Robust Calibration for Localization in Clustered Wireless Sensor Networks

In the multiple linear regression analysis, the ridge regression estimator and the Liu estimator are often used to address multicollinearity. Besides multicollinearity, outliers are also a problem in the multiple linear regression analysis. We propose new biased estimators based on the least trimmed squares (LTS) ridge estimator and the LTS Liu estimator in the case of the presence of both outliers and multicollinearity. For this purpose, a simulation study is conducted in order to see the difference between the robust ridge estimator and the robust Liu estimator in terms of their effectiveness; the mean square error. In our simulations, the behavior of the new biased estimators is examined for types of outliers: X-space outlier, Y-space outlier, and X-and Y-space outlier. The results for a number of different illustrative cases are presented. This paper also provides the results for the robust ridge regression and robust Liu estimators based on a real-life data set combining the problem of multicollinearity and outliers.

Fast and robust bootstrap for LTS

Approximate equity index replication, based on a linear regression setting, is critically reviewed. It is shown that tracking a performance index like the German DAX necessarily leads to violations of basic assumptions of the classical regression model. Violations occur even if the model is formulated in terms of stock price levels. When the model is based on discretely or continuously compounded returns the situation is more critical. Due to these violations, the optimality properties of the regression estimators are generally weak. In the time series context, outliers in financial time series may additionally affect the standard least squares estimator. Despite of these critical points, it is argued that regression techniques may still provide a useful tool for index replication. With respect to outliers, robust estimators can potentially provide an alternative to least squares. Hence, apart from least squares, a non-redescending and a redescending robust estimator is fitted. The empirical results for the DAX are obtained with a subset portfolio containing the most heavily weighted index members. Compared to a naive weighting scheme, the results document that least squares estimation highly improves out-of-sample replication performance. Typically, the use of robust estimators does not show replication improvements. However, when substantial market movements are present in the sample, superior replication can be obtained.

The incorporation of the robust regression methods Least Median Square (LMS) and Least Trimmed Squares (LTS) is proposed in structural equation modeling. Results show that, in situations of high deviations of symmetry, the evaluated methods would be recommended for applications including smaller sample sizes.

Summary In this paper we derive an asymptotic normality result for an adaptive trimmed likelihood estimator of regression starting from initial high breakdownpoint robust regression estimates. The approach leads to quickly and easily computed robust and efficient estimates for regression. A highlight of the method is that it tends automatically in one algorithm to expose the outliers and give least squares estimates with the outliers removed. The idea is to begin with a rapidly computed consistent robust estimator such as the least median of squares (LMS) or least trimmed squares (LTS) or for example the more recent MM estimators of Yohai. Such estimators are now standard in statistics computing packages, for example as in SPLUS or R. In addition to the asymptotics we provide data analyses supporting the new adaptive approach. This approach appears to work well on a number of data sets and is quicker than the related brute force adaptive regression approach described in Clarke (2000). This current approach builds on the work of Bednarski and Clarke (2002) which considered the asymptotics for the location estimator only.

The robust Huber's M-estimator is widely used in signal and image processing, classification, and regression. From an optimization point of view, Huber's M-estimation problem is often formulated as a large-sized quadratic programming (QP) problem in view of its nonsmooth cost function. This paper presents a generalized regression estimator which minimizes a reduced-sized QP problem. The generalized regression estimator may be viewed as a significant generalization of several robust regression estimators including Huber's M-estimator. The performance of the generalized regression estimator is analyzed in terms of robustness and approximation accuracy. Furthermore, two low-dimensional recurrent neural networks (RNNs) are introduced for robust estimation. The two RNNs have low model complexity and enhanced computational efficiency. Finally, the experimental results of two examples and an application to image restoration are presented to substantiate superior performance of the proposed method over conventional algorithms for robust regression estimation in terms of approximation accuracy and convergence rate.

