Mle-equivariance, data transformations and invariant tests of fit

We define data transformations that leave certain classes of distributions invariant, while acting in a specific manner upon the parameters of the said distributions. It is shown that under such transformations the maximum likelihood estimators behave in exactly the same way as the parameters being estimated. As a consequence goodness--of--fit tests based on standardized data obtained through the inverse of this invariant data--transformation reduce to the case of testing a standard member of the family with fixed parameter values. While presenting our results, we also provide a selective review of the subject of equivariant estimators always in connection to invariant goodness--of--fit tests. A small Monte Carlo study is presented for the special case of testing for the Weibull distribution, along with real--data illustrations.Comment: 12 pages, 1 figur

A quasi-Newton optimal method for the global linearisation of the output feedback pole assignment

The paper deals with the problem of output feedback pole assignment by static and dynamic compensators using a powerful method referred to as global linearisation which has addressed both solvability conditions and computation of solutions. The method is based on the asymptotic linearisation of the pole assignment map around a degenerate point and is aiming to reduce the multilinear nature of the problem to the solution of a linear set of equations by using algebro-geometric notions and tools. This novel framework is used as the basis to develop numerical techniques which make the method less sensitive to the use of degenerate solutions. The proposed new computational scheme utilizes a quasi-Newton method modified accordingly so it can be used for optimization goals while achieving (exact or approximate) pole placement. In the present paper the optimisation goal is to maximise the angle between a solution and the degenerate compensator so that less sensitive solutions are achieved

A Grassmann Matrix Approach for the Computation of Degenerate Solutions for Output Feedback Laws

The paper is concerned with the improvement of the overall sensitivity properties of a method to design feedback laws for multivariable linear systems which can be applied to the whole family of determinantal type frequency assignment problems, expressed by a unified description, the so-called Determinantal Assignment Problem (DAP). By using the exterior algebra/algebraic geometry framework, DAP is reduced to a linear problem (zero assignment of polynomial combinants) and a standard problem of multilinear algebra (decomposability of multivectors) which is characterized by the set of Quadratic Plücker Relations (QPR) that define the Grassmann variety of P. This design method is based on the notion of degenerate compensator, which are the solutions that indicate the boundaries of the control design and they provide the means for linearising asymptotically the nonlinear nature of the problems and hence are used as the starting points to generate linearized feedback laws. A new algorithmic approach is introduced for the computation and the selection of degenerate solutions (decomposable vectors) which allows the computation of static and dynamic feedback laws with reduced sensitivity (and hence more robust solutions). This approach is based on alternative, linear algebra type criterion for decomposability of multivectors to that defined by the QPRs, in terms of the properties of structured matrices, referred to as Grassmann Matrices. The overall problem is transformed to a nonlinear maximization problem where the objective function is expressed via the Grassmann Matrices and the first order conditions for optimality are reduced to a nonlinear eigenvalue-eigenvector problem. Hence, an iterative method similar to the power method for finding the largest modulus eigenvalue and the corresponding eigenvector is proposed as a solution for the above problem

Robust estimators of ar-models : a comparison

Many regression-estimation techniques have been extended to cover the case of dependent observations. The majority of such techniques are developed from the classical least squares, M and GM approaches and their properties have been investigated both on theoretical and empirical grounds. However, the behavior of some alternative methods- with satisfactory performance in the regression case- has not received equal attention in the context of time series. A simulation study of four robust estimators for autoregressive models containing innovation or additive outliers is presented. The robustness and efficiency properties of the methods are exhibited, some finite-sample results are discussed in combination with theoretical properties and the relative merits of the estimators are viewed in connection with the outlier-generating scheme.peer-reviewe

Structure assignment problems in linear systems: Algebraic and geometric methods

The Determinantal Assignment Problem (DAP) is a family of synthesis methods that has emerged as the abstract formulation of pole, zero assignment of linear systems. This unifies the study of frequency assignment problems of multivariable systems under constant, dynamic centralized, or decentralized control structure. The DAP approach is relying on exterior algebra and introduces new system invariants of rational vector spaces, the Grassmann vectors and Plücker matrices. The approach can handle both generic and non-generic cases, provides solvability conditions, enables the structuring of decentralisation schemes using structural indicators and leads to a novel computational framework based on the technique of Global Linearisation. DAP introduces a new approach for the computation of exact solutions, as well as approximate solutions, when exact solutions do not exist using new results for the solution of exterior equations. The paper provides a review of the tools, concepts and results of the DAP framework and a research agenda based on open problems

A unified approach to goodness-of-fit testing for spherical and hyperspherical data

We propose a general and relatively simple method for the construction of goodness-of-fit tests on the sphere and the hypersphere. The method is based on the characterization of probability distributions via their characteristic function, and it leads to test criteria that are convenient regarding applications and consistent against arbitrary deviations from the model under test. We emphasize goodness-of-fit tests for spherical distributions due to their importance in applications and the relative scarcity of available methods.Comment: 29 pages, 2 figures, 6 table

Fourier-type monitoring procedures for strict stationarity

We consider model-free monitoring procedures for strict stationarity of a given time series. The new criteria are formulated as L2-type statistics incorporating the empirical characteristic function. Asymptotic as well as Monte Carlo results are presented. The new methods are also employed in order to test for possible stationarity breaks in time-series data from the financial sector

An Innovative Control Framework for District Heating Systems: Conceptualisation and Preliminary Results

This paper presents a holistic innovative solution for the transformation of the current district heating and cooling systems to automated more efficient systems. A variety of technological advancements have been developed and integrated to support the effective energy management of future district heating and cooling sector. First, we identify and discuss the main challenges and needs that are in line with the EU objectives and policy expectations. We give an overview of the main parts that our solution consists of, with emphasis on the forecasting tools and an advanced control system that addresses unit commitment and economic load dispatch problems. The proposed control approach employs distributed and scalable optimisation algorithms for optimising the short-term operations of a district heating and cooling plant subject to technical constraints and uncertainties in the energy demand. To test the performance and validate the proposed control system, a district heating plant with multiple energy generation units and real-life heat load data were used. Simulation experiments were also used to evaluate the benefits of using thermal storage units in district heating systems. The results show that the proposed method could achieve significant cost savings when energy storage is employed. The proposed control strategy can be applied for both operating optimally district heating plants with storage and supporting investment planning for new storage units