Parameters Of Linear Model Research Articles

An empirical study on decoupling PNLSS models illustrated on an airplane

Abstract This paper illustrates a combined nonparametric and parametric system identification framework for modeling nonlinear vibrating structures. First step is the analysis: multiple-input multiple-output measurements are (semi-automatically) preprocessed, and a nonparametric Best Linear Approximation (BLA) method is performed. The outcome of the BLA analysis results in nonparametric frequency response function, noise and nonlinear distortion estimates. Based on this information, a linear parametric (state-space) model is built. This model is used to initialize a high complexity Polynomial Nonlinear State-Space PNLSS model. The nonlinear part of a PNLSS model is manifested as a combination of high-dimensional multivariate polynomials. The last step in the proposed approach is the decoupling: transforming multivariate polynomials into a simplified, alternative basis, thereby dramatically reducing the number of parameters. In this work a novel filtered canonical polyadic decomposition (CPD) is used. The proposed methodology is illustrated on, but of course not limited to, a ground vibration testing measurement of an air fighter.

Ordinary least squares estimation of parameters of linear model

This research article primarily focuses on the method of ordinary least squares estimation of parameters of linear model. Here an innovative proof of Gauss-Markoff theorem for linear estimation has been presented. An extensive discussion in evaluating Best Linear Unbiased Estimator (BLUE) of a linear parametric function of the classical linear model is made by using the Gauss-Markoff theorem. Furthermore the importance of mean vector and covariance matrix of BLUE is discussed. Moreover generalized Gauss-Markoff theorem for linear estimation, properties of OLS estimators and problems of linear model by violating the assumptions are extensively discussed.

Anomaly detection of structural health monitoring data using the maximum likelihood estimation-based Bayesian dynamic linear model

Enormous data are continuously collected by the structural health monitoring system of civil infrastructures. The structural health monitoring data inevitably involve anomalies caused by sensors, transmission errors, or abnormal structural behaviors. It is important to identify the anomalies and find their origin (e.g. sensor fault or structural damage) to make correct interventions. Moreover, online anomaly identification of the structural health monitoring data is critical for timely structural condition assessment and decision-making. This study proposes an online approach for detecting anomalies of the structural health monitoring data based on the Bayesian dynamic linear model. In particular, Bayesian dynamic linear model, consisting of various components, is implemented to characterize the feature of real-time measurements. Expectation maximization algorithm and Kalman smoother are combined to estimate the Bayesian dynamic linear model parameters and generate log-likelihood functions. The subspace identification method is introduced to overcome the initialization issue of the expectation maximization algorithm. The log-likelihood difference of consecutive time steps is then used to determine thresholds without introducing extra anomaly detectors. The proposed Bayesian dynamic linear model-based approach is first illustrated by the simulation data and then applied to the structural health monitoring data collected from two long-span bridges. The results indicate that the proposed method exhibits good accuracy and high computational efficiency and also allows for reconstructing the strain measurements to replace anomalies.

Dynamics of symmetric and asymmetric potential well-based piezoelectric harvesters: A comprehensive review

Small and micro-scale energy harvesting is an essential and viable option for the powering of portable and maintenance free electronic devices, wireless sensor nodes, and similar applications. In this regard, piezoelectric harvesters have presented promising outcomes. This article provides a sequential, comprehensive, and informative survey of potential well based models and studies related to piezoelectric harvesters (PEH). Piezoelectric materials used for energy harvesting are discussed briefly, following which a non-dimensional generalized model is derived to set the discussion on a common platform. Dynamics of various potential well configurations are presented using the generalized model before discussing specific models and related studies. The survey is classified into symmetric and asymmetric potential well categories. Under the symmetric head, lumped and distributed parameter linear models and tuning methods for improving the broadband response are discussed. Subsequently, studies related to nonlinear mono-stable, bi-stable, and tri-stable potentials showing interwell, multi-periodic and chaotic oscillations with improved broadband response are discussed. The asymmetric section studies the influence of asymmetries on the performance of the mono-stable, bi-stable, and tri-stable configurations. Few other configurations outside the cantilever type PEH were mentioned, realizing the widespread research in this field. Important observations and future challenges for performance improvement are also discussed.

Using Bayes weights to remedy the heterogeneity problem of random error variance in linear models

In this research, it was suggested to use the InformativeBayes method in calculating the Bayes weights and use them to treat the of heterogeneity problem when estimating the linear regression model parameters using the weighted least squares method (BWLS). And compare it with the classical method through an experimental side to simulate the generated data from a normal distribution and for several different cases as well as an applied side of real data. The results of the research provided the preference of the proposed method on the classical method by relying on some statistical criteria through a program designed for this purpose in the language of MATLAB.