Linear discriminant analysis, such as Fisher's criterion, is a statistical learning tool traditionally devoted to separating a training dataset into two or even several classes by the way of linear decision boundaries. In this paper, we show that this tool can formalize the robust linear regression problem as a robust estimator will do. More precisely, we develop a one-class Fischer's criterion in which the maximization provides both the regression parameters and the separation of the data in two classes: typical data and atypical data or outliers. This new criterion is built on the statistical properties of the subspace decomposition of the hat matrix. From this angle, we improve the discriminative properties of the hat matrix which is traditionally used as outlier diagnostic measure in linear regression. Naturally, we call this new approach discriminative hat matrix. The proposed algorithm is fully nonsupervised and needs only the initialization of one parameter. Synthetic and real datasets are used to study the performance both in terms of regression and classification of the proposed approach. We also illustrate its potential application to image recognition and fundamental matrix estimation in computer vision.

A pseudo-algorithmic separation of lines from pseudo-lines

ABSTRACTIn large‐scale wireless sensor networks, cost‐effective and energy‐efficient localization of sensor nodes is an important research topic. In spite of their coarse accuracy, range‐free (connectivity‐based) localization methods are considered as cost‐effective alternatives to the range‐based localization schemes with specialized hardware requirements.In this paper, we derive closed‐form expressions for the average minimum transmit powers required for the localization of sensor nodes, under deterministic path loss, log‐normal shadowing, and Rayleigh fading channel models. The impacts of propagation environment and spatial density of anchor nodes on the minimum transmit power for node localization are evaluated analytically as well as through simulations. Knowledge of the minimum transmit power requirements for localizability of a sensor node enables improving energy efficiency and prolonging lifetime of the network. We also propose a novel distance metric for range‐free localization in large‐scale sensor networks. The target and anchor nodes are assumed to be positioned according to two statistically independent two‐dimensional homogeneous Poisson point processes. Analytical expression for the average distance from a target node to its kth nearest neighbor anchor node is derived and is used for estimating the target‐to‐anchor node distances for localization. The Cramér–Rao lower bound on the localization accuracy for the new distance estimator is derived. Simulation results show the accuracy of the proposed distance estimate compared with some existing ones for range‐free localization. The results of our investigation are significant for low‐cost, energy‐efficient localization of wireless sensor nodes. Copyright © 2011 John Wiley & Sons, Ltd.

Abstract. Process-oriented rainfall-runoff models are designed to approximate the complex hydrologic processes within a specific catchment and in particular to simulate the discharge at the catchment outlet. Most of these models exhibit a high degree of complexity and require the determination of various parameters by calibration. Recently, automatic calibration methods became popular in order to identify parameter vectors with high corresponding model performance. The model performance is often assessed by a purpose-oriented objective function. Practical experience suggests that in many situations one single objective function cannot adequately describe the model's ability to represent any aspect of the catchment's behaviour. This is regardless of whether the objective is aggregated of several criteria that measure different (possibly opposite) aspects of the system behaviour. One strategy to circumvent this problem is to define multiple objective functions and to apply a multi-objective optimisation algorithm to identify the set of Pareto optimal or non-dominated solutions. Nonetheless, there is a major disadvantage of automatic calibration procedures that understand the problem of model calibration just as the solution of an optimisation problem: due to the complex-shaped response surface, the estimated solution of the optimisation problem can result in different near-optimum parameter vectors that can lead to a very different performance on the validation data. Bárdossy and Singh (2008) studied this problem for single-objective calibration problems using the example of hydrological models and proposed a geometrical sampling approach called Robust Parameter Estimation (ROPE). This approach applies the concept of data depth in order to overcome the shortcomings of automatic calibration procedures and find a set of robust parameter vectors. Recent studies confirmed the effectivity of this method. However, all ROPE approaches published so far just identify robust model parameter vectors with respect to one single objective. The consideration of multiple objectives is just possible by aggregation. In this paper, we present an approach that combines the principles of multi-objective optimisation and depth-based sampling, entitled Multi-Objective Robust Parameter Estimation (MOROPE). It applies a multi-objective optimisation algorithm in order to identify non-dominated robust model parameter vectors. Subsequently, it samples parameter vectors with high data depth using a further developed sampling algorithm presented in Krauße and Cullmann (2012a). We study the effectivity of the proposed method using synthetical test functions and for the calibration of a distributed hydrologic model with focus on flood events in a small, pre-alpine, and fast responding catchment in Switzerland.

