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This research presents a method for developing optimal health indicators for early fault detection in machine condition monitoring. The devised health indicators are optimal in the Neyman–Pearson sense, as they maximize the probability of detection while maintaining a constant false alarm rate. They are generated through a generalized likelihood ratio test that involves the probability density functions representing the healthy and faulty states. The essence of the approach lies in establishing a framework that defines optimal health indicators as functions of the partial derivatives of the healthy probability density function and a modulation function, representing the distortion of the probability density function in the faulty state. Specific modulation functions lead to the recovery of several traditional health indicators, including kurtosis, skewness, the crest factor, the clearance factor, the smoothness factor, the shape factor, the impulse factor, ℓ p / ℓ q -norms, the negentropy, among others. New health indicators are also derived. As the proposed optimal health indicators asymptotically follow a chi-squared distribution, they come with a statistical threshold. The study comprehensively outlines the methodology, with its performance assessed through simulated and experimental signals. The results reveal that the early transition from healthy to faulty can be well detected via the established optimal health indicators and their thresholds. • Proposal of a theoretical framework for designing health indicators optimal for early fault detection. • The theory provides constant-false-alarm-rate optimality and indicator thresholds. • Recovery of several traditional health indicators along with their statistical thresholds. • Design of new indicators under the generalized Gaussian assumption. • Performance analysis on real data. [ABSTRACT FROM AUTHOR]

Bearing-supported shafts are widely used in various machines. Due to harsh working environments, bearing performance degrades over time. To prevent unexpected bearing failures and accidents, bearing performance degradation assessment becomes an emerging topic in recent years. Bearing performance degradation assessment aims to evaluate the current health condition of a bearing through a bearing health indicator. In the past years, many signal processing and data mining based methods were proposed to construct bearing health indicators. However, the upper and lower bounds of these bearing health indicators were not theoretically calculated and they strongly depended on historical bearing data including normal and failure data. Besides, most health indicators are dimensional, which connotes that these health indicators are prone to be affected by varying operating conditions, such as varying speeds and loads. In this paper, based on the principle of squared envelope analysis, we focus on theoretical investigation of bearing performance degradation assessment in the case of additive Gaussian noises, including distribution establishment of squared envelope, construction of a generalized dimensionless bearing health indicator, and mathematical calculation of the upper and lower bounds of the generalized dimensionless bearing health indicator. Then, analyses of simulated and real bearing run to failure data are used as two case studies to illustrate how the generalized dimensionless health indicator works and demonstrate its effectiveness in bearing performance degradation assessment. Results show that squared envelope follows a noncentral chi-square distribution and the upper and lower bounds of the generalized dimensionless health indicator can be mathematically established. Moreover, the generalized dimensionless health indicator is sensitive to an incipient bearing defect in the process of bearing performance degradation. [ABSTRACT FROM AUTHOR]

We revisit the well-known Behrens–Fisher problem in an original and challenging high-dimensional framework, and propose a testing procedure which accommodates a low-dimensional latent factor model. The developed inferential framework is general, as it applies to problems where the underlying populations may be non-normal, the dimension of the population mean vectors may highly exceed the sample size, the design may be unbalanced, and the loading factor dimensions may be different. Under a high-dimensional asymptotic regime, combined with fairly weak technical conditions, we show that null limiting distributions of the test statistics follow a weighted mixture of chi-square distributions, which depends only on the spectrum of the noise covariance matrix and the number of latent factors. As these latter are usually unknown in practice, we exploit an estimation procedure which builds on recent advances in random matrix theory. The asymptotic power of the proposed test is established. A numerical study confirms good analytical properties of the new test that compares favorably to existing procedures used in a similar context. Real data applications are demonstrated with a study of a leukemia data set. [ABSTRACT FROM AUTHOR]