Shared and unsplittable performance links in network DEA

Data envelopment analysis (DEA) is a broadly used non-parametric technique for performance evaluation and data analytics. While conventional single-stage DEA models overlook the internal interactions of decision making units (DMUs), network DEA opens this black box to investigate the internal structure of DMUs. Practically, many network DEA models involve shared performance measures that are not easily divisible among individual components of a network. Based upon a two-stage network DEA model, the current study treats such performance measures as inseparable links, implying that no proportions are optimized and allocated to the two stages of the network. The shared and unsplittable links in the proposed two-stage DEA model manifest integrality while both ends of the link are maximized or minimized simultaneously, and this setting has not been modeled in any existing DEA studies. The shared and unsplittable links in our model can be considered intermediate measures, but they are different from the two existing types of dual-role intermediate measures, which are traditional intermediate measures and feedback measures. Our performance link is a new type of intermediate measure that is minimized or maximized in both stages of the network. The resulting network DEA model is highly non-linear. To address the non-linearity, a parametric linear model is adopted. The proposed approach is construed in four variants, and then illustrated using a set of 100 banks in the United States.

Detection of transient neurotransmitter response using personalized neural networks

Measurement of stimulus-induced dopamine release and other types of transient neurotransmitter response (TNR) from dynamic positron emission tomography (PET) images typically suffers from limited detection sensitivity and high false positive (FP) rates. Measurement of TNR of a voxel-level can be particularly problematic due to high image noise. In this work, we perform voxel-level TNR detection using artificial neural networks (ANN) and compare their performance to previously used standard statistical tests. Different ANN architectures were trained and tested using simulated and real human PET imaging data, obtained with the tracer [11C]raclopride (a D2 receptor antagonist). A distinguishing feature of our approach is the use of ‘personalized’ ANNs that are designed to operate on the image from a specific subject and scan. Training of personalized ANNs was performed using simulated images that have been matched with the acquired image in terms of the signal, resolution, and noise.In our tests of TNR detection performance, the F-test of the linear parametric neurotransmitter PET model fit residuals was used as the reference method. For a moderate TNR magnitude, the areas under the receiver operating characteristic curves in simulated tests were 0.64 for the F-test and 0.77–0.79 for the best ANNs. At a fixed FP rate of 0.01, the true positive rates were 0.6 for the F-test and 0.8–0.9 for the ANNs. The F-test detected on average 28% of a 8.4 mm cluster with a strong TNR, while the best ANN detected 47%. When applied to a real image, no significant abnormalities in the ANN outputs were observed. These results demonstrate that personalized ANNs may offer a greater detection sensitivity of dopamine release and other types of TNR compared to previously used method based on the F-test.

Ecological models for estimating breakpoints and prediction intervals.

The relationships between an environmental variable and an ecological response are usually estimated by models fitted through the conditional mean of the response given environmental stress. For example, nonparametric loess and parametric piecewise linear regression model (PLRM) are often used to represent simple to complex nonlinear relationships. In contrast, piecewise linear quantile regression models (PQRM) fitted across various quantiles of the response can reveal nonlinearities in its range of variation across the explanatory variable.We assess the number and positions of candidate breakpoints using loess and compare the relative efficiencies of PLRM and PQRM to quantitatively determine the breakpoints' location and precision. We propose a nonparametric method to generate bootstrap confidence intervals for breakpoints using PQRM and prediction bands for loess and PQRM. We illustrated the applications using data from two aquatic studies suspected to exhibit multiple environmental breakpoints: relating a fish multimetric index of community health (MMI) to agricultural activity in wetlands' adjacent drainage basins; and relating cyanobacterial biomass to total phosphorus concentration in Canadian lakes.Two statistically significant breakpoints were detected in each dataset, demarcating boundaries of three linear segments, each with markedly different slopes. PQRM generated less biased, more accurate, and narrower confidence intervals for the breakpoints and narrower prediction bands than PLRM, especially for small samples and large error variability. In both applications, the relationship between the response and environmental variables was weak/nonsignificant below the lower threshold, strong through the midrange of the environmental gradient, and weak/nonsignificant beyond the upper threshold.We describe several advantages of PQRM over PLRM in characterizing environmental relationships where the scatter of points represents natural environmental variation rather than measurement error. The proposed methodology will be useful for detecting multiple breakpoints in ecological applications where the limits of variation are as important as the conditional mean of a function.

