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In a previous paper, the authors introduced a flexible methodology for reconstructing mechanical sources in the frequency domain from prior local information on both their nature and location over a linear and time invariant structure. The proposed approach was derived from Bayesian statistics, because of its ability in mathematically accounting for experimenter’s prior knowledge. However, since only the Maximum a Posteriori estimate was computed, the posterior uncertainty about the regularized solution given the measured vibration field, the mechanical model and the regularization parameter was not assessed. To answer this legitimate question, this paper fully exploits the Bayesian framework to provide, from a Markov Chain Monte Carlo algorithm, credible intervals and other statistical measures (mean, median, mode) for all the parameters of the force reconstruction problem. [ABSTRACT FROM AUTHOR]

Most commonly used distributions on the unit hypersphere S k − 1 = { v ∈ R k : v ⊤ v = 1 } , k ≥ 2 , assume that the data are rotationally symmetric about some direction θ ∈ S k − 1 . However, there is empirical evidence that this assumption often fails to describe reality. We study in this paper a new class of skew-rotationally-symmetric distributions on S k − 1 that enjoy numerous good properties. We discuss the Fisher information structure of the model and derive efficient inferential procedures. In particular, we obtain the first semi-parametric test for rotational symmetry about a known direction. We also propose a second test for rotational symmetry, obtained through the definition of a new measure of skewness on the hypersphere. We investigate the finite-sample behavior of the new tests through a Monte Carlo simulation study. We conclude the paper with a discussion about some intriguing open questions related to our new models. [ABSTRACT FROM AUTHOR]

This paper presents a time-domain method for multi-exciter random environment tests. Traditional random environment test theory has been formulated in the frequency domain, where an important step is taking the inverse of the frequency response function matrices (FRFMs). The accuracy of this inversion tends to be poor, particularly at frequencies near lightly damped resonances. The currently used control algorithms face difficulties in suppressing abnormal spectral lines caused by this inverse problem. In this paper, traditional formulations of the environment test are reformed, and the time-domain method is adopted; this results in a more precise inverse operation in environment tests. To achieve this, reference spectra are converted into time-domain response signals. The finite long driving signals are derived by the state-space method with estimated state vectors. During the process, the inverse of rank-deficient Toeplitz matrices are stabilized with truncated singular value decomposition (TSVD) to suppress all abnormally high-level components in the driving forces; thus, overall, the spectra lines produced by noise within the frequency band are filtered out. A numerical simulation of a single-axis random vibration test of a cantilever beam is conducted using the traditional frequency-domain procedure (FDP) and the proposed time-domain procedure (TDP). The response spectra generated by both procedures are tested by control algorithms, and the result shows that responses generated by the proposed TDP are more easily controlled. The conditions of stability for both the FDP and the TDP are also determined and introduced in the simulation. Moreover, a multi-axis vibration experiment further validates the effectiveness of the TDP. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we address the problem of parameter estimation of a two-dimensional (2D) chirp model under the assumption that the errors are stationary. We define a periodogram-type function, which is based on the extension of the 2D periodogram function, defined for a 2D sinusoidal model, to the 2D chirp model. We put forward an alternative to the least squares estimators (LSEs), called the approximate least squares estimators (ALSEs). The proposed estimators take less time to compute and at the same time, they are asymptotically equivalent to the LSEs. Moreover the asymptotic properties of these estimators are obtained under slightly weaker assumptions than those required for the LSEs. Finally, we propose a sequential method for the estimation of the unknown parameters of a multiple component 2D chirp model. This method significantly reduces the computational difficulty involved in finding the usual LSEs and the ALSEs. To see how the proposed method works, we perform some simulation studies and analyze a data set for illustrative purposes. [ABSTRACT FROM AUTHOR]

Based on the notions of colored and absolute excedances introduced by Bagno and Garber and their affine versions introduced by Mongelli, we compute the signed generating function of such statistics. Moreover, whenever possible, we derive a combinatorial interpretation of the coefficients of such generating functions. This paper is inspired by a paper of S. Sivasubramanian in which the author enumerates signed statistics on the group of classical permutations. [ABSTRACT FROM AUTHOR]