In previous work by Bozchalooi and Liang (Journal of Sound and Vibration 308 (2007) 246–267), the dimensionless smoothness index was defined as the ratio of the geometric mean to the arithmetic mean of the modulus of Gabor wavelet coefficients. Moreover, it was proven that the modulus of Gabor wavelet coefficients follows the Rician distribution and the upper bound of the smoothness index converges to a constant of 0.8455… in the case of a very low signal-to-noise ratio. However, there are two problems in the work of Bozchalooi and Liang. The first problem is that an underlying assumption was made for the Rician distribution, namely, that only one harmonic is retained by the Gabor wavelet transform. For bearing fault diagnosis by envelope analysis, the frequency of the bearing fault and several of its harmonics are required to assess the severity of the fault, because the number of harmonics in the envelope is directly related to information on the geometrics of the fault. Consequently, there is a contradiction between the Rician distribution and the envelope analysis. To solve the first problem, we have mathematically proven that the ratio of the modulus/squared modulus of Gabor wavelet coefficients to the noise standard deviation/variance follows the noncentral chi/chi-square distribution, which does not require the aforementioned underlying assumption. The second problem is that Bozchalooi and Liang assumed that a bearing fault signal is periodic when they calculated the upper bound of the dimensionless smoothness index. In theory, because of slippage of rollers, a bearing fault signal is not purely periodic but slightly random. To solve the second problem, we have incorporated cyclostationary analysis into our proof procedure for calculating the upper bound of the dimensionless smoothness index. Moreover, we have redefined the smoothness index as the ratio of the geometric mean to the arithmetic mean of the squared modulus of the Gabor wavelet coefficients, and we have proven that the upper bound of the smoothness index converges to a constant of 0.5614… in the case of a very low signal-to-noise ratio. [ABSTRACT FROM AUTHOR]

Little is known about consumers' behavior especially their choice behavior toward purchasing and consuming dairy products in developing countries. Hence, the aim of the present work is understanding the factors that affect on consumers' choice behavior toward dairy products in Iran. The study applies the theory of consumption values, which includes the functional values (taste, price, health, and body weight), social value, emotional value, conditional value and epistemic value. The sample were 1420 people (men and women). The data was collected using face to face survey in summer and fall 2015. Chi-square, confirmatory factor analysis, and structural equation modelling is used to assess data collected. The results indicate that functional values, social value, emotional value and epistemic value have a positive impact on choosing dairy products and conditional value didn't have a positive impact. It was concluded that the main influential factors for consumers' choice behavior toward dairy products included consumers experience positive emotion (e.g. enjoyment, pleasure, comfort and feeling relaxed) and functional value-health. This study emphasized the proper pricing of dairy products by producers and sellers. [ABSTRACT FROM AUTHOR]

Likelihood ratio tests (LRTs) for separability of a covariance structure for doubly multivariate data are widely studied in the literature. There are three types of LRT: biased tests based on an asymptotic chi-square null distribution; unbiased/unmodified tests based on an empirical null distribution; and unbiased/modified tests with a test statistic modified to follow a theoretical chi-square null distribution. The Rao’s score test (RST) statistic, an alternative for both biased and unbiased/unmodified versions of the corresponding LRT test statistics, is derived for a common case. In this paper the separability of a covariance structure with the first component as a compound symmetric correlation matrix under the assumption of multivariate normality is tested. For this purpose Monte Carlo simulation studies, which compare the biased LRT to biased RST, and unbiased/unmodified LRT to unbiased/unmodified RST, are conducted. It is shown that the RSTs outperform their corresponding LRTs in the sense of empirical Type I error as well as empirical null distribution. Moreover, since the RST does not require estimation of a general variance–covariance matrix (the alternative hypothesis), RST can be performed for small sample sizes, where the variance–covariance matrix could not be estimated for the corresponding LRT, making the LRT infeasible. Three examples are presented to illustrate and compare statistical inference based on LRT and RST. [ABSTRACT FROM AUTHOR]