The Environmental Kuznets Curve with Recycling: A Partially Linear Semiparametric Approach

This paper is the first to study a comparatively new Environmental Kuznets Curve which traces empirically the relationship between environmental abatement and real GDP. Our model is a partial linear semi parametric model that allows for two way fixed effects to eliminate the bias arising from two sources. We use data for recycling and real GDP, for fifty states of the United States for the years between 1988 and 2017. We find evidence that this relationship is characterized by an increasing curve which confirms the existence of a J curve, a finding that agrees with the predictions from recent theoretical models.

Simplification on Cross-Component Linear Model in Versatile Video Coding

To improve coding efficiency by exploiting the local inter-component redundancy between the luma and chroma components, the cross-component linear model (CCLM) is included in the versatile video coding (VVC) standard. In the CCLM mode, linear model parameters are derived from the neighboring luma and chroma samples of the current block. Furthermore, chroma samples are predicted by the reconstructed samples in the collocated luma block with the derived parameters. However, as the CCLM design in the VVC test model (VTM)-6.0 has many conditional branches in its processes to use only available neighboring samples, the CCLM implementation in parallel processing is limited. To address this implementation issue, this paper proposes including the neighboring sample generation as the first process of the CCLM, so as to simplify the succeeding CCLM processes. As unavailable neighboring samples are replaced with the adjacent available samples by the proposed CCLM, the neighboring sample availability checks can be removed. This results in simplified downsampling filter shapes for the luma sample. Therefore, the proposed CCLM can be efficiently implemented by employing parallel processing in both hardware and software implementations, owing to the removal of the neighboring sample availability checks and the simplification of the luma downsampling filters. The experimental results demonstrate that the proposed CCLM reduces the decoding runtime complexity of the CCLM mode, with negligible impact on the Bjøntegaard delta (BD)-rate.

Beyond Imperviousness: The Role of Antecedent Wetness in Runoff Generation in Urbanized Catchments

AbstractExplaining the response of catchments with a mix of pervious and impervious surfaces requires the inclusion of controls other than catchment imperviousness. In this study, we made use of a large sample of 70,227 events in 852 U.S. catchments to analyze the interplay of total impervious area (TIA) and antecedent soil moisture (ASM) in determining the event runoff ratio (RR). First, we investigated the importance of TIA as a spatial control compared to other catchment attributes (describing climate and catchment landscape) in explaining the differences between catchments in terms of median event‐scale RR. Second, we examined the importance of ASM as a temporal control of the variability of RR in comparison with spatial settings and event characteristics. Third, events were grouped into 30 classes of TIA and 30 classes of ASM, and linear regression models were used to analyze the evolution of RR depending on each one of the two independent variables. Results showed the following: (1) Analysis of the importance of space‐varying catchment descriptors highlighted the relevance of TIA as a control of catchment response, whereas ASM showed a stronger ability compared to other event characteristics. (2) ASM played a significant role in urbanized catchments as in rural ones. The absence of abrupt changes in the linear model parameters indicates that the impact of urbanization on the relationship between RR and ASM was relatively gradual. (3) Differences in RR between rural and intensively urbanized catchments were observable not only for dry pre‐event conditions but also for wet short‐term conditions.

Robust estimation and variable selection in heteroscedastic regression model using least favorable distribution

The assumption of equal variances is not always appropriate and different approaches for modelling variance heterogeneity have been widely studied in the literature. One of these approaches is joint location and scale model defined with the idea that both the location and the scale depend on explanatory variables through parametric linear models. Because the joint location and scale model includes two models, it does not deal well with a large number of irrelevant variables. Therefore, determining the variables that are important for the location and the scale is as important as estimating the parameters of these models. From this point of view, a combine robust estimation and variable selection method is proposed to simultaneously estimate the parameters and select the important variables. This is done using the least favorable distribution and least absolute shrinkage and selection operator method. Under appropriate conditions, we study the consistency, asymptotic distribution and the sparsity property of the proposed robust estimator. Simulation studies and a real data example are provided to demonstrate the advantages of the proposed method over existing methods in literature.

Polymeric Ionic Liquids Derived from L-Valine for the Preparation of Highly Selective Silica-Supported Stationary Phases in Gas Chromatography.

