The effect of recursive detrending on panel unit root tests

This paper analyzes the properties of panel unit root tests based on recursively detrended data. The analysis is conducted while allowing for a (potentially) non-linear trend function, which represents a more general consideration than the current state of affairs with (at most) a linear trend. A new test statistic is proposed whose asymptotic behavior under the unit root null hypothesis, and the simplifying assumptions of a polynomial trend and iid errors are shown to be surprisingly simple. Indeed, the test statistic is not only asymptotically independent of the true trend polynomial, but also is in fact unique in that it is independent also of the degree of the fitted polynomial. However, this invariance property does not carry over to the local alternative, under which it is shown that local power is a decreasing function of the trend degree. But while power does decrease, the rate of shrinking of the local alternative is generally constant in the trend degree, which goes against the common belief that the rate of shrinking should be decreasing in the trend degree. The above results are based on simplifying assumptions. To compensate for this lack of generality, a second, robust, test statistic is proposed, whose validity does not require that the trend function is a polynomial or that the errors are iid.

On the Classification of Recursive Languages

A one-sided classifier for a given class of languages converges to 1 on every language from the class and outputs 0 infinitely often on languages outside the class. A two-sided classifier, on the other hand, converges to 1 on languages from the class and converges to 0 on languages outside the class. The present paper investigates one-sided and two-sided classification for classes of recursive languages. Theorems are presented that help assess the classifiability of natural classes. The relationships of classification to inductive learning theory and to structural complexity theory in terms of Turing degrees are studied. Furthermore, the special case of classification from only positive data is also investigated.

Monotonous trend estimation using recursive prony analysis

This paper presents a solution to the problem of estimating the monotonous tendency of a slow-varying oscillating system. A recursive Prony Analysis (PA) scheme is developed which involves obtaining a dynamic model with parameters identified by implementing the forgetting factor recursive least square (FFRLS) method. A box threshold principle is proposed to separate the dominant components, which results in an accurate estimation of the trend of oscillating systems. Performance of the proposed PA is evaluated using real-time measurements when random noise and vibration effects are present. Moreover, the proposed method is used to estimate monotonous tendency of deck displacement to assist in a safe landing of an unmanned aerial vehicle (UAV). It is shown that the proposed method can estimate instantaneous mean deck satisfactorily, making it well suited for integration into ship-UAV approach and landing guidance systems.

Experience, recursive awareness and understanding in autism spectrum disorders : insights of parents and teachers in Singapore

Provision of an individually responsive education requires a comprehensive understanding of the inner worlds of learners, such as their feelings and thoughts. However, this is difficult to achieve when learners, such as those with Autism Spectrum Disorders (ASD) and cognitive difficulties, have problems with communication. To address this issue, the current exploratory descriptive study sought the views of 133 Singaporean parents and teachers of school-age learners with ASD and cognitive difficulties regarding the inner experience of their children and students. The findings highlight the variety of abilities and difficulties found in how these learners experience their own mental states and understand those of others. These abilities and difficulties are characterized according to type of mental state and analysed in line with three qualia, those of experience, recursive awareness and understanding. The findings indicate that learners show a greater awareness of their own mental states compared to their ability to understand these same mental states in others. Educational implications are discussed.

Recursive pathways to marginal likelihood estimation with prior-sensitivity analysis

We investigate the utility to computational Bayesian analyses of a particular family of recursive marginal likelihood estimators characterized by the (equivalent) algorithms known as "biased sampling" or "reverse logistic regression" in the statistics literature and "the density of states" in physics. Through a pair of numerical examples (including mixture modeling of the well-known galaxy dataset) we highlight the remarkable diversity of sampling schemes amenable to such recursive normalization, as well as the notable efficiency of the resulting pseudo-mixture distributions for gauging prior-sensitivity in the Bayesian model selection context. Our key theoretical contributions are to introduce a novel heuristic ("thermodynamic integration via importance sampling") for qualifying the role of the bridging sequence in this procedure, and to reveal various connections between these recursive estimators and the nested sampling technique.

Recursive actuator fault detection and diagnosis for emergency landing of UASs

This paper presents a practical recursive fault detection and diagnosis (FDD) scheme for online identification of actuator faults for unmanned aerial systems (UASs) based on the unscented Kalman filtering (UKF) method. The proposed FDD algorithm aims to monitor health status of actuators and provide indication of actuator faults with reliability, offering necessary information for the design of fault-tolerant flight control systems to compensate for side-effects and improve fail-safe capability when actuator faults occur. The fault detection is conducted by designing separate UKFs to detect aileron and elevator faults using a nonlinear six degree-of-freedom (DOF) UAS model. The fault diagnosis is achieved by isolating true faults by using the Bayesian Classifier (BC) method together with a decision criterion to avoid false alarms. High-fidelity simulations with and without measurement noise are conducted with practical constraints considered for typical actuator fault scenarios, and the proposed FDD exhibits consistent effectiveness in identifying occurrence of actuator faults, verifying its suitability for integration into the design of fault-tolerant flight control systems for emergency landing of UASs.

Short-data recursive HMM parameter estimation for rapid vision-based aircraft heading estimation

Rapid recursive estimation of hidden Markov Model (HMM) parameters is important in applications that place an emphasis on the early availability of reasonable estimates (e.g. for change detection) rather than the provision of longer-term asymptotic properties (such as convergence, convergence rate, and consistency). In the context of vision- based aircraft (image-plane) heading estimation, this paper suggests and evaluates the short-data estimation properties of 3 recursive HMM parameter estimation techniques (a recursive maximum likelihood estimator, an online EM HMM estimator, and a relative entropy based estimator). On both simulated and real data, our studies illustrate the feasibility of rapid recursive heading estimation, but also demonstrate the need for careful step-size design of HMM recursive estimation techniques when these techniques are intended for use in applications where short-data behaviour is paramount.

