Econometric notes

Lecture notes for a course of Introductory Econometrics (linear regression model and ordinary least squares, including concepts of Linear Algebra and Inferential Statistics), and for a second course of Econometrics (simultaneous equations, instrumental variables, limited and full information estimation methods, maximum likelihood)

Game mechanics and aesthetics differences for tangible and intangible goods provided via social media

Companies aspire to fulfil consumers’ needs, wants and desires by offering products and services. Due to globalization and digitization, the world became a small village by facilitating the obtainability of products/services across the globe. Furthermore, the online purchasing via social platforms mirrors the traditional purchasing process. Gamification, game techniques and elements have been employed in the different domain for engaging and motivating consumers, students, end-users in numerous countries and cultures. Gamification is considered the appliance of game techniques and game elements in the non-game environment. It’s been adjusted in different models founded as a need to explore and explain variables, phenomena and theories. Game mechanics as one of the game elements are applied in different disciplines to achieve better performance, fruitful collaboration, active and enthusiastic participation, creating enjoyable, pleasurable and entertaining environment. Aesthetics are described as the sensory part that game evoke within the player. To identify the differences within consumers who purchase via social media when game mechanics and aesthetics are applied, the chi-square test for independence has been employed. The results estimate that the association between products and services as variables is not statistically significant and the relationship between them is weak or moderated. The findings of this research are useful for private companies and other interested stakeholders. © 2019, Sciendo. All rights reserved.Internal Grant Agency of Tomas Bata University in Zlin [IGA/FaME/2018/2020

Parameter bounds evaluation for linearsystem with output backlash

In this paper a procedure is presented for deriving parameters bounds of linear systems with output backlash when the output measurement errors are bounded. First, using steady-state input/output data, parameters of the backlash are bounded. Then, given the estimated uncertain backlash and the output measurements collected exciting the system with a PRBS, bounds on the unmeasurable inner signal are computed. Finally, such bounds, together with the input sequence, are used for bounding the parameters of the linear block

Bounded error identification of Hammerstein systemswith backlash

Actuators and sensors commonly used in control systems may exhibit a variety of nonlinear behaviours that may be responsible for undesirable phenomena such as delays and oscillations, which may severely limit both the static and the dynamic performance of the system under control (see, e.g., [22]). In particular, one of the most relevant nonlinearities affecting the performance of industrial machines is the backlash (see Figure 22.1), which commonly occurs in mechanical, hydraulic and magnetic components like bearings, gears and impact dampers (see, e.g., [17]). This nonlinearity, which can be classified as dynamic (i.e., with memory) and hard (i.e. non-differentiable), may arise from unavoidable manufacturing tolerances or sometimes may be deliberately incorporated into the system in order to describe lubrication and thermal expansion effects [3]. The interested reader is referred to [22] for real-life examples of systems with either input or output backlash nonlinearities

Hammerstein systems parameters bounding through sparse polynomial optimization

A single-stage procedure for the evaluation of tight bounds on the parameters of Hammerstein systems from output measurements affected by bounded errors is presented. The identification problem is formulated in terms of polynomial optimization, and relaxation techniques based on linear matrix inequalities are proposed to evaluate parameters bounds by means of convex optimization. The structured sparsity of the identification problem is exploited to reduce the computational complexity of the convex relaxed problem. Convergence proper ties, complexity analysis and advantages of the proposed technique with respect to previously published ones are discussed

SM identification of IO LPV models with uncertain time-varying parameters

In this chapter, we consider the identification of single-input single-output linear-parameter-varying models when both the output and the time-varying parameter measurements are affected by bounded noise. First, the problem of computing exact parameter uncertainty intervals is formulated in terms of semialgebraic optimization. Then, a suitable relaxation tecnique is presented to compute parameter bounds by means of convex optimization. Advantages of the presented approach with respect to previously published results are discussed

Improved parameters bounds for set-membership EIV problems

In this paper, we consider the set-membership error-in-variables identification problem, that is the identification of linear dynamic systems when output and input measurements are corrupted by bounded noise. A new approach for the computation of parameters uncertainty intervals is presented. First, the problem is formulated in terms of nonconvex optimization. Then, a relaxation procedure is proposed to compute parameter bounds by means of semidefinite programming techniques. Finally, accuracy of the estimate and computational complexity of the proposed algorithm are discussed. Advantages of the proposed technique with respect to previously published ones are discussed both theoretically and by means of a simulated exampl

An SDP approach for l0-minimization : application to ARX model segmentation

Minimizing the l0-seminorm of a vector under convex constraints is a combinatorial (NP-hard) problem. Replacement of the l0-seminorm with the l1-norm is a commonly used approach to compute an approximate solution of the original l0-minimization problem by means of convex programming. In the theory of compressive sensing, the condition that the sensing matrix satisfies the Restricted Isometry Property (RIP) is a sufficient condition to guarantee that the solution of the l1-approximated problem is equal to the solution of the original l0-minimization problem. However, the evaluation of the conservativeness of the l1-relaxation approaches is recognized to be a difficult task in case the RIP is not satisfied. In this paper, we present an alternative approach to minimize the l0-norm of a vector under given constraints. In particular, we show that an l0-minimization problem can be relaxed into a sequence of semidefinite programming problems, whose solutions are guaranteed to converge to the optimizer (if unique) of the original combinatorial problem also in case the RIP is not satisfied. Segmentation of ARX models is then discussed in order to show, through a relevant problem in system identification, that the proposed approach outperforms the l1-based relaxation in detecting piece-wise constant parameter changes in the estimated model

Bounded error identification of Hammerstein systems through sparse polynomial optimization

In this paper we present a procedure for the evaluation of bounds on the parameters of Hammerstein systems, from output measurements affected by bounded errors. The identification problem is formulated in terms of polynomial optimization, and relaxation techniques, based on linear matrix inequalities, are proposed to evaluate parameter bounds by means of convex optimization. The structured sparsity of the formulated identification problem is exploited to reduce the computational complexity of the convex relaxed problem. Analysis of convergence properties and computational complexity is reported