Non-normal Measurement Research Articles

비정규지표를 이용한 Well-Conditioned 관측기 설계

In this paper, the well-conditioned observer is designed to be insensitive to the ill-conditioning factors in transient and steady-state observer performance. A condition number based on 12-norm of the eigenvector matrix of the observer matrix has been proposed on a principal index in the observer performance. For the well-conditioned observer design, the non-normality measure and the observability condition of the observer matrix are utilized. The two constraints are specified into observer gain boundary region that guarantees a small condition number and a stable observer. The observer gain selected in this region guarantees a well-conditioned and observable property. In this study, this method is applied to the Luenberger observer and Kalman filters for small order systems. In designing Kalman filters, the ratio of the process noise covariance to the measurement noise covariance is a design parameter and its effect on the condition number is investigated.

T-2-4-1 Design of the Well-Conditioned Observer Using the Non-Normality Measure

T-2-4-1 Design of the Well-Conditioned Observer Using the Non-Normality Measure

Tests of goodness of fit based on the $L_2$-Wasserstein distance

We consider the Wasserstein distance between a sample distribution and the set of normal distributions as a measure of nonnormality. By considering the standardized version of this distance we obtain a version of Shapiro–Wilk’s test of normality. The asymptotic behavior of the statistic is studied using approximations of the quantile process by Brownian bridges. This method differs from the “ad hoc” method of de Wet and Venter and permits a similar analysis for testing other location scale families.

Reproducibility of electromyographic recordings of submaximal concentric and eccentric muscle contractions in humans

Objectives: to determine the intratester and intertester reliability of measures of electromyographic activity (EMG) of submaximal concentric and eccentric contractions and to compare the reliability of normalized and non-normalized measures of EMG. There were 10 subjects, of 22–33 years old. Methods: Subjects performed submaximal concentric and eccentric contractions at 60°/s, and maximal isometric contractions (MIC) of their knee extensors. The target power of the submaximal contractions was 90%±10% of the subject's maximal concentric power. EMG was recorded via bipolar surface electrodes from 3 of the quadriceps femoris muscles. The rmsEMG for submaximal contractions that were within the target power range were determined. The rmsEMG for the submaximal contractions were normalized to the rmsEMG of the maximal isometric contractions. Intraclass correlation coefficients (ICC version 1.1) were calculated to determine intratester and intertester reliability. Results: For non-normalized rmsEMG, ICC values for intratester reliability ranged from 0.62 to 0.91 for concentric and from 0.84 to 0.97 for eccentric contractions. ICC values for intertester reliability ranged from 0.66 to 0.96 for concentric and 0.78 to 0.90 for eccentric contractions. Conclusions: Non-normalized rmsEMG of submaximal concentric and eccentric isokinetic contractions were found to be reliable. Normalization did not lead to consistently improved reliability.

Accurate test limits under nonnormal measurement error

When screening a production process for nonconforming items the objective is to improve the average outgoing quality level. Due to measurement errors specification limits cannot be checked directly and hence test limits are required, which meet some given requirement, here given by a prescribed bound on the consumer loss. Classical test limits are based on normality, both for the product characteristic and for the measurement error. In practice, often nonnormality occurs for the product characteristic as well as for the measurement error. Recently, nonnormality of the product characteristic has been investigated. In this paper attention is focussed on the measurement error. Firstly, it is shown that nonnormality can lead to serious failure of the test limit. New test limits are therefore derived, which have the desired robustness property: a small loss under normality and a large gain in case of nonnormality when compared to the normal test limit. Monte Carlo results illustrate that the asymptotic theory is in agreement with moderate sample behaviour.

A Non-Normality Measure of the Condition Number for Monitoring and Control

Because the behavior of the condition number can have highly steep and multi-modal structure, optimal control and monitoring problems based on the condition number cannot be easily solved. In this paper, a minimization problem is formulated for κ2(P), the condition number of an eigensystem (P) of a matrix in terms of the L2 norm. A new non-normality measure is shown to exist that guarantees small values for the condition number. In addition, this measure can be minimized by proper selection of controller and observer gains. Application to the design of well-conditioned controller and observer-based monitors is illustrated.

Detecting powder mixture inhomogeneity for non-normal measurement errors

Since the 1940s the technique of mixing indices has been used to determine the level of inhomogeneity in powder mixtures. In 1995, the application of the analysis of variance technique (ANOVA) to this problem was introduced and was shown to overcome several critical limitations of the index approach. However, one possible limitation of ANOVA is its normality assumption. Thus, this article examines the robustness of this assumption using several very non-normal distributions for measurement errors and compares the ANOVA technique with the nonparametric Kruskal-Wallis method in a Monte Carlo simulation study. The Kruskal-Wallis method makes no assumption regarding the distribution of the data.

