Absolute Deviation Method Research Articles

Energy management strategy in cloud computing: a perspective study

Optimizing energy consumption in cloud computing is yet a challenge despite the diversity of the proposed energy management strategies. Indeed, and during our related work study we have observed that the different elements or components which should be considered in order to be able to properly manage energy consumption in a cloud computing context are not well defined and/or discussed in terms of importance. This makes the proper classification and/or comparison of the different proposed strategies or techniques very difficult. Consequently, this paper aims, on the one hand, at defining and discussing properly such components in order to create a guideline and, on the other hand, to ease both the classification and the comparison of these proposed strategies and techniques. Second and after discussing some common weaknesses related to the current energy consumption optimization techniques and methods, this paper proposes energy-saving technique which uses a novel load detecting policy. This policy is based on the median absolute deviation method which uses the median and the standard deviation to calculate upper and lower thresholds which aim to classify hosts into either overloaded or under-loaded state. Simulation results have shown better results of the proposed technique compared to the existing ones especially in reducing energy consumption and the number of virtual machine migrations in addition to better active host time. Indeed, we found that the average of saved energy is around 40% compared to the built in techniques in cloudSim.

A note on “A new fuzzy regression model based on absolute deviation”

Li et al. (2016) proposed a least absolute deviation method to find such fuzzy regression models whose all the parameters are trapezoidal fuzzy numbers. Since, the method, proposed by Li et al., is published in Engineering Applications of Artificial Intelligence (a very reputed International Journal) as well as it is easy to apply Li et al. method in real life problems. So, other researchers may be attracted to apply the method, proposed by Li et al., to find the solution of real life problems. However, after a deep study of the work done by Li et al., it is noticed that the multiplication of two trapezoidal fuzzy numbers, proposed by Li et al. as well as used in this method, is not valid. Hence, the aim of this note is to make the researchers aware about the valid multiplication of trapezoidal fuzzy numbers that should be used in Li et al. method.

A Simulation Study of Impacts of Estimated Method and Uncertainty on Parameters in Length-Weight Relationship

To acknowledge the impacts of estimated method and uncertainty introduced into the weight on parameters in length - weight relationship, take the morphometric traits of Fenneropenaeus chinensis as example, the parameters a and b were estimated by using power of the absolute residuals (m, 1 ≤m (natural number) ≤ 20) methods, and error in the form of exponent was introduced into length – weight relationship. The study showed that the values of parameters in the relationship between length and weight were related to estimation methods. With the exponential increase of absolute residual, parameter a increased, while parameter b was highly uncertain. For the stability of parameter estimates, it was better to use the least absolute deviation method than the least square method and higher exponent of absolute residua to estimate the parameters. Uncertainty introduced into weight did not greatly impact the mean and median of the parameters a and b in the relationship between body length and weight. However, with increasing uncertainty, the fluctuation of parameter estimation increased, while the stability of the fitting effect of the length - weight relationship decreased. So, the estimated method and uncertainty should be taken into account for estimating the parameters in length - weight relationship, and the least absolute deviation method was proposed to estimate the parameters in length - weight relationship.

Detecting outliers in GARCH(p,q) models

ABSTRACTThis article is concerned with the outliers in GARCH models. An iterative procedure is given for testing the presence of any type of the four common outliers. Since the distribution of test statistic cannot be obtained analytically, its distributional behavior is investigated via a simulation study. The simulation study is based on estimation of residuals standard deviation (σν), which are obtained using two methods, median absolute deviation method (MAD), and omit-one method. The proposed procedure is employed for testing the presence of outliers in weekly light oil price Indexes of Iran during 1997 to 2010.

PERBANDINGAN METODE MCD-BOOTSTRAP DAN LAD-BOOTSTRAP DALAM MENGATASI PENGARUH PENCILAN PADA ANALISIS REGRESI LINEAR BERGANDA

Outliers are observations that are far away from other observations. Outlier can be interfered with the process of data analysis which influence the regression parameters estimation. Methods that are able to deal with outliers are Minimum Covariance Determinant and Least Absolute Deviation methods. However, if both methods are applied with small sample the validity of both methods is being questioned. This research applies bootstrap to MCD and LAD methods to small sample. Resampling using 500, 750,and 1000 with confidence interval of 95% and 99% shows that both methods produce an unbiased estimators at 10%, 15%, and 20% outliers. The confidence interval of MCD-Bootstrap method is shorter than LAD-Bootstrap method. Both are, MCD-Bootstrap method is a better thus than LAD-Bootstrap method.

