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While the main purpose of reporting – e.g. reporting for taxes – is to gauge the economic state of a company, the fact that reporting is done at pre-determined dates distorts the reporting results. For example, to create a larger impression of their productivity, companies fire temporary workers before the reporting date and re-hire then right away. The purpose of this study is to decide how to avoid such distortion.

This study aims to come up with a solution which is applicable for all possible reasonable optimality criteria. Thus, a general formalism for describing and analyzing all such criteria is used.

This study shows that most distortion problems will disappear if the fixed pre-determined reporting dates are replaced with individualized random reporting dates. This study also shows that for all reasonable optimality criteria, the optimal way to assign reporting dates is to do it uniformly.

This study shows that for all reasonable optimality criteria, the optimal way to assign reporting dates is to do it uniformly.

It is found that the individualized random tax reporting dates would be beneficial for economy.

It is found that the individualized random tax reporting dates would be beneficial for society as a whole.

This study proposes a new idea of replacing the fixed pre-determining reporting dates with randomized ones. On the informal level, this idea may have been proposed earlier, but what is completely new is our analysis of which randomization of reporting dates is the best for economy: it turns out that under all reasonable optimality criteria, uniform randomization works the best.

A progressive hybrid censoring scheme (PHCS) becomes impractical for ensuring dependable outcomes when there is a low likelihood of encountering a small number of failures prior to the predetermined terminal time T. The generalized progressive hybrid censoring scheme (GPHCS) efficiently addresses to overcome the limitation of the PHCS.

In this article, estimation of model parameter, survival and hazard rate of the Unit-Lindley distribution (ULD), when sample comes from the GPHCS, have been taken into account. The maximum likelihood estimator has been derived using Newton–Raphson iterative procedures. Approximate confidence intervals of the model parameter and their arbitrary functions are established by the Fisher information matrix. Bayesian estimation procedures have been derived using Metropolis–Hastings algorithm under squared error loss function. Convergence of Markov chain Monte Carlo (MCMC) samples has been examined. Various optimality criteria have been considered. An extensive Monte Carlo simulation analysis has been shown to compare and validating of the proposed estimation techniques.

The Bayesian MCMC approach to estimate the model parameters and reliability characteristics of the generalized progressive hybrid censored data of ULD is recommended. The authors anticipate that health data analysts and reliability professionals will get benefit from the findings and approaches presented in this study.

The ULD has a broad range of practical utility, making it a problem to estimate the model parameters as well as reliability characteristics and the significance of the GPHCS also encourage the authors to consider the present estimation problem because it has not previously been discussed in the literature.

This new paper aims to combine the recent new contributions about direct data driven control and other safety property to form an innovative direct data driven safety control for aircraft flight system. More specifically, within the framework of direct data driven strategy, the collected data are dealt with to get the identified plant and designed controller. After reviewing some priori information about aircraft flight system, a closed loop system with the unknown plant and controller simultaneously is considered. Data driven estimation is proposed to identify the plant and controller only through the ratios of two correlation functions, computed from the collected data. To achieve the dual missions about perfect tracking and safety property, a new notion about safety controller is introduced. To design this safety controller, direct data driven safety controller is proposed to solve one constrain optimization problem. Then the authors apply the Karush–Kuhn–Tucker (KKT) optimality conditions to derive the explicit safety controller.

First, consider one closed loop system corresponding to aircraft flight system with the unknown plant and feed forward controller, data driven estimation is used to identify the plant and feed forward controller. This identification process means nonparametric estimation. Second, to achieve the perfect tracking one given transfer function and guarantee the closed loop output response within one limited range simultaneously, safety property is introduced. Then direct data driven safety control is proposed to design the safety controller, while satisfying the dual goals. Third, as the data driven estimation and direct data driven safety control are all formulated as one constrain optimization problem, the KKT optimality conditions are applied to obtain the explicit safety controller.

Some aircraft system identification and aircraft flight controller design can be reformulated as their corresponding constrain optimization problems. Then through solving these constrain optimization problems, the optimal estimation and controller are yielded, while satisfying our own priori goals. First, data driven estimation is proposed to get the rough estimation about the plant and controller. Second, data driven safety control is proposed to get one safety controller before our mentioned safety concept.