Let X ∼ N v ( 0 , Λ ) be a normal vector in v ( ≥ 1 ) dimensions, where Λ is diagonal. With reference to the truncated distribution of X on the interior of a v -dimensional Euclidean ball, we completely prove a variance inequality and a covariance inequality that were recently discussed by Palombi and Toti (2013). These inequalities ensure the convergence of an algorithm for the reconstruction of Λ only on the basis of the covariance matrix of X truncated to the Euclidean ball. The concept of monotone likelihood ratio is useful in our proofs. Moreover, we also prove and utilize the fact that the cumulative distribution function of any positive linear combination of independent chi-square variates is log-concave, even though the same may not be true for the corresponding density function. [ABSTRACT FROM AUTHOR]

In this paper, we consider the application of the empirical likelihood method to a partly linear model with measurement errors in possibly all the variables. It is shown that the empirical log-likelihood ratio at the true parameters converges to the standard chi-square distribution. Also, a class of estimators for the parameter are constructed, and the asymptotic distributions of the proposed estimators are obtained. Some simulations and an application are conducted to illustrate the proposed method. [ABSTRACT FROM AUTHOR]

A general linear hypothesis testing (GLHT) problem in heteroscedastic one-way MANOVA for high-dimensional data is considered and a normal reference L 2 -norm based test for the problem is proposed. Different from a few existing methodologies on the GLHT problem which impose strong assumptions on the underlying covariance matrices so that the associated tests' null distributions are asymptotically normal, it is shown that under some regularity conditions, the proposed test statistic under the null hypothesis and a chi-square type mixture have the same normal or non-normal limiting distributions. It is then suggested to approximate the test's null distribution using the distribution of the chi-square type mixture, which can be further approximated by the Welch–Satterthwaite chi-square-approximation with approximation parameters consistently estimated. Several simulation studies and a real data application are presented to demonstrate the good performance of the proposed test. [ABSTRACT FROM AUTHOR]

Abstract: Objectives: There is limited data regarding physical strain and minimally invasive gynecologic surgery (MIS). We sought to evaluate ergonomic strain among gynecologic oncologists. Methods: An online survey was sent to all physician members of the Society of Gynecologic Oncology in North America in 2010. The survey contained 42 questions and data was analyzed using univariate and bivariate analyses with summary statistics, t-tests, and chi-squared test. Results: There were 260 respondents (31.2%) to the survey. Case mix was 26% benign and 64% oncologic surgery. Over 52% of respondents had been in practice for greater than 11years and 52% practice in an academic setting. Physical discomfort related to MIS was reported in 88% (216/244) of surgeons with 52% reporting persistent pain. Increased pain symptoms were associated with surgeon''s height, glove size, age and female gender. Patient body mass index (BMI) was associated with pain symptoms in surgeons performing conventional laparoscopic surgery, but not robotic surgery. To decrease pain, surgeons changed positions (78%), limited the number of cases per day (14%), spread cases throughout the week (6%), or limited the total number of cases (3%). Only 29% had received treatment at any time for pain symptoms. Treatment included physical therapy (59%), medical management (28%), surgery (13%), and time off (1%). Only 16% of those with pain symptoms had received formal ergonomic training. Conclusion: Physical strain rates of 88% are far greater than previously reported. Such prevalent occupational strain presents a growing problem in the face of increasing demand for MIS. [Copyright &y& Elsevier]