Unequally spaced transducer rings make it possible to extend the range of detectable azimuthal modes. The disadvantage is that the response of the mode detection algorithm to a single mode is distributed over all detectable modes, similarly to the Point Spread Function of Conventional Beamforming with microphone arrays. With multiple modes the response patterns interfere, leading to a relatively high “noise floor” of spurious modes in the detected mode spectrum, in other words, to a low dynamic range. In this paper a deconvolution strategy is proposed for increasing this dynamic range. It starts with separating the measured sound into shaft tones and broadband noise. For broadband noise modes, a standard Non-Negative Least Squares solver appeared to be a perfect deconvolution tool. For shaft tones a Matching Pursuit approach is proposed, taking advantage of the sparsity of dominant modes. The deconvolution methods were applied to mode detection measurements in a fan rig. An increase in dynamic range of typically 10–15 dB was found. [ABSTRACT FROM AUTHOR]

Intuition suggests that for a conditional to be evaluated as true, there must be some kind of connection between its component clauses. In this paper, we formulate and test a new psychological theory to account for this intuition. We combined previous semantic and psychological theorizing to propose that the key to the intuition is a relevance-driven, satisficing-bounded inferential connection between antecedent and consequent. To test our theory, we created a novel experimental paradigm in which participants were presented with a soritical series of objects, notably colored patches (Experiments 1 and 4) and spheres (Experiment 2), or both (Experiment 3), and were asked to evaluate related conditionals embodying non-causal inferential connections (such as “If patch number 5 is blue, then so is patch number 4”). All four experiments displayed a unique response pattern, in which (largely determinate) responses were sensitive to parameters determining inference strength, as well as to consequent position in the series, in a way analogous to belief bias. Experiment 3 showed that this guaranteed relevance can be suppressed, with participants reverting to the defective conditional. Experiment 4 showed that this pattern can be partly explained by a measure of inference strength. This pattern supports our theory’s “principle of relevant inference” and “principle of bounded inference,” highlighting the dual processing characteristics of the inferential connection. [ABSTRACT FROM AUTHOR]

Orthogonal linear regression is a standard statistical method which is used to fit a line to a scatter plot of data points ( x i , y i ) in situations where both variables have errors. Until now the US American R.J. Adcock has been considered to be the first who published this method, which is based on the method of least squares. We show that Julius Weisbach, professor of mathematics and engineering at Bergakademie Freiberg in Saxony (Germany) had already published in 1840 a paper in which the method is fully described and applied to an interesting problem. We discuss the context of his discovery in order to understand the type of problems mining surveyors faced in that time and why the use of this method was found to be relevant in geodesy. Weisbach's method of solution is then explained in all detail. We show that he implicitly used the method of least squares, but presented the solution in terms of geometrical arguments adapted to the readership of the journal in which he published. [ABSTRACT FROM AUTHOR]

As the vibro-acoustic requirements of modern products become more stringent, the need for robust identification methods increases proportionally. Sometimes the identification of a component is greatly complicated by the presence of a supporting structure that cannot be removed during testing. This is where substructure decoupling finds its main applications. However, despite some recent advances in substructure decoupling, the number of successful applications has so far been limited. The main reason for this is the poor conditioning of the problem that tends to amplify noise and other measurement errors. This paper proposes a new approach that uses a modal model to filter the experimental frequency response functions (FRFs). This can reduce the impact of noise and mass loading considerably for decoupling applications and decrease the quality requirements for experimental data. Furthermore, based on the uncertainty of the observed eigenfrequencies, an arbitrary number of consistent (all FRFs exhibit exactly the same poles) FRF matrices can be generated that are all contained within the variation of the original measurement. This way, the variation that is observed within the measurement is taken into account. The result is a distribution of decoupled FRFs of which the average can be used as the decoupled FRF set while the spread on the results highlights the sensitivity or reliability of the obtained results. After briefly reintroducing the theory of FRF-based substructure decoupling, the main problems in decoupling are summarized. Afterwards, the new methodology is presented and tested on both numerical and experimental cases. [ABSTRACT FROM AUTHOR]

