Method Of Least Absolute Deviations Research Articles

Evaluating the Characteristics of Spatial Variability of Soil in Vertical Direction Highly Heterogeneous Region Based on Cone Penetration Test

Abstract Key parameters describing the spatial variability of soil properties based on the random field theory are the scale of fluctuation (SOF) and coefficient of variation (COV). To characterize the spatial variability of soil properties, reducing the impact of these errors and uncertainties is necessary. To accomplish this, for the five main layers of soil, we collected 18 cone penetration test (CPT) data from a highly heterogeneous region in Lianyungang New Airport, Jiangsu Province, China, and used the control variable method to analyze the influence of the estimation method of tendency, its function type and outliers. The results show that, compared with the ordinary least square method (OLSM), the least absolute deviation method (LADM) can more truly reflect the trend component of CPT parameters in the vertical direction, and the influence of other factors on SOF and COV is also studied, such as outliers and estimation functions of trend components. On this basis, a reasonable calculation process of SOF and COV is summarized, which provides a reference for the calculation of SOF and COV in vertical direction in the future. By comparing the SOF calculated by different models, the results show that the squared exponential (SQX) model has the highest SOF in 68.3% of the evaluation, and the single exponential (SNX) model has the lowest SOF in 64.4% of the evaluation. Moreover, we compared the SOF and COV of cone tip resistance (qc) and sleeve friction (fs), which showed that SOF of qc and COV of qc is lower than that of fs in 54.4 and 73.3% of all evaluations, respectively.

Regression analysis of data based on the method of least absolute deviations in dynamic estimation problems

The use of regression analysis in dynamic problems of system estimation requires a high-speed algorithm of model parameter determination. Moreover, the original data may have stochastic heterogeneity which entails the necessity of the estimates of model parameters be resistant to various data anomalies. However, stable estimation methods, including the least absolute deviations method, are significantly inferior to the parametric ones. The goal of the study is to describe a computationally efficient algorithm for implementing the method of least absolute deviations for dynamic estimation of regression models and to study its capabilities for solving practical problems. This algorithm is based on descending along nodal lines. In this case, instead of the values of the objective function, its derivative in the direction of descent is considered. The computational complexity of the algorithm is also reduced due to the use of the solution of the problem at the previous step as a starting point and efficient updating of observations in the current data sample. The external performance of the proposed dynamic version of the algorithm of gradient descent along nodal lines has been compared with the static version and with the least squares method. It is shown that the dynamic version of the algorithm of gradient descent along the nodal lines make it possible to bring the speed close to that of the least squares method for common practical situations and to use the proposed version in dynamic estimation problems for a wide class of systems.

A Comparison Two Ridge Regression Using LAD method with Simulation

The multicollinearity is the one of the important and contained problems in regression analysis, because its effect on model estimators, the problem is that the independent variables are so closely related that the results of the regression are not clear, the aim of this research is to solve the problem of multicollinearity. one of the solutions get of this problem has deal with, which is the ridge regression of least absolute deviation (LAD) estimators, by adding a proposed a ridge parameter which is considered as contribution to solving the problem of multicollinearity by modify B M Golam Kibria () then compared it between them. The () is the best estimator by simulation study and mean square error (MSE) critical.

Algorithms for descent along nodal straight lines in the problem of estimating regression equations using the least absolute deviations method

A problem of estimating linear regression equations by the least absolute deviations method is considered. The exact methods of implementation of the method are significantly inferior in performance to the least square method. The fastest algorithm based on coordinate descent along nodal straight lines has a computational complexity proportional to the square of the number of observations, which limits the practical application of the method to monitoring and diagnostic tasks. The goal of the study is to describe a faster version of the descent along the nodal straight lines, as well as to evaluate the performance. Reduction of the computational costs is achieved due to the fact that instead of calculating the values of the objective function at nodal points, we find the derivative of the objective function in the vicinity of these points along the nodal line. The computational efficiency of gradient descent along nodal straight lines is estimated. For a typical computer, a comparative analysis of the average calculation time for various algorithms of descent along nodal straight lines is performed. A simple example is given to illustrate the implementation of a gradient descent procedure. Along with reduction of the computational costs, we also eliminated the possibility of accumulating computational errors when determining the values of the objective function for large samples. Moreover, gradient descent is quite simple for implementation. This makes it possible to use the method of least absolute deviations as an alternative to the least square method in various practical applications.