Jet Engine Health Signal Denoising Using Optimally Weighted Recursive Median Filters

The removal of noise and outliers from health signals is an important problem in jet engine health monitoring. Typically, health signals are time series of damage indicators, which can be sensor measurements or features derived from such measurements. Sharp or sudden changes in health signals can represent abrupt faults and long term deterioration in the system is typical of gradual faults. Simple linear filters tend to smooth out the sharp trend shifts in jet engine signals and are also not good for outlier removal. We propose new optimally designed nonlinear weighted recursive median filters for noise removal from typical health signals of jet engines. Signals for abrupt and gradual faults and with transient data are considered. Numerical results are obtained for a jet engine and show that preprocessing of health signals using the proposed filter significantly removes Gaussian noise and outliers and could therefore greatly improve the accuracy of diagnostic systems. [DOI: 10.1115/1.3200907].

A Recursive Perspective on Discursive Legitimation and Organizational Action in Mergers and Acquisitions

This paper challenges the predominant view that legitimation is merely a specific phase in merger or acquisition processes. We argue that a better understanding of postmerger organizational dynamics calls for conceptualization of discursive legitimation as an inherent part of unfolding merger processes. In particular, we focus on the recursive relationship between legitimation and organizational action. We have two objectives: to outline a theoretical model that helps one to understand the dynamics of discursive legitimation and organizational action in postmerger organizations, and to examine a revealing case to distinguish the inherent risks and problems in discursive legitimation. Our case analysis focuses on the merger between the French pharmaceutical companies BioMérieux and Pierre Fabre. We adopt a critical multimethod approach and distinguish specific discursive dynamics and pathological tendencies in this case. The analysis highlights the unintended consequences of discursive legitimation, the central role of sensegiving and sensehiding in discursive legitimation, the inherently political nature of legitimation and the risks associated with politicization, the special problems associated with fashionable discourses and the role of the media, the use of specific discursive strategies for legitimation and delegitimation, and the crucial role of actual integration results. This analysis adds to the existing research on mergers and acquisitions by treating discursive legitimation as part of the merger dynamics. In particular, our case analysis provides a new explanation for merger failure. We also believe that the recursive model connecting discursive legitimation and delegitimation strategies to concrete organizational action makes a more general contribution to our understanding of organizational legitimation.

A recursive perspective on discursive legitimation and organizational action in mergers and acquisitions

This paper challenges the predominant view that legitimation is merely a specific phase in merger or acquisition processes. We argue that a better understanding of postmerger organizational dynamics calls for conceptualization of discursive legitimation as an inherent part of unfolding merger processes. In particular, we focus on the recursive relationship between legitimation and organizational action. We have two objectives: to outline a theoretical model that helps one to understand the dynamics of discursive legitimation and organizational action in postmerger organizations, and to examine a revealing case to distinguish the inherent risks and problems in discursive legitimation. Our case analysis focuses on the merger between the French pharmaceutical companies BioMérieux and Pierre Fabre. We adopt a critical multimethod approach and distinguish specific discursive dynamics and pathological tendencies in this case. The analysis highlights the unintended consequences of discursive legitimation, the central role of sensegiving and sensehiding in discursive legitimation, the inherently political nature of legitimation and the risks associated with politicization, the special problems associated with fashionable discourses and the role of the media, the use of specific discursive strategies for legitimation and delegitimation, and the crucial role of actual integration results. This analysis adds to the existing research on mergers and acquisitions by treating discursive legitimation as part of the merger dynamics. In particular, our case analysis provides a new explanation for merger failure. We also believe that the recursive model connecting discursive legitimation and delegitimation strategies to concrete organizational action makes a more general contribution to our understanding of organizational legitimation.

Incremental attribute evaluation through recursive procedures

Incremental semantic analysis in a programming environment based on Attribute Grammars is performed by an Incremental Attribute Evaluator (IAE). Current IAEs are either table-driven or make extensive use of graph structures to schedule reevaluation of attributes. A method of compiling an Ordered Attribute Grammar into mutually recursive procedures is proposed. These procedures form an optimal time Incremental Attribute Evaluator for the attribute grammar, which does not require any graphs or tables.

Managing interprocessor delays in distributed recursive algorithms

For a class of distributed recursive algorithms, it is shown that a stochastic approximation-like tapering stepsize routine suppresses the effects of interprocessor delays.

Recursive parametrization of quark flavour mixing matrices

We examine quark flavour mixing matrices for three and four generations using the recursive parametrization of U(n) and SU(n) matrices developed earlier. After a brief summary of the recursive parametrization, we obtain expressions for the independent rephasing invariants and also the constraints on them that arise from the requirement of mod symmetry of the flavour mixing matrix.

Three- and Seven-Point Optimally Weighted Recursive Median Filters for Gas Turbine Diagnostics

Measured health signals incorporate significant details about any malfunction in a gas turbine. The attenuation of noise and removal of outliers from these health signals while preserving important features is an important problem in gas turbine diagnostics. The measured health signals are a time series of sensor measurements such as the low rotor speed, high rotor speed, fuel flow, and exhaust gas temperature in a gas turbine. In this article, a comparative study is done by varying the window length of acausal and unsymmetrical weighted recursive median filters and numerical results for error minimization are obtained. It is found that optimal filters exist, which can be used for engines where data are available slowly (three-point filter) and rapidly (seven-point filter). These smoothing filters are proposed as preprocessors of measurement delta signals before subjecting them to fault detection and isolation algorithms.