Liu et al. (2015) proposed a novel link-free procedure for testing whether two multi-index models share identical indices via the sufficient dimension reduction approach. However, their method can only be applied to data with two populations. In practice, we often deal with situations where the same variables are being measured on objects from three or more groups, and we would like to know how similar these groups are with respect to some overall features. In this paper, we propose a link-free method which could test if three or more multi-index models share the same indices. The asymptotic properties of our test statistic are developed. Numerical studies and a real data analysis are conducted to illustrate the performance of our method. [ABSTRACT FROM AUTHOR]

For general repeated measures designs the Wald-type statistic (WTS) is an asymptotically valid procedure allowing for unequal covariance matrices and possibly non-normal multivariate observations. The drawback of this procedure is its poor performance for small to moderate samples, i.e., decisions based on the WTS may become quite liberal. It is the aim of the present paper to improve the small-sample behavior of the WTS by means of a novel permutation procedure. In particular, it is shown that a permutation version of the WTS inherits its good large-sample properties while yielding a very accurate finite-sample control of the type-I error as shown in extensive simulations. Moreover, the new permutation method is motivated by a practical data set of a split plot design with a factorial structure on the repeated measures. [ABSTRACT FROM AUTHOR]

This paper proposes a new conditional kernel CCA (canonical correlation analysis) algorithm and exploits statistical consistency of it via modified Tikhonov regularization scheme, which is a continuous study of [11] . A new measure which characterizes consistency of learning ability is discussed based on the notion of distance between feature subspaces. The consistency analysis is conducted under the assumptions of normalized cross-covariance operators, which is mild and can be constructed by means of mean square contingency. Meantime, the relationship between this new measure and previous consistency scheme is investigated. Furthermore, we study conditional kernel CCA in a more general scenario by means of the trace operator. [ABSTRACT FROM AUTHOR]

Based on data mining technology, this paper incorporates Bayesian networks to examine ecosystem data in order to investigate the static and dynamic benefits of returning farmland to forests and ecological compensation. The restricted network structure is suggested to reduce training costs and simplify model structure. Simultaneously, in order to increase prediction accuracy over a single model, ensemble learning is utilized to train multiple models to solve the same problem. Furthermore, based on data mining, this article explores the ecosystem's development purpose, constituent elements, and static framework, illustrates its operation and evolution mechanism, and constructs an evaluation system for returning farmland to forest and ecological compensation. Finally, this article incorporates current situation to determine the static and dynamic benefits, and then systematically verifies it using experiments and mathematical statistics. The research findings indicate that the impact of the framework built in this paper meets the standards of the construction model which could be used in practice. • Evaluate the static benefits and dynamic effects of returning farmland. • Analyzed ecological compensation benefits & established dynamic cycle compensation model. • Illustrates operation & evolution mechanism, and constructs an evaluation system for returning farmland. [ABSTRACT FROM AUTHOR]

We show how it is possible to assess the rate of convergence in the Gaussian approximation of triangular arrays of U -statistics, built from wavelets coefficients evaluated on a spherical Poisson field of arbitrary dimension. For this purpose, we exploit the Stein–Malliavin approach introduced in the seminal paper by Peccati, Solé, Taqqu and Utzet (2011); we focus in particular on statistical applications covering evaluation of variance in non-parametric density estimation and Sobolev tests for uniformity. [ABSTRACT FROM AUTHOR]

This paper is concerned with the development of a general methodology for identifying mechanical sources from prior local information on both their nature and location over the studied structure. For this purpose, the formulation of the identification problem is derived from the Bayesian statistics, that provides a flexible way to account for local a priori on the distribution of sources. Practically, the resulting optimization problem can be seen as a group generalized Tikhonov regularization, that is solved in an iterative manner. The main features of the proposed identification method are illustrated with both numerical and experimental examples. In particular, it is shown that properly exploiting the local spatial information drastically improves the quality of the source identification. [ABSTRACT FROM AUTHOR]