A series of silica-supported polymeric ionic liquid (PIL)-based stationary phases derived from a vinylic L-valine ionic liquid monomer and divinylbenzene (DVB) as the crosslinking agent have been prepared and studied as gas chromatographic stationary phases. These coated gas chromatographic columns exhibited good thermal stabilities (230–300 °C) and high efficiencies (1700–2700 plates/m), and were characterized using a linear solvation parameter model in order to understand the effects of the amount of DVB on the features of the resulting composite systems. Their retention behavior and separation efficiencies were demonstrated using the Grob test. By tuning the crosslinking degree for the IL-derived stationary phase, the separation selectivity and resolution of different compounds were improved. The different retention behaviors observed for many analytes indicate that these stationary phases may be applicable as new types of GC stationary phases.

Demographic and migration processes of labor potential: a case study the agricultural sector of the Republic of Kazakhstan

It is very important to study the demographic and migration processes in the country when forming the labor potential of rural areas. Using these indicators affecting the labor potential, we calculated the parameters of linear trend models, checking their adequacy of the constructed models, calculated the determination coefficients, and built confidential intervals for the forecasts. In order to present a quantitative model expressing the general tendency of the time series change over time, we used the analytical alignment of the time series. In this case, the actual levels were replaced by levels calculated on the basis of certain data. As a result, we got the result of a change in time of the studied indicators in a positive direction. Obtained results: outflow of external and internal migration is the reason for the decline of labor potential in the country, but in general does not affect the efficiency of labor potential of the village; indicators of the population in general, i.e., the population of cities and villages, internal and external migration with natural population growth are quite close to one, what means that their forecast changes are insignificant and do not undergo significant changes in the future. Finally, with a 95% probability, we can expect that in 2020 - 2021, the indicators under consideration will not take values less than the lower limits of confidence forecast intervals and not greater than their upper limits. Obtain results are very important for development of a strategy for the effective use of labor potential.

A Multi Linear Regression Model to Derive Dust PM10 in the Sahel Using AERONET Aerosol Optical Depth and CALIOP Aerosol Layer Products

Due to a limited number of monitoring stations in Western Africa, the impact of mineral dust on PM10 surface concentrations is still poorly known. We propose a new method to retrieve PM10 dust surface concentrations from sun photometer aerosol optical depth (AOD) and CALIPSO/CALIOP Level 2 aerosol layer products. The method is based on a multi linear regression model that is trained using co-located PM10, AERONET and CALIOP observations at 3 different locations in the Sahel. In addition to the sun photometer AOD, the regression model uses the CALIOP-derived base and top altitude of the lowermost dust layer, its AOD, the columnar total and columnar dust AOD. Due to the low revisit period of the CALIPSO satellite, the monthly mean annual cycles of the parameters are used as predictor variables rather than instantaneous observations. The regression model improves the correlation coefficient between monthly mean PM10 and AOD from 0.15 (AERONET AOD only) to 0.75 (AERONET AOD and CALIOP parameters). The respective high and low PM10 concentration during the winter dry season and summer season are well produced. Days with surface PM10 above 100 μg/m3 are better identified when using the CALIOP parameters in the multi linear regression model. The number of true positives (actual and predicted concentrations above the threshold) is increased and leads to an improvement in the classification sensitivity (recall) by a factor 1.8. Our methodology can be extrapolated to the whole Sahel area provided that satellite derived AOD maps are used in order to create a new dataset on population exposure to dust events in this area.

Structural Identification of Masonry Residential Buildings Considering Wall Openings

Although one-story residential masonry structures are thought not to be vulnerable to seismic actions, many heavily damaged and/or collapsed instances of these types of structures have been observed in the past strong earthquake events. Hence, the evaluation of their safety requires much attention in terms of more precise numerical models. In-situ vibration tests together with laboratory tests on masonry specimens provide valuable information for structural parameter identification that can be used to develop accurate numerical models. These numerical models then can be used for evaluation of the response and seismic safety. While many specific methods and parameters can be adopted in numerical modeling, linear material properties of a structure are expedient in response analysis. Hence, an equation to be used to determine the homogenized linear model parameters for masonry walls with openings is proposed in this study. The equation has been developed based on the percentage of the openings on the wall. The effect of wall openings on the stiffness and the total strength of one-story masonry structures have been evaluated by using the experimental data and the calibrated finite element models. In-situ ambient vibration and material tests have been conducted on three masonry buildings with identical materials and the results from these experiments were used to verify the accuracy of the formulation.