Abstract: Objective: To test the hypothesis that the use of closed suction pelvic drains placed at time of large bowel resection (LBR) for ovarian cancer (OC) decreases morbidity following anastomotic leak (AL). Methods: Consecutive cases of LBR for OC between 01/01/1994 and 06/20/2011 were retrospectively identified. Drains were routinely used until bowel movement. AL was defined as: 1) feculent fluid from drains/wound/vagina, 2) radiographic evidence of AL, or 3) AL found at reoperation. Descriptive statistics, Wilcoxon rank-sum, Pearson''s chi-square and Fisher''s exact test were used. Results: 43 cases met inclusion criteria. AL was characterized by method of diagnosis as follows: change in drain output only (DO, n=8); change in drain output associated with ambiguous clinical signs/symptoms (D-SSX, n=11); or clinical signs/symptoms only (SSX, n=24). The sensitivity of drains in diagnosing AL was 50%. Time to diagnosis was earlier in DO/D-SSX (median 7 vs. 11days, P =0.003), however, no significant differences were observed in rates of reoperation, length of stay, time to chemotherapy (TTC), and 30- and 90-day mortality between DO/D-SSX and SSX. Comparing cases where no drains were placed (n=5) vs. those with drain (n=38), we observed no differences in outcomes. TTC though statistically significant (47 vs. 59days, P =0.023) was not clinically significant. Conclusions: Though a change in drain output correlated with earlier diagnosis, this did not appear to impact overall outcomes. We did not find strong evidence supporting routine prolonged drainage after LBR for OC. Additionally, absence of change in drain output does not rule out presence of AL. [Copyright &y& Elsevier]

Abstract: The Bartlett-type adjustment is a higher-order asymptotic method for improving the chi-squared approximation to the null distributions of various test statistics. Though three influential papers were published in 1991—Chandra and Mukerjee (1991) , Cordeiro and Ferrari (1991) and Taniguchi (1991) in alphabetical order, the only CF-approach has been frequently applied in the literature during the last two decades, provided that asymptotic expansion for the null distribution of a given test statistic is available. Revisiting the CM/T-approaches developed in the absence of a nuisance parameter, this paper suggests general adjustments for a class of test statistics that includes, in particular, the likelihood ratio, Rao’s and Wald’s test statistics in the presence of a nuisance parameter. [Copyright &y& Elsevier]

Abstract: This article deals with the inference on a right-censored partially linear single-index model (RCPLSIM). The main focus is the local empirical likelihood-based inference on the nonparametric part in RCPLSIM. With a synthetic data approach, an empirical log-likelihood ratio statistic for the nonparametric part is defined and it is shown that its limiting distribution is not a central chi-squared distribution. To increase the accuracy of the confidence interval, we also propose a corrected empirical log-likelihood ratio statistic for the nonparametric function. The resulting statistic is proved to follow a standard chi-squared limiting distribution. Simulation studies are undertaken to assess the finite sample performance of the proposed confidence intervals. A real example is also considered. [Copyright &y& Elsevier]

Abstract: Double-sampling designs are commonly used in real applications when it is infeasible to collect exact measurements on all variables of interest. Two samples, a primary sample on proxy measures and a validation subsample on exact measures, are available in these designs. We assume that the validation sample is drawn from the primary sample by the Bernoulli sampling with equal selection probability. An empirical likelihood based approach is proposed to estimate the parameters of interest. By allowing the number of constraints to grow as the sample size goes to infinity, the resulting maximum empirical likelihood estimator is asymptotically normal and its limiting variance–covariance matrix reaches the semiparametric efficiency bound. Moreover, the Wilks-type result of convergence to chi-squared distribution for the empirical likelihood ratio based test is established. Some simulation studies are carried out to assess the finite sample performances of the new approach. [Copyright &y& Elsevier]

Abstract: In logistic regression models, we consider the deviance statistic (the log likelihood ratio statistic) as a goodness-of-fit test statistic. In this paper, we show the derivation of an expression of asymptotic expansion for the distribution of under a null hypothesis. Using the continuous term of the expression, we obtain a Bartlett-type transformed statistic that improves the speed of convergence to the chi-square limiting distribution of . By numerical comparison, we find that the transformed statistic performs much better than . We also give a real data example of being more reliable than for testing a hypothesis. [Copyright &y& Elsevier]