Estimators of partial parameters in general linear models involve some complicated operations of the submatrices in the given matrices and their generalized inverses in the models. In this case, more efforts are needed to find variety of properties hidden behind these estimators. In this paper, we use some new analytical tools in matrix theory to investigate the connections between the ordinary least-squares estimators and the best linear unbiased estimators of the whole and partial unknown parameters in general linear model with restrictions. In particular, we derive necessary and sufficient conditions for the ordinary least-squares estimators to be the best linear unbiased estimators of the whole and partial unknown parameters in the model. [ABSTRACT FROM AUTHOR]

Given a probability measure μ , on the space of strictly positive densities M μ , we construct a topological manifold on which the elements are connected by κ -exponential models in the form q = exp κ ⁡ ( u ⊖ κ K p , κ ( u ) ) p , where exp κ ⁡ ( x ) = ( 1 + κ 2 x 2 + κ x ) 1 / κ , x ⊖ κ y = x 1 + κ 2 y 2 − y 1 + κ 2 x 2 , p , q ∈ M μ , and their local representations are elements of an Orlicz space, i.e. the manifold is modeled on Orlicz spaces. Parameter k is the G. Kaniadakis parameter for κ -deformed exponentials which is strongly relevant to relativity and statistical complex models in statistical mechanics. Functional K p , κ is the deformed counterpart of the cumulant mapping and satisfies that, if κ → 0 , we obtain the usual cumulant functional of the exponential manifold; moreover in this limit case the exponential manifold constructed by Pistone and Sempi is recovered. In the context of deformed exponentials, we prove that the function ϕ κ ( ⋅ ) = cosh κ ⁡ ( ⋅ ) − 1 , where cosh κ ⁡ ( x ) is the κ -deformed hyperbolic cosine, is a Young function and generates the Orlicz space on which the κ -exponential manifold is modeled, namely L ϕ κ ( p ⋅ μ ) . This construction differs from the one made by Pistone on the paper κ-exponential models from the geometrical viewpoint , since this last one is based on divergence functionals and modeled on Lebesgue spaces L 1 / κ ( p ⋅ μ ) . The use of κ -deformed models is interesting since they generalize the exponential models and extend them to non-additive systems. [ABSTRACT FROM AUTHOR]

In this paper, we present a new reversible data hiding method based on histogram shifting using localization. Our proposed method selects peak point as the reference point, then uses the two neighboring points of the peak point to achieve secret data embedding based on histogram shifting and the peak point keeps unchanged. In the extraction end, we no longer need the key information about the peak point, we can directly find the peak point from the histogram to extract the secret data. We also exploit the localization to make the histogram of embedded cover image become almost the same as the histogram of the original cover image. The embedding capacity is also increased rapidly by the localization with multilayer embedding. Experimental results show that our proposed method is effective and superior. [ABSTRACT FROM AUTHOR]

Inference for variance components in linear mixed models of ANOVA type, including estimation and testing, has been investigated when the number of fixed effects is fixed. However, for high-dimensional data, this number is large and would be regarded as a divergent value as the sample size goes to infinity. In this paper, existing tests are extended to handle this problem with a sparse model structure. To avoid the impact from insignificant fixed effects, the proposed tests are post-selection-based with an orthogonality-based selection of SCAD type applied to selecting significant fixed effects into working model. The selection and estimation of fixed effects are under the assumption on the existence of second order moments for errors. Two types of tests for random effects are considered and some new insights are obtained. The proposed tests are distribution-free, though they request the existence of the fourth moments of random effects and errors. The proposed methods are illustrated by simulation studies and a real data analysis. [ABSTRACT FROM AUTHOR]

The class of Dirichlet random vectors is central in numerous probabilistic and statistical applications. The main result of this paper derives the exact tail asymptotics of the aggregated risk of powers of Dirichlet random vectors when the radial component has df in the Gumbel or the Weibull max-domain of attraction. We present further results for the joint asymptotic independence and the max–sum equivalence. [ABSTRACT FROM AUTHOR]