Threshold Estimation in TAR

Одной из важнейших моделей описания нелинейных временных рядов является модель пороговой авторегрессии. При решении задачи идентификации пороговой авторегрессионной модели возникает необходимость в оценивании величины порога. Наиболее распространенным методом оценивания порога является метод наименьших квадратов, менее распространен метод наименьших модулей. Оба метода являются частными случаями М-метода.

Fuzzy least absolute linear regression

The distance between triangular fuzzy numbers is an important research topic in many fields. In this paper, we introduce a new distance between triangular fuzzy numbers, merge least absolute deviation method with the new distance and propose fuzzy regression model. We also investigate the properties and model algorithm of fuzzy least absolute linear regression model in detail by transforming this model into linear programming. Further, we use three numerical examples to illustrate our proposed model reasonable and make some comparisons with some existing fuzzy regression models. Finally, we investigate the robust property of our proposed model and apply our model in the missing data set to verify model data.

Comparison of efficiency of estimates by the methods of least absolute deviations and least squares in the autoregression model with random coefficient

For the model of autoregression with a random coefficient, the estimate by the least absolute deviations (LAD) method was proved to be consistent and asymptotically normal. For the asymptotic relative efficiency of the estimate by the LAD method as compared to the least squares method, an analytical expression was obtained. For the case where the innovative field of the autoregression process has the Tukey distribution, consideration was given to the behavior of the relative asymptotic efficiency.

Exploration geochemistry data-application for anomaly separation based on discriminant function analysis in the Parkam porphyry system (Iran)

There are several statistical methodologies presented for separating anomalous values from background leading to determination of anomalous areas. These methods range from simple approaches to complicated ones. A common objective method for anomaly detection in geochemical exploration is target delineation by discriminant function analysis. Discriminant analysis (DA) is a multivariate statistical technique that classifies each observation into a specific group based on observed predictor variables and predefined groups. In the present study, to achieve this target, two populations of anomaly and background were determined using combination of Mahalanobis distance (MD) and median absolute deviation (MAD) method, using borehole data set. For this purpose, in the first step, Mahalanobis distance values should be determined and then MAD method should be applied on Mahalanobis distance values of boreholes data (grade of copper and molybdenum). Thus for separating anomaly from background of surface samples and determining anomaly areas, algorithm of DA method is applied on grade of Cu and Mo (surface samples). Results show that samples indicated by the DA methods as anomalous are more regular; less dispersed and are more accurate than other multivariate methods (e.g., MD method) and other univarite methods since anomalous samples are determined based on several variables. Finally, bivariate lithogeochemical map of the study area is provided for copper and molybdenum which has been prepared using DA method. In this map, the delineated Cu-Mo mineralization is closely associated with the defined zone of potassic alteration, which is also consistent with the field and microscopic observation of the Cu mineralization in this alteration zone. Moreover, it is associated with the phyllic alteration and is spatially conformable with the zone defined for it.

Rank-based group variable selection

A robust rank-based estimator for variable selection in linear models, with grouped predictors, is studied. The proposed estimation procedure extends the existing rank-based variable selection [Johnson, B.A., and Peng, L. (2008), ‘Rank-based Variable Selection’, Journal of Nonparametric Statistics, 20(3):241–252] and the ww-scad [Wang, L., and Li, R. (2009), ‘Weighted Wilcoxon-type Smoothly Clipped Absolute Deviation Method’, Biometrics, 65(2):564–571] to linear regression models with grouped variables. The resulting estimator is robust to contamination or deviations in both the response and the design space.The Oracle property and asymptotic normality of the estimator are established under some regularity conditions. Simulation studies reveal that the proposed method performs better than the existing rank-based methods [Johnson, B.A., and Peng, L. (2008), ‘Rank-based Variable Selection’, Journal of Nonparametric Statistics, 20(3):241–252; Wang, L., and Li, R. (2009), ‘Weighted Wilcoxon-type Smoothly Clipped Absolute Deviation Method’, Biometrics, 65(2):564–571] for grouped variables models. This estimation procedure also outperforms the adaptive hlasso [Zhou, N., and Zhu, J. (2010), ‘Group Variable Selection Via a Hierarchical Lasso and its Oracle Property’, Interface, 3(4):557–574] in the presence of local contamination in the design space or for heavy-tailed error distribution.

