Wavelet-based Estimation Research Articles

Wavelet Probabilistic Neural Networks.

In this article, a novel wavelet probabilistic neural network (WPNN), which is a generative-learning wavelet neural network that relies on the wavelet-based estimation of class probability densities, is proposed. In this new neural network approach, the number of basis functions employed is independent of the number of data inputs, and in that sense, it overcomes the well-known drawback of traditional probabilistic neural networks (PNNs). Since the parameters of the proposed network are updated at a low and constant computational cost, it is particularly aimed at data stream classification and anomaly detection in off-line settings and online environments where the length of data is assumed to be unconstrained. Both synthetic and real-world datasets are used to assess the proposed WPNN. Significant performance enhancements are attained compared to state-of-the-art algorithms.

A new wavelet-based estimation of conditional density via block threshold method

A new wavelet-based estimator of the conditional density is investigated. The estimator is constructed by combining a special ratio technique and applying a non negative estimator to the density function in the denominator. We used a wavelet shrinkage technique to find an adaptive estimator for this problem. In particular, a block thresholding estimator is proposed, and we prove that it enjoys powerful mean integrated squared error properties over Besov balls. Moreover, it is shown that convergence rates for the mean integrated squared error (MISE) of the adaptive estimator are optimal under some mild assumptions. Finally, a numerical example has been considered to illustrate the performance of the estimator.

Wavelet-based estimation method for online condition monitoring of dc-link capacitors of distributed energy resources

This paper proposes a novel capacitor condition monitoring for dc-link of power converters employed in distributed energy resources systems. It follows the active methodology, in which an intermittent noncharacteristic signal is injected into the dc-link to estimate the equivalent series resistance (ESR) and capacitance (C) of dc-link capacitors. A real-time stationary discrete wavelet packet transform (RT-SDWPT) performs the capacitor parameter estimations. In this scheme, an interharmonic is used as a noncharacteristic signal to prevent the influence of the system’s inherent harmonic components, mitigating estimation errors. Moreover, the interharmonic frequency is chosen in the region influenced by the ESR and C parameters to ensure capacitor degradation condition. Besides, to mitigate quality issues, the interharmonic’s amplitude, duration, and the time interval between two signal injections follow the recommendations defined by standards. Furthermore, a parameter deviation detection scheme is employed to adaptively adjust the time interval between two estimations, improving failure detection. Experimental results obtained from a microgrid laboratory setup demonstrate the effectiveness and feasibility of the proposed method.

Wavelet block thresholding for copula density estimation under biased sampling

In this paper, we consider the non-parametric estimation of the copula density under biased data. The contributions are both theoretical and practical. In the first part, we propose and develop a new wavelet-based methodology for this problem. In particular, a BlockShrink estimator is constructed, and we prove that it enjoys powerful mean integrated squared error properties over Besov balls. The second part is devoted to the applied aspect: we compare the performance of the wavelet-based estimator with that of a recently introduced kernel-based estimator through a detailed simulation study.

Block thresholding wavelet estimation of copula density based on NSD assumption

In this article, we consider the wavelet estimation of copula density for negatively superadditive dependent random variables. Using wavelet methods, we propose and develop a new estimation procedure for this problem. In particular, a BlockShrink estimator is constructed and we prove that it enjoys powerful mean integrated squared error properties over Besov balls. The main result is prepared to display the performance of the wavelet-based estimator and a simulation study to compare the behavior of the proposed wavelet estimator with the kernel copula density estimator are also given. Finally, we consider a real life application in hydrology for rainfall intensity data.

A Wavelet-Based Approach to FRF Identification From Incomplete Data

Frequency Response Function (FRF) estimation from measured data is an essential step in the design, the control, and the analysis of complex dynamical systems, including thermal and motion systems. Especially for systems that require long measurement time, missing samples in the data record, e.g., due to measurement interruptions, often occur. The aim of this paper is to achieve accurate identification of non-parametric FRF models of periodically excited systems from noisy output measurements with missing samples. An identification framework is established that exploits a wavelet-based transform to separate the effect of the missing samples in the time domain from the system characteristics in the frequency domain. The framework encompasses both a time-invariant and a time-varying wavelet-based estimator, which provide different mechanisms to address the missing samples. Experimental results from a thermo-dynamical system confirm that the estimators enable accurate identification.

Asymptotic distribution of the wavelet-based estimators of multivariate regression functions under weak dependence

Asymptotic distribution of the wavelet-based estimators of multivariate regression functions under weak dependence

Nonlinear wavelet-based estimation to spectral density for stationary non-Gaussian linear processes

Nonlinear wavelet-based estimators for spectral densities of non-Gaussian linear processes are considered. The convergence rates of mean integrated squared error (MISE) for those estimators over a large range of Besov function classes are derived, and it is shown that those rates are identical to minimax lower bounds in standard nonparametric regression model within a logarithmic term. Thus, those rates could be considered as nearly optimal. Therefore, the resulting wavelet-based estimators outperform traditional linear methods if the degree of smoothness of spectral densities varies considerably over the interval of interest, such as sharp spike, cusp, bump, etc., since linear estimators are not able to attain these rates. Unlike in classical nonparametric regression with Gaussian noise errors where thresholds are determined by normal distribution, we determine the thresholds based on a Bartlett type approximation of a quadratic form with dependent variables by its corresponding quadratic form with independent identically distributed (i.i.d.) random variables and Hanson-Wright inequality for quadratic forms in sub-gaussian random variables. The theory is illustrated with some numerical examples, and our simulation studies show that our proposed estimators are comparable to the current ones.