To the best of the authors’ knowledge, some existing theories about nonparametric estimation and tube model predictive control are very mature, but few contributions are applied in practice, such as aircraft system identification and aircraft flight controller design. This new paper shows the new theories about data driven estimation and data driven safety control on aircraft, being corresponded to the classical nonparametric estimation and tube model predictive control. Specifically, data driven estimation gives the rough estimations for the aircraft and its feed forward controller. Furthermore, after introducing the safety concept, data driven safety control is introduced to achieve the desired dual missions with the combination of KKT optimality conditions.

Motivated by empirical features that characterize cryptocurrency volatility data, the authors develop a forecasting strategy that can account for both model uncertainty and heteroskedasticity of unknown form. The theoretical investigation establishes the asymptotic optimality of the proposed heteroskedastic model averaging heterogeneous autoregressive (H-MAHAR) estimator under mild conditions. The authors additionally examine the convergence rate of the estimated weights of the proposed H-MAHAR estimator. This analysis sheds new light on the asymptotic properties of the least squares model averaging estimator under alternative complicated data generating processes (DGPs). To examine the performance of the H-MAHAR estimator, the authors conduct an out-of-sample forecasting application involving 22 different cryptocurrency assets. The results emphasize the importance of accounting for both model uncertainty and heteroskedasticity in practice.

There is growing empirical evidence that firm heterogeneity is technologically non-neutral. This chapter extends the Gandhi, Navarro, and Rivers (2020) proxy variable framework for structurally identifying production functions to a more general case when latent firm productivity is multi-dimensional, with both factor-neutral and (biased) factor-augmenting components. Unlike alternative methodologies, the proposed model can be identified under weaker data requirements, notably, without relying on the typically unavailable cross-sectional variation in input prices for instrumentation. When markets are perfectly competitive, point identification is achieved by leveraging the information contained in static optimality conditions, effectively adopting a system-of-equations approach. It is also shown how one can partially identify the non-neutral production technology in the traditional proxy variable framework when firms have market power.

Topology optimization of structures under self-weight loading is a challenging problem which has received increasing attention in the past years. The use of standard formulations based on compliance minimization under volume constraint suffers from numerous difficulties for self-weight dominant scenarios, such as non-monotonic behaviour of the compliance, possible unconstrained character of the optimum and parasitic effects for low densities in density-based approaches. This paper aims to propose an alternative approach for dealing with topology design optimization of structures into three spatial dimensions subject to self-weight loading.

In order to overcome the above first two issues, a regularized formulation of the classical compliance minimization problem under volume constraint is adopted, which enjoys two important features: (a) it allows for imposing any feasible volume constraint and (b) the standard (original) formulation is recovered once the regularizing parameter vanishes. The resulting topology optimization problem is solved with the help of the topological derivative method, which naturally overcomes the above last issue since no intermediate densities (grey-scale) approach is necessary.

A novel and simple approach for dealing with topology design optimization of structures into three spatial dimensions subject to self-weight loading is proposed. A set of benchmark examples is presented, showing not only the effectiveness of the proposed approach but also highlighting the role of the self-weight loading in the final design, which are: (1) a bridge structure is subject to pure self-weight loading; (2) a truss-like structure is submitted to an external horizontal force (free of self-weight loading) and also to the combination of self-weight and the external horizontal loading; and (3) a tower structure is under dominant self-weight loading.

An alternative regularized formulation of the compliance minimization problem that naturally overcomes the difficulties of dealing with self-weight dominant scenarios; a rigorous derivation of the associated topological derivative; computational aspects of a simple FreeFEM implementation; and three-dimensional numerical benchmarks of bridge, truss-like and tower structures.

This chapter tells the story of how the concept of Pareto efficiency was shipped from Lausanne to the modern US theory of competitive general equilibrium, focusing on the specific role of Maurice Allais. It identifies similarities in both epistemological approach and theoretical achievements realized first by Pareto, then by Allais, and finally by Debreu and Arrow and Hahn. It also shows that these similarities are not casual, since historical circumstances account for the influence of Pareto on Allais and later of Allais on Arrow and Debreu.