Abstract: This article proposes the efficient empirical-likelihood-based inferences for the single component of the parameter and the link function in the single-index model. Unlike the existing empirical likelihood procedures for the single-index model, the proposed profile empirical likelihood for the parameter is constructed by using some components of the maximum empirical likelihood estimator (MELE) based on a semiparametric efficient score. The empirical-likelihood-based inference for the link function is also considered. The resulting statistics are proved to follow a standard chi-squared limiting distribution. Simulation studies are undertaken to assess the finite sample performance of the proposed confidence intervals. An application to real data set is illustrated. [Copyright &y& Elsevier]

Abstract: One important step in regression analysis is to identify significant predictors from a pool of candidates so that a parsimonious model can be obtained using these significant predictors only. However, most of the existing methods assume linear relationships between response and predictors, which may be inappropriate in some applications. In this article, we discuss a link-free method that avoids specifying how the response depends on the predictors. Therefore, this method has no problem of model misspecification, and it is suitable for selecting significant predictors at the preliminary stage of data analysis. A test statistic is suggested and its asymptotic distribution is derived. Examples are used to demonstrate the proposed method. [ABSTRACT FROM AUTHOR]

Abstract: Empirical likelihood (EL) ratio tests are developed for testing for or against the hypothesis that -population means are isotonic with respect to some quasi-order on . The null asymptotic distributions are derived and are shown to be of chi-bar squared type. The asymptotic power of the proposed test for testing for equality of these means against the order restriction is derived under contiguous alternatives and a simulation study is carried out to investigate the finite sample behaviors of this test. In addition, an adjusted EL test is used to improve the small size performance of our test and an example is also discussed to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

Abstract: Proteomics uses tandem mass spectrometers and correlation algorithms to match peptides and their fragment spectra to amino acid sequences. The replication of multiple liquid chromatography experiments with electrospray ionization of peptides and tandem mass spectrometry (LC–ESI–MS/MS) produces large sets of MS/MS spectra. There is a need to assess the quality of large sets of experimental results by statistical comparison with that of random expectation. Classical frequency-based statistics such as goodness-of-fit tests for peptide-to-protein distributions could be used to calculate the probability that an entire set of experimental results has arisen by random chance. The frequency distributions of authentic MS/MS spectra from human blood were compared with those of false positive MS/MS spectra generated by a computer, or instrument noise, using the chi-square test. Here the mechanics of the chi-square test to compare the results in toto from a set of LC–ESI–MS/MS experiments with those of random expectation is detailed. The chi-square analysis of authentic spectra demonstrates unambiguously that the analysis of blood proteins separated by partition chromatography prior to tryptic digestions has a low probability that the cumulative peptide-to-protein distribution is the same as that of random or noise false positive spectra. [Copyright &y& Elsevier]

Abstract: In this paper, we investigate the empirical likelihood for constructing a confidence region of the parameter of interest in a multi-link semiparametric model when an infinite-dimensional nuisance parameter exists. The new model covers the commonly used varying coefficient, generalized linear, single-index, multi-index, hazard regression models and their generalizations, as its special cases. Because of the existence of the infinite-dimensional nuisance parameter, the classical empirical likelihood with plug-in estimation cannot be asymptotically distribution-free, and the existing bias correction is not extendable to handle such a general model. We then propose a link-based correction approach to solve this problem. This approach gives a general rule of bias correction via an inner link, and consists of two parts. For the model whose estimating equation contains the score functions that are easy to estimate, we use a centering for the scores to correct the bias; for the model of which the score functions are of complex structure, a bias-correction procedure using simpler functions instead of the scores is given without loss of asymptotic efficiency. The resulting empirical likelihood shares the desired features: it has a chi-square limit and, under-smoothing technique, high order kernel and parameter estimation are not needed. Simulation studies are carried out to examine the performance of the new method. [Copyright &y& Elsevier]

Abstract: We present a complete description of the analytic properties of the Barnes double zeta and Gamma functions. [Copyright &y& Elsevier]