Identification of Mistuning Based on Forced Response Measurements and Assessment for a Real Compressor Blisk

Abstract We develop a novel method for the identification of mistuned blisks. The method relies on forced response measurements in a certain target frequency band. Modal stiffness deviations and an overall structural damping coefficient are obtained using a least-squares fit, fully consistent with a component-mode-based reduced-order model. To achieve a high frequency resolution in a very short test, we carry out rapid frequency sweeps and use a noise-robust, wavelet-based estimation of the steady-state response. The forcing is eliminated from the equations governing the mistuning parameters, and it is identified separately to reconstruct the forced response if requested. We first validate the method numerically and then apply it experimentally to a compressor blisk with an alternating (B-A) mistuning pattern. While most previous works on mistuning identification are limited to the lowest 1-2 mode families, we assess the method for the seventh (1C) and eighth (3T) mode family. Measured and reconstructed frequency responses are in good to very good agreement. We conclude that the developed method is useful to obtain high-quality estimates of mistuning parameters, which can then be used for vibration prediction.

Wavelet-Based Identification for Spinning Projectile with Gasodynamic Control Aerodynamic Coefficients Determination.

Identification of a spinning projectile controlled with gasodynamic engines is shown in this paper. A missile model with a measurement inertial unit was developed from Newton’s law of motion and its aerodynamic coefficients were identified. This was achieved by applying the maximum likelihood principle in the wavelet domain. To assess the results, this was also performed in the time domain. The outcomes were obtained for two cases: when noise was not present and when it was included in the data. In all cases, the identification was performed in the passive mode, i.e., no special system identification experiments were designed. In the noise-free case, aerodynamic coefficients were estimated with high accuracy. When noise was included in the data, the wavelet-based estimates had a drop in their accuracy, but were still very accurate, whereas for the time domain approach the estimates were considered inaccurate.

Multivariate wavelet estimators for weakly dependent processes: strong consistency rate

The present article focuses on the non parametric estimation of multivariate density and regression functions. We consider the non parametric linear wavelet-based estimators and investigate the strong consistency from the theoretical viewpoint. In particular, we prove the strong uniform consistency properties of these estimators, over compact subsets of with the determination of the corresponding rates of convergence. As a main contribution, we relax some standard dependence conditions by considering the general concept of the causal -weak dependence, including mixing concepts and adapted to diverse classes of interesting statistical processes, essentially the general Bernoulli shifts and the Markov sequences.

The Effect of Money Growth on Inflation and GDP in the Selected Asia-Pacific Markets – Wavelet-Based Bayesian Quantile Estimates

The Effect of Money Growth on Inflation and GDP in the Selected Asia-Pacific Markets – Wavelet-Based Bayesian Quantile Estimates

Wavelet-based robust estimation and variable selection in nonparametric additive models

This article studies M-type estimators for fitting robust additive models in the presence of anomalous data. The components in the additive model are allowed to have different degrees of smoothness. We introduce a new class of wavelet-based robust M-type estimators for performing simultaneous additive component estimation and variable selection in such inhomogeneous additive models. Each additive component is approximated by a truncated series expansion of wavelet bases, making it feasible to apply the method to nonequispaced data and sample sizes that are not necessarily a power of 2. Sparsity of the additive components together with sparsity of the wavelet coefficients within each component (group), results into a bi-level group variable selection problem. In this framework, we discuss robust estimation and variable selection. A two-stage computational algorithm, consisting of a fast accelerated proximal gradient algorithm of coordinate descend type, and thresholding, is proposed. When using nonconvex redescending loss functions, and appropriate nonconvex penalty functions at the group level, we establish optimal convergence rates of the estimates. We prove variable selection consistency under a weak compatibility condition for sparse additive models. The theoretical results are complemented with some simulations and real data analysis, as well as a comparison to other existing methods.

Uniform almost sure convergence and asymptotic distribution of the wavelet-based estimators of partial derivatives of multivariate density function under weak dependence

This paper is devoted to the estimation of partial derivatives of multivariate density functions. In this regard, nonparametric linear wavelet-based estimators are introduced, showing their attractive properties from the theoretical point of view. In particular, we prove the strong uniform consistency properties of these estimators, over compact subsets of , with the determination of the corresponding convergence rates. Then, we establish the asymptotic normality of these estimators. As a main contribution, we relax some standard dependence conditions; our results hold under a weak dependence condition allowing the consideration of mixing, association, Gaussian sequences and Bernoulli shifts.