Robust Estimation Based on the Least Absolute Deviations Method and the Kalman Filter

We propose a new approach for solving the filtering problem in linear systems based on incomplete measurements, where the characteristics of the dynamic noise are not known exactly, and measurements may contain anomalous non-Gaussian errors. The proposed algorithm is based on the idea of using the adaptive Kalman filter and the generalized least absolute deviations method jointly. With numerical modeling, we show that, compared to the classical optimal linear filtering method, our solution has lower sensitivity to short-term outliers in measurements and provides a quick adjustment of the parameters of the system dynamics. The proposed algorithm can be used to solve onboard navigation and tracking problems on aircrafts. To implement the method of least absolute deviations, we use an efficient L1-optimization algorithm.

Про усереднення чисел та лінійних сплайнів

Problems of unconstrained minimization of convex functions for finding the minimal linear splines in -norm for cases and are considered. They are constructed analogically with similar problems for finding a number that is different minimally in -norm from the given numbers . If , then the non-smooth function is used, and if then the smooth function is used. It is shown, that with a certain choice of parameter , the optimization problems generate the known methods: the method of least squares, the method of least absolute deviations, and the Chebyshev minimax method. The properties of solutions of problems with are given

Mitigation of Multipath Errors Using the Iterative Least Absolute Deviation Approach

The least squares (LS) approach has been widely used for solving the GPS navigation solution. Despite its many superior properties, however, the LS estimate can be sensitive to outliers and its performance in terms of accuracy and statistical inferences may be compromised when the errors are large and heterogeneous. The GPS signal is strongly affected by the multipath propagation errors. The LS is not able to cope with the above condition to provide a useful and plausible solution. In this paper, an alternative approach based on the least absolute deviation (LAD) criterion for estimating the navigation solution is carried out. The LAD method, which is also known as the L1 method, provides a useful and plausible solution. Unlike the LS method, the LAD method is not as sensitive to the outliers and so as to provide more robust estimates. Simulation results show that the method can effectively mitigate the GPS multipath errors.

Improved Cole parameter extraction based on the least absolute deviation method

The Cole function is widely used in bioimpedance spectroscopy (BIS) applications. Fitting the measured BIS data onto the model and then extracting the Cole parameters (R0, R∞, α and τ) is a common practice. Accurate extraction of the Cole parameters from the measured BIS data has great significance for evaluating the physiological or pathological status of biological tissue. The traditional least-squares (LS)-based curve fitting method for Cole parameter extraction is often sensitive to noise or outliers and becomes non-robust. This paper proposes an improved Cole parameter extraction based on the least absolute deviation (LAD) method. Comprehensive simulation experiments are carried out and the performances of the LAD method are compared with those of the LS method under the conditions of outliers, random noises and both disturbances. The proposed LAD method exhibits much better robustness under all circumstances, which demonstrates that the LAD method is deserving as an improved alternative to the LS method for Cole parameter extraction for its robustness to outliers and noises.

Processing the results of SINS bench tests by methods of nonsmooth optimization in the presence of faults

A new approach to detecting jumps in biases of angular rate sensors in strapdown inertial navigation systems (SINS) is proposed. It is based on the method of least absolute deviations for dynamic systems, which provides for determining instants and magnitudes of jumps with a desired accuracy.

On robust spectral analysis by least absolute deviations

The method of least absolute deviations has been successfully used in construction of robust tools for spectral analysis under the conditions of outliers and heavy-tailed statistical distributions. This article compares two such spectral analyzers, called the Laplace periodograms of the first and second kind, which can be viewed as robust alternatives to the ordinary periodogram. The article proves that the Laplace periodogram of the second kind has a similar asymptotic distribution to the Laplace periodogram of the first kind which established its association with the zero-crossing spectrum in a recent publication. The article also demonstrates that the Laplace periodogram of the second kind has a smoother sample path which is more suitable for visualization, identification, and estimation of arbitrarily located narrowband components. Extensions of the results to complex time series are discussed.