Big data analytics: integrating penalty strategies

We present efficient estimation and prediction strategies for the classical multiple regression model when the dimensions of the parameters are larger than the number of observations. These strategies are motivated by penalty estimation and Stein-type estimation procedures. More specifically, we consider the estimation of regression parameters in sparse linear models when some of the predictors may have a very weak influence on the response of interest. In a high-dimensional situation, a number of existing variable selection techniques exists. However, they yield different subset models and may have different numbers of predictors. Generally speaking, the least absolute shrinkage and selection operator (Lasso) approach produces an over-fitted model compared with its competitors, namely the smoothly clipped absolute deviation (SCAD) method and adaptive Lasso (aLasso). Thus, prediction based only on a submodel selected by such methods will be subject to selection bias. In order to minimize the inherited bias, we suggest combining two models to improve the estimation and prediction performance. In the context of two competing models where one model includes more predictors than the other based on relatively aggressive variable selection strategies, we plan to investigate the relative performance of Stein-type shrinkage and penalty estimators. The shrinkage estimator improves the prediction performance of submodels significantly selected from existing Lasso-type variable selection methods. A Monte Carlo simulation study is carried out using the relative mean squared error (RMSE) criterion to appraise the performance of the listed estimators. The proposed strategy is applied to the analysis of several real high-dimensional data sets.

A new fuzzy regression model based on least absolute deviation

Fuzzy set theory is a powerful tool to describe and process uncertainty information which exist in real world, and fuzzy regression is an important research topic which can be used to fulfill predicting by establishing the functional relationship between fuzzy variables. Trapezoidal fuzzy number is a common one which can represent other types of fuzzy numbers, and least absolute deviation is a robust method which is insensitive to outliers. So, in this paper, we propose a new fuzzy regression model based on trapezoidal fuzzy number and least absolute deviation method. Firstly, we introduce a new distance measure between trapezoidal fuzzy numbers which is the basis for applications, and merge least absolute deviation with the proposed distance measure to investigate fuzzy regression model whose parameters can be trapezoidal fuzzy numbers. Meanwhile, we investigate the model algorithms for three cases in detail, including different types of inputs, outputs and regression coefficients. Finally, we use four numerical examples to illustrate that our proposed model is reasonable, compare our proposed model with some existing fuzzy regression models, and do comprehensive analysis about the proposed model. The results show that our proposed model is robust, and has better fitting effect.

Correcting Data Corruption Errors for Multivariate Function Approximation

We discuss the problem of constructing an accurate function approximation when data are corrupted by unexpected errors. The unexpected corruption errors are different from the standard observational noise in the sense that they can have much larger magnitude and in most cases are sparse. By focusing on overdetermined case, we prove that the sparse corruption errors can be effectively eliminated by using $\ell_1$-minimization, also known as the least absolute deviations method. In particular, we establish probabilistic error bounds of the $\ell_1$-minimization solution with the corrupted data. Both the lower bound and the upper bound are related only to the errors of the $\ell_1$- and $\ell_2$-minimization solutions with respect to the uncorrupted data and the sparsity of the corruption errors. This ensures that the $\ell_1$-minimization solution with the corrupted data are close to the regression results with uncorrupted data, thus effectively eliminating the corruption errors. Several numerical examples ...

Randomly weighted LAD-estimation for partially linear errors-in-variables models

The authors consider the partially linear model relating a response Y to predictors (x, T) with a mean function x T β 0+g(T) when the x′s are measured with an additive error. The estimators of parameter β 0 are derived by using the nearest neighbor-generalized randomly weighted least absolute deviation (LAD for short) method. The resulting estimator of the unknown vector β 0 is shown to be consistent and asymptotically normal. In addition, the results facilitate the construction of confidence regions and the hypothesis testing for the unknown parameters. Extensive simulations are reported, showing that the proposed method works well in practical settings. The proposed methods are also applied to a data set from the study of an AIDS clinical trial group.

Effect of re-extraction parameters and drying temperature on the antioxidant properties and dietary fiber of Red sorrel (Hibiscus sabdariffa L.) calyces residues

Effect of re-extraction and drying temperature on the antioxidant capacity and dietary fibers of Hibiscus sabdariffa L. calyces residues were studied using response surface methodology with respect to 3 factors Doehlert experimental design. Mathematical models were obtained for the effect of re-extraction parameters on ascorbic acid, TPC, TFC, ABTS, SDF, and SDF/IDF ratio. The suitability of each response model was judged using the average absolute deviation method and the calculation of the Bias factors. No significant difference was observed for the total dietary fiber content among different samples. Soluble dietary fibers in the residues varied from 47 to 216gkg−1 dry matter. Insoluble dietary fiber represented more than 75% of total dietary fibers. Samples exhibited high scavenging activity of ABTS cation radical (TEAC ranging from 2.488 to 9.416mMeq. Trolox) and DPPH free radical with IC50 values ranging from 0.915 to 0.062mgmL−1. TEAC and IC50 values were correlated to TPC and TFC. The study indicated that H. sabdariffa L. calyces residues can be a potential source of additive/ingredient for the food industry and the re-extraction at lower temperatures further improves the dietary fiber composition of the residue.

