in a semiparametric model. In this paper, we use the empirical likelihood thought to construct confidence intervals for some differences of two populations in a nonparametric model. A version of Wilks' theorem is developed.     

Strong Universal Pointwise Consistency of Recursive Regression Estimates

For semi-recursive and recursive kernel estimates of a regression of Y on X (d-dimensional random vector X, integrable real random variable Y), introduced by Devroye and Wagner and by Révész, respectively, strong universal pointwise consistency is shown, i.e. strong consistency P _X -almost everywhere for general distribution of (X, Y). Similar results are shown for the corresponding partitioning estimates.     

Nonparametric ANCOVA with two and three covariates

Fully nonparametric analysis of covariance with two and three covariates is considered. The approach is based on an extension of the model of Akritas et al. (Biometrika 87(3) (2000) 507). The model allows for possibly nonlinear covariate effect which can have different shape in different factor level combinations. All types of ordinal data are included in the formulation. In particular, the response distributions are not restricted to comply to any parametric or semiparametric model. In this nonparametric model, hypotheses of no main effect no interaction and no simple effect, which adjust for the covariate values, are defined through a decomposition of the conditional distribution functions of the response given to the factor level combination and covariate values. The test statistics are based on averages over the covariate values of certain Nadaraya–Watson regression quantities. Under their respective null hypotheses, such test statistics are shown to have a central χ² distribution. Small sample corrections are also provided. Simulation results and the analysis of two real datasets are also presented.     

Local powers of two-sample and multi-sample rank tests for Lehmann's contaminated alternative

Summary Local powers of two- andk-sample rank tests under alternatives of contaminated distributions are investigated. It is shown that the rank tests based on normal scores and Wilcoxon scores are superior to thet-test or theF-test for many choices of alternatives of contaminated distributions and that the values of the asymptotic relative efficiency of the rank test based on Wilcoxon scores with respect to the normal scores are about one in all the investigated cases.     

Nonasymptotic Bounds on the L 2 Error of Neural Network Regression Estimates

The estimation of multivariate regression functions from bounded i.i.d. data is considered. The L ₂ error with integration with respect to the design measure is used as an error criterion. The distribution of the design is assumed to be concentrated on a finite set. Neural network estimates are defined by minimizing the empirical L ₂ risk over various sets of feedforward neural networks. Nonasymptotic bounds on the L ₂ error of these estimates are presented. The results imply that neural networks are able to adapt to additive regression functions and to regression functions which are a sum of ridge functions, and hence are able to circumvent the curse of dimensionality in these cases.     

Comparative analysis of automotive paints by laser induced breakdown spectroscopy and nonparametric permutation tests

Laser-induced breakdown spectroscopy (LIBS) has been investigated for the discrimination of automobile paint samples. Paint samples from automobiles of different makes, models, and years were collected and separated into sets based on the color, presence or absence of effect pigments and the number of paint layers. Twelve LIBS spectra were obtained for each paint sample, each an average of a five single shot “drill down” spectra from consecutive laser ablations in the same spot on the sample. Analyses by a nonparametric permutation test and a parametric Wald test were performed to determine the extent of discrimination within each set of paint samples. The discrimination power and Type I error were assessed for each data analysis method. Conversion of the spectral intensity to a log-scale (base 10) resulted in a higher overall discrimination power while observing the same significance level. Working on the log-scale, the nonparametric permutation tests gave an overall 89.83% discrimination power with a size of Type I error being 4.44% at the nominal significance level of 5%. White paint samples, as a group, were the most difficult to differentiate with the power being only 86.56% followed by 95.83% for black paint samples. Parametric analysis of the data set produced lower discrimination (85.17%) with 3.33% Type I errors, which is not recommended for both theoretical and practical considerations. The nonparametric testing method is applicable across many analytical comparisons, with the specific application described here being the pairwise comparison of automotive paint samples.     

A nonparametric method of multi-step ahead forecasting in diffusion processes

This paper provides a nonparametric model of multi-step ahead forecasting in diffusion processes. The model is constructed from the local linear model with the Gaussian kernel. The paper provides simulation studies to evaluate its performance of multi-step ahead forecasting by comparing with the global linear model, showing the better forecasting performance of the nonparametric model than the global linear model. The paper also conducts empirical analysis for forecasting using intraday data of the Japanese stock price index and the time series of heart rates. The result shows the performance of forecasting does not differ much in the Japanese stock price index, but that the nonparametric model shows significantly better performance in the analysis of the heart rates.     

Empirical likelihood for balanced ranked-set sampled data

Ranked-set sampling (RSS) often provides more efficient inference than simple random sampling (SRS). In this article, we propose a systematic nonparametric technique, RSS-EL, for hypothesis testing and interval estimation with balanced RSS data using empirical likelihood (EL). We detail the approach for interval estimation and hypothesis testing in one-sample and two-sample problems and general estimating equations. In all three cases, RSS is shown to provide more efficient inference than SRS of the same size. Moreover, the RSS-EL method does not require any easily violated assumptions needed by existing rank-based nonparametric methods for RSS data, such as perfect ranking, identical ranking scheme in two groups, and location shift between two population distributions. The merit of the RSS-EL method is also demonstrated through simulation studies. This work was supported by National Natural Science Foundation of China (Grant No. 10871037)