Least Quartic Regression Criterion to Evaluate Systematic Risk in the Presence of Co-Skewness and Co-Kurtosis

This article proposes a new method for the estimation of the parameters of a simple linear regression model which is based on the minimization of a quartic loss function. The aim is to extend the traditional methodology, based on the normality assumption, to also take into account higher moments and to provide a measure for situations where the phenomenon is characterized by strong non-Gaussian distribution like outliers, multimodality, skewness and kurtosis. Although the proposed method is very general, along with the description of the methodology, we examine its application to finance. In fact, in this field, the contribution of the co-moments in explaining the return-generating process is of paramount importance when evaluating the systematic risk of an asset within the framework of the Capital Asset Pricing Model. We also illustrate a Monte Carlo test of significance on the estimated slope parameter and an application of the method based on the top 300 market capitalization components of the STOXX® Europe 600. A comparison between the slope coefficients evaluated using the ordinary Least Squares (LS) approach and the new Least Quartic (LQ) technique shows that the perception of market risk exposure is best captured by the proposed estimator during market turmoil, and it seems to anticipate the market risk increase typical of these periods. Moreover, by analyzing the out-of-sample risk-adjusted returns we show that the proposed method outperforms the ordinary LS estimator in terms of the most common performance indices. Finally, a bootstrap analysis suggests that significantly different Sharpe ratios between LS and LQ yields and Value at Risk estimates can be considered more accurate in the LQ framework. This study adds insights into market analysis and helps in identifying more precisely potentially risky assets whose extreme behavior is strongly dependent on market behavior.

Linear Kalman Filter-Based Grid Synchronization Technique: An Alternative Implementation

Grid synchronization techniques play a significant role in integrating renewable energy sources to the electric power grid. In this context, estimating the phase and frequency of the grid voltage signal is an interesting problem. Out of various techniques available in the literature, linear Kalman filter (LKF) is one of the most popular one. In this article, we propose an alternative implementation of the LKF for grid synchronization application. The proposed implementation uses a linear parametric model of the grid voltage signal including dc offset. It does not involve any quadrature signal generation, rather it works by estimating the phase angle. This helps to estimate the unknown grid frequency directly from the phase angle. This clearly differentiates the proposed alternative implementation with respect to the existing implementations. Performance improvement by the proposed technique is verified extensively through comparative numerical simulation and experimental studies. Comparative results demonstrate the suitability of the proposed technique with respect to other state-of-the-art techniques namely second-order generalized integrator phase-locked loop and enhanced phase-locked loop.

Labour market marginalisation in young refugees with and without common mental disorders

Abstract Background This study explored how inequality in labour market marginalisation (LMM) between refugees and their peers developed during early adulthood in Denmark and Sweden (DK/SE), and the role of common mental disorders (CMD) in these trends. Methods Using registry data, all refugees living in DK/SE in 2009-2012 who were born 1986-1993 and who immigrated as children (aged 0-17) were included (N = 13,390/45,687) and 1:5 matched on age, sex and municipality size to individuals born in DK/SE with at least one parent also born in DK/SE (N = 69,650/227,287). Information on psychiatric care (hospital and medicine) during 2009-2011 indicated CMD, while LMM was measured during 2012-2015 using income-based indicators. Probabilities of LMM were standardized by multiplying the estimated parameters of linear probability models in SE (adjusted for age, sex, municipality size, age of arrival, origin country, and accompanying family) onto the mean of the covariates in DK. Results The risk of LMM was 2-2.5 times higher for refugees across ages 20-29 in DK/SE. The risk tended to decrease in SE but increased in DK for refugees. The increase was accentuated for youth with CMD. However, CMD did not explain the inequality between refugee and majority youth. The increase in DK was driven by birth-cohort differences, while the trend in SE was consistent across birth cohorts. Conclusions CMD did not capture the vulnerability that sets refugees apart from their peers. While immigration and integration policy differences between DK and SE increased, the integration outcomes diminished, suggesting the importance of factors other than national level policies. Key messages Young refugees in DK/SE were more at risk of labour market marginalization than their majority peers. Healthcare contact for common mental disorders raised levels, but did not reduce inequalities. Labour market marginalisation decreased with age in Sweden but increased for refugees in Denmark, driven by birth cohort difference.

Beyond Deep Learning: An Econometric Example

In the past, in many areas, the best prediction models were linear and nonlinear parametric models. In the last decade, in many application areas, deep learning has shown to lead to more accurate predictions than the parametric models. Deep learning-based predictions are reasonably accurate, but not perfect. How can we achieve better accuracy? To achieve this objective, we propose to combine neural networks with parametric model: namely, to train neural networks not on the original data, but on the differences between the actual data and the predictions of the parametric model. On the example of predicting currency exchange rate, we show that this idea indeed leads to more accurate predictions.