Extreme value regression models: A useful reparameterization for the survival function

In this paper, we consider some aspects of accurate approximate inferences for the survival function at a specifed time t 0 , considering extreme value regression models using a modified form of reparameterization proposed by Guerrero and Johnson, and exploring a non-normality measure for likelihood functions and posterior densities introduced by Kass and Slate. We illustrate the proposed methodology, considering a lifetime data set with two treatments introduced by Lee.

Gli indici di proiezione nella Projection Pursuit

In this paper the different measures of non normality, proposed in the statistical literature on projection pursuit as projection indices, are critically reviewed. In order to guarantee an affine invariant final solution, evidence is given for the preferability of affine invariant indices, rather than sphere data. Starting from these considerations, the affine invariant version of each of the presented indices is reported, and the results, obtained on real and simulated data, are compared highlighting the confirmations and the denials towards the ones reported in the literature for sphere data.

Moments of regression F-statistics under non-normality

Assuming the errors to be non-normal with finite moments, the mean, variance, skewness and kurtosis of the null distribution of the F-statistics in a linear regression model (while testing a subset, or all the coefficients to be equal to zero) are derived to the order O(1/n2), where n is the sample size. It is found that non-normality of errors has insignificant effect on the mean. The variance is sensitive to kurtosis but insensitive to skewness of the error distribution. The extent of his sensitivity depends upon the kurtosis-type measure of non-normality of the “test” regressors.The test regressors are the ones for whose coefficients are tested to be zeroes. In contrast, both skewness and kurtosis of the F-statistics are found to be sensitive to both skewness and kurtosis of the error distributions. Again, the extent of this sensitivity depends upon the skewness and kurtosis-type measures of non-normality of the test regressors. These effects are all of order O(l/n), so that they are negligible in larg...

Some Diagnostics of Maximum Likelihood and Posterior Nonnormality

Standard large-sample maximum likelihood and Bayesian inference, based on limiting multivariate normal distributions, may be dubious when applied with small or moderate sample sizes. We define and discuss several measures of nonnormality of MLE and posterior distributions that may be used as diagnostics and can indicate whether reparameterization will be effective in improving inferences. We begin by showing how the nonlinearity measures introduced by Beale and Bates and Watts for nonlinear regression may be generalized to exponential family nonlinear models. We replace the exponential family regression surface with another surface defined in terms of the parameterization in which the third derivatives of the loglikelihood function vanish at the MLE, and then we compute "curvatures" of the latter surface. This generalization effectively replaces the normal-theory Euclidean geometry with an $\alpha$-connection geometry of Amari identified by Kass, yet it may be understood and implemented without reference to that foundational argument. We also discuss alternative diagnostics based on the observed third derivatives of the loglikelihood function, or the third derivatives of a $\log$ posterior density. These may be viewed as multiparameter generalizations of a nonnormality measure proposed by Sprott. We show how one of these diagnostics may be quickly and easily computed using approximations of Tierney, Kass and Kadane.

Measuring Toxics Use Reduction in the Metal Intensive Industries

This study examined toxics use reduction measurement among metal intensive manufacturers (SIC 34-39) located in Massachusetts. Of the 110 study firms chosen from a stratified random sample, less than half said they documented and measured their toxics use reduction progress. During on-site visits with twenty-eight of these firms, roughly half measured their progress accurately. Toxics use reduction measurement errors were most frequently due to one or a combination of five causes: use of poor normalization factors, inaccurate math calculations, materials accounting mistakes, incorrect chemical balances, and poor production unit definitions. In reconciling these errors, chemical input data was found to be more accurate than byproduct and emission data. Using chemical input data, the study documented over 2.4 million pounds of toxics use reduction at 28 metal-intensive firms. To adjust reductions to the level of business activity, linear regression techniques were used to choose normalization measures which correlated with chemical use. The study found that for 20 chemicals, there was only a 5% difference between normalized and non-normalized measures of toxics use reduction.

On measures of nonnormality of matrices

This paper discusses several measures of nonnormality of matrices, i.e., functions v: C n, n → R plus where v( A)=0 iff A is normal. Besides measures already in the literature, we introduce new ones and give comparisons between them at length. Some of these comparisons, e.g. (C14), (C15), and (C17) manifest well-known phenomena of ill-conditioned eigenproblems.

Selection of Trimming Proportions for Robust Adaptive Trimmed Means

Abstract Asymptotic variances of trimmed means for a family of symmetric distributions including the uniform, normal, and double exponential are examined and used to suggest forms of adaptive trimmed means as robust estimators of location. The proportions of trimming in the adaptive estimators are based on simple functions of easily obtained measures of nonnormality.

Selection of Trimming Proportions for Robust Adaptive Trimmed Means

Abstract Asymptotic variances of trimmed means for a family of symmetric distributions including the uniform, normal, and double exponential are examined and used to suggest forms of adaptive trimmed means as robust estimators of location. The proportions of trimming in the adaptive estimators are based on simple functions of easily obtained measures of nonnormality.

On Measures of Non-Normality for Matrices

On Measures of Non-Normality for Matrices