Classification arises in a wide range of applications. A variety of statistical tools have been developed for learning classification rules from data. Understanding of their relative merits and comparisons help users to choose a proper method in practice. This paper focuses on theoretical comparison of model-based classification methods in statistics with algorithmic methods in machine learning in terms of the error rate. Extending Efron’s comparison of logistic regression with linear discriminant analysis (LDA) under the normal setting, we contrast such algorithmic methods as the support vector machine (SVM) and boosting with the LDA and logistic regression and study their relative efficiencies in reducing the error rate based on the limiting behavior of the classification boundary of each method. We show that algorithmic methods are generally less effective than model-based methods in the normal setting. In particular, loss of efficiency in error rate is typically about 33% to 60% for the SVM and 50% to 80% for boosting when compared to the LDA. However, a smooth variant of the SVM is shown to be even more efficient than logistic regression. In addition to the theoretical study, we present results from numerical experiments under various settings for comparisons of finite-sample performance and robustness to mislabeling and model misspecification. [ABSTRACT FROM AUTHOR]

Statistical methods for functional data are of interest for many applications. In this paper, we prove a central limit theorem for random variables taking their values in a Hilbert space. The random variables are assumed to be weakly dependent in the sense of near epoch dependence, where the underlying process fulfills some mixing conditions. As parametric inference in an infinite dimensional space is difficult, we show that the nonoverlapping block bootstrap is consistent. Furthermore, we show how these results can be used for degenerate von Mises-statistics. [ABSTRACT FROM AUTHOR]

In this paper, we focus on the variable selection for semiparametric varying coefficient partially linear models with longitudinal data. A new variable selection procedure is proposed based on the combination of the basis function approximations and quadratic inference functions. The proposed procedure simultaneously selects significant variables in the parametric components and the nonparametric components. With appropriate selection of the tuning parameters, we establish the consistency and asymptotic normality of the resulting estimators. Extensive Monte Carlo simulation studies are conducted to examine the finite sample performance of the proposed variable selection procedure. We further illustrate the proposed procedure by an application. [ABSTRACT FROM AUTHOR]

Abstract: The current note discusses the consistency proof for the penalized maximum likelihood estimator of a Gaussian mixture from the paper ‘Inference for multivariate normal mixtures’ by J. Chen and X. Tan. A soft spot in that proof is identified and a rigorous alternative proof based on a uniform law of iterated logarithm is given. [Copyright &y& Elsevier]

Abstract: The minimum covariance determinant (MCD) estimator of scatter is one of the most famous robust procedures for multivariate scatter. Despite the quite important research activity related to this estimator, culminating in the recent thorough asymptotic study of Cator and Lopuhaä (2010, 2012), no results have been obtained on the corresponding estimator of shape, which is the parameter of interest in many multivariate problems (including principal component analysis, canonical correlation analysis, testing for sphericity, etc.) In this paper, we therefore propose and study MCD-based inference procedures for shape, that inherit the good robustness properties of the MCD. The main emphasis is on asymptotic results, for point estimation (Bahadur representation and asymptotic normality results) as well as for hypothesis testing (asymptotic distributions under the null and under local alternatives). Influence functions of the MCD-estimators of shape are obtained as a corollary. Monte-Carlo studies illustrate our asymptotic results and assess the robustness of the proposed procedures. [Copyright &y& Elsevier]

This paper proposes a novel system to analyze human-object interaction events happening between hands and faces in real time. Two challenging problems in this event analysis must be addressed, i.e. , there is no prior knowledge (like shape, color, size, and texture) about the handheld objects, and there are large spatial–temporal variations in event representation. For the first challenge, a novel ratio histogram is proposed to find important color bins to locate handheld objects and their trajectories via a code book technique. This scheme is different from other boosted methods which require very time-consuming estimations to search reliable body configurations. For the second challenge, a mixture of HMMs is proposed to describe an event not only from its dynamic context but also its multiplicity context. It can be performed in real time because an exhaustive search process is avoided to find possible interaction pairs between objects and body parts. [ABSTRACT FROM AUTHOR]