Comparison of Robust Estimators’ Performance for Detecting Outliers in Multivariate Data

In multivariate data, outliers are difficult to detect especially when the dimension of the data increase. Mahalanobis distance (MD) has been one of the classical methods to detect outliers for multivariate data. However, the classical mean and covariance matrix in MD suffered from masking and swamping effects if the data contain outliers. Due to this problem, many studies used a robust estimator instead of the classical estimator of mean and covariance matrix. In this study, the performance of five robust estimators namely Fast Minimum Covariance Determinant (FMCD), Minimum Vector Variance (MVV), Covariance Matrix Equality (CME), Index Set Equality (ISE), and Test on Covariance (TOC) are investigated and compared. FMCD has been widely used and is known as among the best robust estimator. However, there are certain conditions that FMCD still lacks. MVV, CME, ISE and TOC are innovative of FMCD. These four robust estimators improve the last step of the FMCD algorithm. Hence, the objective of this study is to observe the performance of these five estimator to detect outliers in multivariate data particularly TOC as TOC is the latest robust estimator. Simulation studies are conducted for two outlier scenarios with various conditions. There are three performance measures, which are pout, pmask and pswamp used to measure the performance of the robust estimators. It is found that the TOC gives better performance in pswamp for most conditions. TOC gives better results for pout and pmask for certain conditions.

Invariance property of a five matrix product involving two generalized inverses

Matrix expressions composed by generalized inverses can generally be written as f(A − 1, A − 2, . . ., A − k ), where A 1, A 2, . . ., A k are a family of given matrices of appropriate sizes, and (·)− denotes a generalized inverse of matrix. Once such an expression is given, people are primarily interested in its uniqueness (invariance property) with respect to the choice of the generalized inverses. As such an example, this article describes a general method for deriving necessary and sufficient conditions for the matrix equality A 1 A − 2 A 3 A − 4 A 5 = A to always hold for all generalized inverses A − 2 and A − 4 of A 2 and A 4 through use of the block matrix representation method and the matrix rank method, and discusses some special cases of the equality for different choices of the five matrices.

Left-censored dementia incidences in estimating cohort effects

We estimate the dementia incidence hazard in Germany for the birth cohorts 1900 until 1954 from a simple sample of Germany’s largest health insurance company. Followed from 2004 to 2012, 36,000 uncensored dementia incidences are observed and further 200,000 right-censored insurants included. From a multiplicative hazard model we find a positive and linear trend in the dementia hazard over the cohorts. The main focus of the study is on 11,000 left-censored persons who have already suffered from the disease in 2004. After including the left-censored observations, the slope of the trend declines markedly due to Simpson’s paradox, left-censored persons are imbalanced between the cohorts. When including left-censoring, the dementia hazard increases differently for different ages, we consider omitted covariates to be the reason. For the standard errors from large sample theory, left-censoring requires an adjustment to the conditional information matrix equality.

A curious matrix-sum identity and certain finite sums identities

In this paper, we consider two generalized binary sequences and then give a generalization of a matrix equality proposed as an advanced problem. Then, we derive new certain finite sums including the generalized binary sequences as applications.

Robust Output Observer-Based Control of Neutral Uncertain Systems with Discrete and Distributed Time Delays

In this paper, the robust control problem of output dynamic observer-based control for a class of uncertain neutral systems with discrete and distributed time delays is considered. Linear matrix inequality (LMI) optimization approach is used to design the new output dynamic observer-based controls. Three classes of observer-based controls are proposed and the maximal perturbed bound is given. Based on the results of this paper, the constraint of matrix equality is not necessary for designing the observer-based controls.

Design of IIR Digital Filters with Arbitrary Flatness Using Iterative Quadratic Programming

This paper presents a design method of Chebyshev-type and inverse-Chebyshev-type infinite impulse response (IIR) filters with an approximately linear phase response. In the design of Chebyshev-type filters, the flatness condition in the stopband is preincorporated into a transfer function, and an equiripple characteristic in the passband is achieved by iteratively solving the QP problem using the transfer function. In the design of inverse-Chebyshev-type filters, the flatness condition in the passband is added to the constraint of the QP problem as the linear matrix equality, and an equiripple characteristic in the stopband is realized by iteratively solving the QP problem. To guarantee the stability of the obtained filters, we apply the extended positive realness to the QP problem. As a result, the proposed method can design the filters with more high precision than the conventional methods. The effectiveness of the proposed design method is illustrated with some examples.

H∞ SYNCHRONIZATION OF SWITCHED CHAOTIC SYSTEMS AND ITS APPLICATION TO SECURE COMMUNICATIONS

This paper deals with the H∞ synchronization problem of switched chaotic systems accompanied by a time-driven switching law and its application to secure communications. Based on the Lyapunov stability theory and linear matrix inequality (LMI) and linear matrix equality (LME) optimization techniques, an output feedback controller that guarantees the synchronization of switched master-slave chaotic systems is designed. A chaotic encryption technique that uses synchronization is proposed for securely transmitting a message over public channels. Numerical simulations of both analog and digital security communication systems are conducted to demonstrate the effectiveness of the proposed methods.

Synchronization Analysis of Two Coupled Complex Networks with Time Delays

This paper studies the synchronized motions between two complex networks with time delays, which include individual inner synchronization in each network and outer synchronization between two networks. Based on the Lyapunov stability theory and the linear matrix equality (LMI), a synchronous criterion for inner synchronization inside each network is derived. Numerical examples are given which fit the theoretical analysis. In addition, the involved numerical results show that the delays between two networks have little effect on inner synchronization. It is also shown that synchronous motions within each network or between two networks are not enhanced if individual intranetwork connections are allowed.