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This paper studies the statistical behavior of the normalized subband adaptive filtering (NSAF) algorithm. An accurate statistical model of the NSAF algorithm is obtained. In the derivation, we focus on Gaussian correlated input signals. By assuming that the analysis filter bank is paraunitary and taking into account the full band adaptation mechanism of the NSAF, expressions for the first and the second moments of the adaptive filter weights are derived without invoking the slow adaptation assumption. In the derivations, several hyperelliptic integrals appear. To tackle those integrals induced by Gaussian correlated inputs, we first give a solution by resorting to the adaptive Lobatto quadrature. By invoking the averaging principle, two other approximation methods, the chi-square method and the partial fraction expansion method, are presented to approximate the statistical model as well. Monte Carlo (MC) simulation results corroborate our predictions. The Lobatto quadrature method achieves a good agreement with the MC simulation results, even for a relatively large step size. Compared with the chi-square method and the partial fraction expansion method, the Lobatto quadrature method gives better performance in terms of predicting the mean square error when the length of the adaptive filters is small to medium. The chi-square approximation method and the partial fraction expansion method give a satisfactory performance with a relatively low computational complexity when the filter length is large. [ABSTRACT FROM PUBLISHER]

In this paper we consider partial linear regression models when all the variables are measured with multiplicative distortion measurement errors. To eliminate the effect caused by the distortion, we propose the conditional absolute mean calibration, which avoids to use the nonzero expectation conditions imposed on the variables. With these calibrated variables, a profile least squares estimator is obtained, associated with its normal approximation based and empirical likelihood based confidence intervals. For the hypothesis testing on parameters, a restricted estimator under the null hypothesis and a test statistic are proposed. A smoothly clipped absolute deviation penalty is employed to select the relevant variables. The resulting penalized estimators are shown to be asymptotically normal and have the oracle property. Lastly, a score-type test statistic is then proposed for checking the validity of partial linear models. We derive asymptotic distribution of the proposed test statistic. The quadratic form of the scaled test statistic has an asymptotic chi-squared distribution under the null hypothesis and follows a noncentral chi-squared distribution under local alternatives, which converge to the null hypothesis at a parametric rate. Simulation studies demonstrate the performance of our proposed procedure and a real example is analyzed as illustrate its practical usage. [ABSTRACT FROM AUTHOR]

Abstract Clustering is one of the most commonly used techniques in data mining. Its main goal is to group objects into clusters so that each group contains objects that are more similar to each other than to objects in other clusters. The evaluation of a clustering solution is a task carried out through the application of validity indices. These indices measure the quality of the solution and can be classified as either internal that calculate the quality of the solution through the data of the clusters, or as external indices that measure the quality by means of external information such as the class. Generally, indices from the literature determine their optimal result through graphical representation, whose results could be imprecisely interpreted. The aim of this paper is to present a new external validity index based on the chi-squared statistical test named Chi Index, which presents accurate results that require no further interpretation. Chi Index was analyzed using the clustering results of 3 clustering methods in 47 public datasets. Results indicate a better hit rate and a lower percentage of error against 15 external validity indices from the literature. [ABSTRACT FROM AUTHOR]

Abstract Estimation and hypothesis tests for partial linear multiplicative models are considered in this paper. A profile least product relative error estimation method is proposed to estimate unknown parameters. We employ the smoothly clipped absolute deviation penalty to do variable selection. A Wald-type test statistic is proposed to test a hypothesis on parametric components. The asymptotic properties of the estimators and test statistics are established. We also suggest a score-type test statistic for checking the validity of partial linear multiplicative models. The quadratic form of the scaled test statistic has an asymptotic chi-squared distribution under the null hypothesis and follows a non-central chi-squared distribution under local alternatives, converging to the null hypothesis at a parametric convergence rate. We conduct simulation studies to demonstrate the performance of the proposed procedure and a real data is analyzed to illustrate its practical usage. [ABSTRACT FROM AUTHOR]

Abstract Traditionally, simple correspondence analysis is performed by decomposing a matrix of standardised residuals using singular value decomposition where the sum-of-squares of these residuals gives Pearson’s chi-squared statistic. Such residuals, which are treated as being asymptotically normally distributed, arise by assuming that the cell frequencies are Poisson random variables so that their mean and variance are the same. However, studies in the past reveal that this is not the case and that the cell frequencies are prone to overdispersion. There are a growing number of remedies that have been proposed in the statistics, and allied, literature. One such remedy, and the focus of this paper, is to stabilise the variance using the Freeman–Tukeytransformation. Therefore, the properties that stem from performing correspondence analysis will be examined by decomposing the Freeman–Tukey residuals of a two-way contingency table. The application of this strategy shall be made by studying one large, and sparse, set of archaeological data. [ABSTRACT FROM AUTHOR]

This paper proposes a chi-square method (CSM) to obtain a priority vector for group decision making (GDM) problems where decision-makers’ (DMs’) assessment on alternatives is furnished as incomplete reciprocal preference relations with missing values. Relevant theorems and an iterative algorithm about CSM are proposed. Saaty’s consistency ratio concept is adapted to judge whether an incomplete reciprocal preference relation provided by a DM is of acceptable consistency. If its consistency is unacceptable, an algorithm is proposed to repair it until its consistency ratio reaches a satisfactory threshold. The repairing algorithm aims to rectify an inconsistent incomplete reciprocal preference relation to one with acceptable consistency in addition to preserving the initial preference information as much as possible. Finally, four examples are examined to illustrate the applicability and validity of the proposed method, and comparative analyses are provided to show its advantages over existing approaches. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we propose a test of fit based on maximum entropy. The asymptotic distribution of the proposed test statistic is established and a corrected form for small and medium sample sizes is furnished. The performance of the test is investigated through extensive Monte Carlo simulations. Real examples are also presented and analyzed. [Copyright &y& Elsevier]

This paper studies the problem of estimating a parameter vector from measurements having a multivariate chi-squared distribution. Maximum likelihood estimation in this setting is unfeasible because the multivariate chi-squared distribution has no closed form expression. The typical approach to go around this consists in considering a sub-optimal solution by replacing the chi-squared distribution with a normal one. We investigate the theoretical properties of this approximation as the number of measurements approach infinity. More precisely, we show that this approximation is strongly consistency, asymptotically normal and asymptotically efficient. We consider a source localization problem as a case study. [ABSTRACT FROM AUTHOR]

The article discusses research on safety and efficiency of telephone consultations on occupational health (OH) matters. Compared to face-to-face meetings, the benefits of telephone consultations include reduction in appointment waiting times, less travel costs, and convenience for clients and OH practitioners. It acknowledged rapid expansion of OH practice supported by electronic communication and processes. The adoption of telephone consultations within OH by the corporate sector is noted.