An iterative algorithm for l 1-norm approximation in dynamic estimation problems

In this paper, an approach to state estimation in dynamic systems is considered, which consists in solving an l1-norm approximation problem. An algorithm is proposed for the solution of this problem, the so-called weight and time recursion method, which combines the ideas of weighted variational quadratic approximations and smoothing Kalman filtering. For the iterations of the proposed method, estimates of levels of nonoptimality are computed; this is considered as an extension of earlier results obtained by the authors for the classical least absolute deviation method.

Weight and Time Recursions in Dynamic State Estimation Problem With Mixed-Norm Cost Function

The mixed-norm cost functions arise in many applied optimization problems. As an important example, we consider the state estimation problem for a linear dynamic system under a nonclassical assumption that some entries of state vector admit jumps in their trajectories. The estimation problem is solved by means of mixed $l_{1}/l_{2} $ -norm approximation. This approach combines the advantages of the well-known quadratic smoothing and the robustness of the least absolute deviations method. For the implementation of the mixed-norm approximation, a dynamic iterative estimation algorithm is proposed. This algorithm is based on weight and time recursions and demonstrates the high efficiency. It well identifies the rare jumps in the state vector and has some advantages over more customary methods in the typical case of a large amount of measurements. Nonoptimality levels for current iterations of the algorithm are constructed. Computation of these levels allows to check the accuracy of iterations.

Power-Expected-Posterior Priors for Variable Selection in Gaussian Linear Models

In the context of the expected-posterior prior (EPP) approach to Bayesian variable selection in linear models, we combine ideas from power-prior and unit-information-prior methodologies to simultaneously (a) produce a minimally-informative prior and (b) diminish the effect of training samples. The result is that in practice our power-expected-posterior (PEP) methodology is sufficiently insensitive to the size n* of the training sample, due to PEP’s unit-information construction, that one may take n* equal to the full-data sample size n and dispense with training samples altogether. This promotes stability of the resulting Bayes factors, removes the arbitrariness arising from individual training-sample selections, and greatly increases computational speed, allowing many more models to be compared within a fixed CPU budget. We find that, under an independence Jeffreys (reference) baseline prior, the asymptotics of PEP Bayes factors are equivalent to those of Schwartz’s Bayesian Information Criterion (BIC), ensuring consistency of the PEP approach to model selection. Our PEP prior, due to its unit-information structure, leads to a variable-selection procedure that — in our empirical studies — (1) is systematically more parsimonious than the basic EPP with minimal training sample, while sacrificing no desirable performance characteristics to achieve this parsimony; (2) is robust to the size of the training sample, thus enjoying the advantages described above arising from the avoidance of training samples altogether; and (3) identifies maximum-a-posteriori models that achieve better out-of-sample predictive performance than that provided by standard EPPs, the g-prior, the hyper-g prior, non-local priors, the Least Absolute Shrinkage and Selection Operator (LASSO) and Smoothly-Clipped Absolute Deviation (SCAD) methods.

Efficient collision attacks on smart card implementations of masked AES

Collision attack is often employed against some cryptographic algorithms such as AES and DES. As a usual countermeasure, masking can resist such attacks to some extent. In CHES 2011, Clavier et al. proposed a collision-correlation attack based on Pearson correlation coefficient against masking. In this paper, a collision distinguisher based on least absolute deviation against masking is proposed. Subsequently, we suggest three other distinguishers based on least square method, least exponent method, and central moment product, respectively. Our experiments and simulations show that in practice, our distinguishers based on least absolute deviation and least square method perform much better than collision-correlation attack and other proposed distinguishers in this paper. We also give four application examples, which show that even if the masks are not reused, new distinguishers are competent to collision attacks.

Performance of Robust Regression Methods in Real-Time Polymerase Chain Reaction Calibration

The ordinary least squares (OLS) method is routinely used to estimate the unknown concentration of nucleic acids in a given solution by means of calibration. However, when outliers are present it could appear sensible to resort to robust regression methods. We analyzed data from an External Quality Control program concerning quantitative real-time PCR and we found that 24 laboratories out of 40 presented outliers, which occurred most frequently at the lowest concentrations. In this article we investigated and compared the performance of the OLS method, the least absolute deviation (LAD) method, and the biweight MM-estimator in real-time PCR calibration via a Monte Carlo simulation. Outliers were introduced by replacement contamination. When contamination was absent the coverages of OLS and MM-estimator intervals were acceptable and their widths small, whereas LAD intervals had acceptable coverages at the expense of higher widths. In the presence of contamination we observed a trade-off between width and coverage: the OLS performance got worse, the MM-estimator intervals widths remained short (but this was associated with a reduction in coverages), while LAD intervals widths were constantly larger with acceptable coverages at the nominal level.