Abstract: Let denote the digamma function. We study the linear independence of at rational arguments over algebraic number fields. We also formulate a variant of a conjecture of Rohrlich concerning linear independence of the log gamma function at rational arguments and report on some progress. We relate these conjectures to non-vanishing of certain L-series. [Copyright &y& Elsevier]

Abstract: For a class of multivariate skew normal distributions, the noncentral skew chi-square distribution is studied. The necessary and sufficient conditions under which a sequence of quadratic forms is generalized noncentral skew chi-square distributed random variables are obtained. Several examples are given to illustrate the results. [Copyright &y& Elsevier]

Abstract: The normal distribution based likelihood ratio (LR) statistic is widely used in structural equation modeling. Under a sequence of local alternative hypotheses, this statistic has been shown to asymptotically follow a noncentral chi-square distribution. In practice, the population mean vector and covariance matrix as well as the model and sample size are always fixed. It is hard to justify the validity of the noncentral chi-square distribution for the resulting LR statistic even when data are normally distributed and sample size is large. By extending results in the literature, this paper develops normal distributions to describe the behavior of the LR statistic for mean and covariance structure analysis. A sequence of local alternative hypotheses is not necessary for the proposed distributions to be asymptotically valid. When the effect size is medium and above or when the model is not trivially misspecified, empirical results indicate that a refined normal distribution describes the behavior of the LR statistic better than the commonly used noncentral chi-square distribution, as measured by the Kolmogorov–Smirnov distance. Quantile–quantile plots are also provided to better understand the different distributions. [Copyright &y& Elsevier]

We propose a significance test to determine if data on a regular d -dimensional grid can be assumed to be a realization of Gaussian process. By accounting for the spatial dependence of the observations, we derive statistics analogous to sample skewness and kurtosis. We show that the sum of squares of these two statistics converges to a chi-square distribution with two degrees of freedom. This leads to a readily applicable test. We examine two variants of the test, which are specified by two ways the spatial dependence is estimated. We provide a careful theoretical analysis, which justifies the validity of the test for a broad class of stationary random fields. A simulation study compares several implementations. While some implementations perform slightly better than others, all of them exhibit very good size control and high power, even in relatively small samples. An application to a comprehensive data set of sea surface temperatures further illustrates the usefulness of the test. [ABSTRACT FROM AUTHOR]

Some patients with psychogenic nonepileptic seizures (PNES) remit when given the diagnosis. It is not realistically possible to test this potential therapeutic effect in an Randomized Controlled Trial (RCT) so we aim to statistically demonstrate it using the temporal relationship between the communication of the diagnosis and the timing of remission. Re-analysis of data from a study of PNES, where diagnosis was communicated, and outcomes recorded in 54 patients. Making conservative assumptions and using the binomial distribution, the Poisson distribution and the chi-squared test distribution, we calculated likelihoods of the null hypothesis: that communication of the diagnosis and remission of seizures had occurred in random temporal relationship. Remission occurred in the week following communication of the diagnosis in 15 out of 54 patients. The χ2 test assigned this result a p value of < 0.00001. Binomial and Poisson distribution calculations also indicated that remission was highly unlikely to have occurred by chance and that, in a dataset similar to ours, was unlikely to be due to chance if occurring in more than 9 patients (16.7%). We showed that the observed remissions were highly unlikely to be due to chance. Where an intervention is 'short and sharp' and the outcome can be measured with reasonable temporal acuity, then this type of method may provide an alternative to RCT methodology when the latter is impracticable. • Psychogenic nonepileptic seizures often stop when the diagnosis is given. • We used the timing of seizure cessation to calculate a likelihood that seizure cessation happened by chance. • We demonstrated that giving the diagnosis of PNES is therapeutically effective. • Our method offers a way of assessing the effectiveness of strategies for communicating the diagnosis of PNES. [ABSTRACT FROM AUTHOR]