This paper is focusing on the application of robust method in multiple linear regression (MLR) model towards diabetes data. The objectives of this study are to identify the significant variables that affect diabetes by using MLR model and using MLR model with robust method, and to measure the performance of MLR model with/without robust method. Robust method is used in order to overcome the outlier problem of the data. There are three robust methods used in this study which are least quartile difference (LQD), median absolute deviation (MAD) and least-trimmed squares (LTS) estimator. The result shows that multiple linear regression with application of LTS estimator is the best model since it has the lowest value of mean square error (MSE) and mean absolute error (MAE). In conclusion, plasma glucose concentration in an oral glucose tolerance test is positively affected by body mass index, diastolic blood pressure, triceps skin fold thickness, diabetes pedigree function, age and yes/no for diabetes according to WHO criteria while negatively affected by the number of pregnancies. This finding can be used as a guideline for medical doctors as an early prevention of stage 2 of diabetes.

Prolonged network lifetime, scalability and efficient load balancing are essential for optimal performance of a wireless sensor network. Clustering provides an effective way of extending the lifetime of a sensor network. Clustering is the process that divides sensor networks into smaller localized group (called clusters) of members with a cluster head. Clustering protocols need to elect optimal number of clusters in hierarchically structured wireless sensor networks. Any clustering scheme that elects clusters uniformly (irrespective of the distance from Base Station) incurs excessive energy usage on clusters proximal and distant to Base Station. In single hop networks a gradual increment in the energy depletion rate is observed as the distance from the cluster head increases[17]. This work focuses on the analysis of wasteful energy consumption within a uniform cluster head election model (EPEM) and provides an analytical solution to reduce the overall consumption of energy usage amongst the clusters elected in a wireless sensor network. A circular model of sensor network is considered, where the sensor nodes are deployed around a centrally located Base Station. The sensor network is divided into several concentric rings centred at the Base Station. A model, Unequal Probability Election Model (UEPEM), which elects cluster heads non-uniformly is proposed. The probability of cluster head election depends on the distance from the Base Station. UEPEM reduces the overall energy usage by about 21% over EPEM. The performance of UEPEM improves as the number of rings is increased.

Recent trend to steer Wireless Sensor Networks towards a broad outdoor environment allows to monitor harsh areas and prevent a disaster situation. To guarantee an extensive work of the system and smooth cooperation among involved devices a new clustering approach needs to be found. In this paper, we present a new algorithm for an Event-oriented Focal Weight-based clustering for Wireless Sensor Network which will be able to monitor various parameters (physical, biological, and chemical) of the outdoor environment and signal the current situation further to the network. Shown results demonstrate the applicability of the algorithm for the large amount of nodes with various power levels. The use of a dual-band transceiver and advanced processing elements allow to accommodate new features in the nodes and guarantee a high performance with the low power consumption which is crucial for the outdoor system with no human attendance.

Wireless sensor networks is a key technology for new ways of interaction between computers and the physical environment. However, the energy constrained and limited computing resources of the sensor nodes present major challenges in gathering data. Since sensor nodes are densely deployed, redundant data may occur. While cluster-based data gathering is efficient at energy and bandwidth, it's difficult to cluster network efficiently. In this work, a new distributed clustering algorithm for ubiquitous sensor network is presented. Clustering is based on the distance between nodes and the number in a cluster for wireless sensor networks. Simulation results show that the proposed algorithm balances the energy dissipation over the whole network thus increase the amount of data delivery to the sink

In recent years wireless sensor networks researches have gained much attention .Where extended network lifetime, is important necessity for many sensor network applications. Clustering is a useful technique for achieving these objectives. This work introduces Review on Grid Protocols Clustering for Wireless Sensor Networks. Grid routing plays an important task in the performance of WSNs, and research related with routing is always a focus. We have surveyed the state-of-art of different Grid clustering algorithms. Finally we provides the concluding remarks.