Improved residue function and reduced flow dependence in MR perfusion using least-absolute-deviation regularization

Cerebral blood flow (CBF) estimates derived from singular value decomposition (SVD) of time intensity curves from Gadolinium bolus perfusion-weighted imaging are known to underestimate CBF, especially at high flow rates. We report the development of a model-independent delay-invariant deconvolution technique using least-absolute-deviation (LAD) regularization to improve the CBF estimation accuracy. Computer simulations were performed to compare the accuracy of CBF estimates derived from LAD, reformulated SVD (rSVD) and standard SVD (sSVD) techniques. Simulations were performed at image signal-to-noise ratios ranging from 20 to 400, cerebral blood volumes from 1% to 10%, and CBF from 2.5 mL/100 g/min to 176.5 mL/100 g/min to estimate the effect of these parameters on the accuracy of CBF estimation. The LAD method improved the CBF estimation accuracy by up to 32% in gray matter and 23% in white matter compared with rSVD and sSVD methods. LAD method also reduces the systematic bias of rSVD and sSVD methods to baseline SNR while producing more accurate and reproducible residue function calculation than either rSVD or sSVD method. Initial clinical implementation of the method on six representative clinical cases confirm the advantages of the LAD method over rSVD and sSVD methods.

Computational algorithm of least absolute deviation method for determining number of outliers under normality

In this paper, we suggest a least absolute deviation (LAD) method for the determination of the number of upper or lower outliers in normal sample by minimizing its sample mean absolute deviation. In consequence of computation of the criterion for LAD method need to use iterative numerical analysis, we also give a computational algorithm of LAD method to find the number of upper or lower outliers in normal sample. Finally, we give two examples to study the practical performance of the LAD method.

A unique estimate of linear regression function by least-absolute-deviations method

The purpose of this article is to fill a gap in the method of least absolute deviations. While the method of least squares always gives a unique result, l.a.d., in some cases, does not. In literature and computer programs is the problem solved by convention. Our suggestion of unique estimation generalizes one rather unknown definition of median for even number of observation from [1].

Alternative Spatial Estimators for Ground‐Water and Soil Measurements

AbstractDetail in mapping studies of spatial data results from spatial interpolation of field or laboratory measurements. The interpolation method used can markedly affect the interpolated estimates and thus the appearance of the resulting map. A popular method, oridinary kriging, is based on several assumptions, including normally distributed observations. For data containing outliers or “hotspots,” which are common in ground‐water monitoring, kriging may not be the most appropriate interpolation method. A robust, nonparametric alternative was developed, tested, and demonstrated using case‐study data from the San Luis Valley in Colorado. The method uses a robust measure of spatial correlation, called the medogram, as an inverse‐distance weight for estimates based on LAD (least‐absolute‐deviation) regression. For both synthetic and real case‐study data containing a few high values (outliers or “hotspots”), this LAD method showed improved performance over ordinary kriging. While performance of the LAD method is slightly better than kriging in terms of the mean squared interpolation error for the “contaminated” data sets studied, the significant advantage of the LAD approach is that it does not produce concentric contours around observations and thus provides more realistic maps.

Least absolute deviation estimation of stationary time series models

This paper is concerned with practical aspects of least absolute deviation (LAD) estimation of Box-Jenkins models for single time series. Formulation of the LAD method as a non-linear programming problem is described. The method is applied to a multiplicative seasonal moving average model for monthly rice sales data and to US airline passenger data.

Two Stage Least Absolute Deviations Estimators

In this paper the method of least absolute deviations is applied to the estimation of the parameters of a structural equation in the simultaneous equations model. A class of estimators called two stage least absolute deviations estimators is defined, their asymptotic properties are derived, and the problem of finding the optimal member of the class is considered. IN THIS PAPER WE APPLY the method of least absolute deviations to the estimation of the parameters of a structural equation in the simultaneous equations model. We define a class of estimators called two stage least absolute deviations estimators (2SLAD) and derive their asymptotic properties. They are so named as their relationship to the two stage least squares estimator (2SLS) is analogous to the relationship of the least absolute deviations estimator (LAD) to the least squares estimator (LS) in the standard regression model. The LAD estimation has been extensively studied in the context of the standard regression model and its usefulness is universally recognized. In this paper we show that the advantage of 2SLAD over 2SLS in the simultaneous equations model can be as great as that of LAD over LS in the standard regression model, if 2SLAD is properly defined. This last clause is very important, since the results of this paper indicate that the LAD analogue of 2SLS that has been considered before in the literature is not an appropriate method.