Robust wavelet-based estimation for varying coefficient dynamic models under long-dependent structures

This paper considers a class of robust estimation problems for varying coefficient dynamic models via wavelet techniques, which can adapt to local features of the underlying functions and has less restriction to the smoothness of the functions. The convergence rates and asymptotic distributions of the robust wavelet-based estimator are established when the design variables are stationary short-range dependent (SRD) and the errors are long-range dependent (LRD). Particularly, a rate of convergence [Formula: see text] in terms of estimation consistency can be achievable when the true components satisfy certain smoothness for a LRD process. Furthermore, an asymptotic property of the proposed estimator is given to indicate the confidence level of our proposed method for varying coefficient models with LRD.

Multiresolution analysis of point processes and statistical thresholding for Haar wavelet-based intensity estimation

We take a wavelet-based approach to the analysis of point processes and the estimation of the first-order intensity under a continuous-time setting. A Haar wavelet multiresolution analysis is formulated which motivates the definition of homogeneity at different scales of resolution, termed J-th level homogeneity. Further to this, the activity in a point process’ first-order behaviour at different scales of resolution is also defined and termed L-th level innovation. Likelihood ratio tests for both these properties are proposed with asymptotic distributions provided, even when only a single realization is observed. The test for L-th level innovation forms the basis for a collection of statistical strategies for thresholding coefficients in a wavelet-based estimator of the intensity function. These thresholding strategies outperform the existing local hard thresholding strategy on a range of simulation scenarios. This methodology is applied to NetFlow data, characterizing multiscale behaviour on computer networks.

A Note on Wavelet-Based Estimator of the Hurst Parameter.

The signals in numerous fields usually have scaling behaviors (long-range dependence and self-similarity) which is characterized by the Hurst parameter H. Fractal Brownian motion (FBM) plays an important role in modeling signals with self-similarity and long-range dependence. Wavelet analysis is a common method for signal processing, and has been used for estimation of Hurst parameter. This paper conducts a detailed numerical simulation study in the case of FBM on the selection of parameters and the empirical bias in the wavelet-based estimator which have not been studied comprehensively in previous studies, especially for the empirical bias. The results show that the empirical bias is due to the initialization errors caused by discrete sampling, and is not related to simulation methods. When choosing an appropriate orthogonal compact supported wavelet, the empirical bias is almost not related to the inaccurate bias correction caused by correlations of wavelet coefficients. The latter two causes are studied via comparison of estimators and comparison of simulation methods. These results could be a reference for future studies and applications in the scaling behavior of signals. Some preliminary results of this study have provided a reference for my previous studies.

Wavelet pointwise estimations under multiplicative censoring

In this paper, we investigate the wavelet-based estimators of a kind of censored mixture density and discuss their pointwise asymptotic convergence rates over Hölder spaces. We first consider the linear wavelet estimator and give its upper bound. However, the linear one is nonadaptive and not applicable since it is related to the unknown space parameter. Finally, we use the hard threshold method to explore adaptive nonlinear wavelet estimator and obtain the same convergence order as the linear one up to a logarithmic penalty.

Wavelet estimation of copula function based on censored data

In this paper, we consider wavelet analysis to obtain an estimator of a copula function based on censored data. We show that optimal convergence rates for the mean integrated squared error (MISE) of linear wavelet-based function estimators are exact under right censoring model. Moreover, we derive asymptotic formulae for MISE. Finally, the simulation results and the analysis of real data validate the proposed procedure.

Global Effects of Focal Brain Tumors on Functional Complexity and Network Robustness: A Prospective Cohort Study.

BACKGROUNDNeurosurgical management of brain tumors has entered a paradigm of supramarginal resections that demands thorough understanding of peritumoral functional effects. Historically, the effects of tumors have been believed to be local, and long-range effects have not been considered.OBJECTIVETo test the hypothesis that tumors affect the brain globally, producing long-range gradients in cortical function.METHODSResting-state functional magnetic resonance imaging (fMRI) data were acquired from 11 participants with glioblastoma and split into discovery and validation datasets in a single-center prospective cohort study. Fractal complexity was computed with a wavelet-based estimator of the Hurst exponent. Distance-related effects of the tumors were tested with a tumor mask-dilation technique and parcellation of the underlying Hurst maps.RESULTSFractal complexity demonstrates a penumbra of suppression in the peritumoral region. At a global level, as distance from the tumor increases, this initial suppression is balanced by a subsequent overactivity before finally normalizing. These effects were best fit by a quadratic model and were consistent across different network construction pipelines. The Hurst exponent was correlated with graph theory measures of centrality including network robustness, but graph theory measures did not demonstrate distance-dependent effects.CONCLUSIONThis work provides evidence supporting the theory that focal brain tumors produce long-range gradients in function. Consequently, the effects of focal lesions need to be interpreted in terms of the global changes on functional complexity and network architecture rather than purely in terms of functional localization. Determining whether peritumoral changes represent potential plasticity may facilitate extended resection of tumors without functional cost.