Applied econometricians frequently apply the inverse hyperbolic sine (or arcsinh) transformation to a variable because it approximates the natural logarithm of that variable and allows retaining ...zero‐valued observations. We provide derivations of elasticities in common applications of the inverse hyperbolic sine transformation and show empirically that the difference in elasticities driven by ad hoc transformations can be substantial. We conclude by offering practical guidance for applied researchers.
Metatechnology frontier and convexity: A restatement Kerstens, Kristiaan; O’Donnell, Christopher; Van de Woestyne, Ignace
European journal of operational research,
06/2019, Letnik:
275, Številka:
2
Journal Article
Recenzirano
Odprti dostop
•We revisit the definition of the metaset in the frontier literature.•A metaset as a union of group-specific frontiers is normally non-convex.•The seminal articles suggest a convexification strategy ...consisting in estimating a convex metaset.•We establish new propositions on the union operator of technologies.•An empirical illustration shows that the convexification strategy is unreliable.
This article reconsiders the way metafrontiers and associated measures of efficiency are obtained from nonparametric estimates of underlying group-specific frontiers. Both convex and non-convex metasets have been applied, but the large majority of articles applying this popular methodology assume that the metafrontier envelops a convex metaset. We argue that associated estimates of efficiency are potentially unreliable. We develop a refined methodology for nonparametric envelopment of non-convex metasets. We apply our methodology to a secondary data set to illustrate the potential errors associated with the currently established methods. Anticipating our main conclusion, we find that the convexification strategy consisting in assuming a convex metaset generally leads to erroneous results.
Dissolved Gas Analysis (DGA) is a standout diagnostic strategy to recognise incipient faults and monitor the condition of oil-immersed transformers. It correlates the concentration of various ...insulation degradation by-products dissolved in oil with the nature of faults. DGA standards provide various interpretation methods for fault diagnosis and estimation of the useful life of insulation. These economic and widely used methods have significant limitations that hamper their resourcefulness. The uncertainty in diagnostic outcomes due to manual handling of fault data, boundary conditions, unresolved fault cases due to over-range ratios, inability to diagnose concurrently existing faults (multiple faults) and lack of severity information about incipient faults are worth mentioning. This paper reviews various solutions provided by researchers for addressing these uncertain and unresolved isssues in incipient fault diagnosis. Paper presents a systematic review of the literature that includes the application of intelligent and mathematical techniques in DGA based diagnosis. Further, it critically analyses the reported works on composite methods and finally, progress in sensor-based condition monitoring of transformer is also deliberated. This article is first of its kind where AI (Artificial Intelligence), integrated methods, mathematical and experimental approaches in DGA based diagnostics are simultaneously reviewed and analysed. The paper concludes the best possible solution for reliabile diagnosis and also explores pertinent issues of research in the area of DGA based transformer health monitoring.
•The paper reviews solutions for addressing the uncertain and unresolved issues in DGA- based transformer fault diagnosis.•This includes the application of intelligent techniques to DGA based monitoring and emerging sensor-based monitoring.•The paper concludes best possible solution for reliable diagnosis and also explores pertinent research gaps in this area.
We introduce a novel parametrization of the correlation matrix. The reparametrization facilitates modeling of correlation and covariance matrices by an unrestricted vector, where positive ...definiteness is an innate property. This parametrization can be viewed as a generalization of Fisher’s Z-transformation to higher dimensions and has a wide range of potential applications. An algorithm for reconstructing the unique n × n correlation matrix from any vector in ℝn(n-1)/2 is provided, and we derive its numerical complexity.
•A review of Data analytics approaches that were used to estimate building occupancy is presented.•Unique literature pertaining to occupancy detection is categorized into three main groups: Occupancy ...detection, counting and tracking/special applications.•A comprehensive table comparing various methods is presented as a guideline to readers.
A review of the literature pertaining to building occupancy detection, counting, and tracking – three areas under the umbrella of building occupancy estimation – is presented with a focus on mathematical approaches and corresponding metrics. The idea is to provide the reader with a background on the hardware and techniques used for occupancy inference, subsequent to data collection, with emphasis placed on the algorithmic characterization of occupancy estimation. The various approaches employed by researchers to tackle the problem are surveyed and summarized, including: data collection, cleaning processes, algorithm utilization and categorization, as well as data structuring and organization. The scope of prediction and performance metrics are used to establish a benchmarking system through a comprehensive summary of (indoor) occupancy estimation, presented in the context of the mathematical tools utilized.
We propose a pseudospectral method to solve heterogeneous-agent models in continuous time. The solution is approximated as a sum of smooth global basis functions, in our case polynomials represented ...by their values at Chebyshev nodes. We illustrate the method by applying it to a Krusell-Smith model. It solves the differential equations characterizing the steady-state efficiently and precisely, despite using only very few nodes. System dynamics are then automatically differentiated to simulate a linearized model. The full solution takes a third of a second and only uses standard software. A benchmark against finite differences shows that pseudospectral methods achieve far greater precision for a given number of nodes and for a given runtime. We conclude by discussing the methods' applicability, which is promising for smooth multi-dimensional models.
Technological advances in science and engineering have led to the routine collection of large and complex data objects, where the dependence structure among those objects is often of great interest. ...Those complex objects (e.g., different brain subcortical structures) often reside in some Banach spaces, and hence their relationship cannot be well characterized by most of the existing measures of dependence such as correlation coefficients developed in Hilbert spaces. To overcome the limitations of the existing measures, we propose Ball Covariance as a generic measure of dependence between two random objects in two possibly different Banach spaces. Our Ball Covariance possesses the following attractive properties: (i) It is nonparametric and model-free, which make the proposed measure robust to model mis-specification; (ii) It is nonnegative and equal to zero if and only if two random objects in two separable Banach spaces are independent; (iii) Empirical Ball Covariance is easy to compute and can be used as a test statistic of independence. We present both theoretical and numerical results to reveal the potential power of the Ball Covariance in detecting dependence. Also importantly, we analyze two real datasets to demonstrate the usefulness of Ball Covariance in the complex dependence detection.
Supplementary materials
for this article are avaiable online.
A monotone function interval is the set of monotone functions that lie pointwise between two fixed, -monotone functions. We characterize the set of extreme points of monotone function intervals and ...apply this to a number of economic settings. First, we leverage the main result to characterize the set of distributions of posterior quantiles that can be induced by a signal, with applications to political economy, Bayesian persuasion, and the psychology of judgment. Second, we combine our characterization with properties of convex optimization problems to unify and generalize seminal results in the literature on security design under adverse selection and moral hazard. (JEL C61, C65, D72, D82, D91, G12)
Blackwell's theorem on the comparison of information structures is by now sufficiently well-understood for a finite state space, but important gaps remain in the infinite case. While the equivalence ...of (i) sufficiency and (ii) more-informativeness is known, we present a comprehensive theory that establishes equivalences between these two orders (in both their original and almost all versions) and three additional prior-dependent criteria on general (Polish) state spaces. We consider (iii) Bayesian preference, (iv) convex dominance, and (v) mean-preserving-spread (dilation) for all priors as well as for a given full-support prior. We provide counterexamples to underscore the necessity of the assumptions underlying some of our findings, and offer a generalization of the Hirschleifer-Schlee theorem as an application.
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