Robust optimization in spline regression models for multi-model regulatory networks under polyhedral uncertainty

In our study, we integrate the data uncertainty of real-world models into our regulatory systems and robustify them. We newly introduce and analyse robust time-discrete target–environment regulatory systems under polyhedral uncertainty through robust optimization. Robust optimization has reached a great importance as a modelling framework for immunizing against parametric uncertainties and the integration of uncertain data is of considerable importance for the model’s reliability of a highly interconnected system. Then, we present a numerical example to demonstrate the efficiency of our new robust regression method for regulatory networks. The results indicate that our approach can successfully approximate the target–environment interaction, based on the expression values of all targets and environmental factors.     

Parametric estimation for simple branching diffusion processes, II

Consider a simple branching diffusion process, which is a branching process in which the individuals move and live and die in space. The offspring distribution has finite moments of all orders. A parametric estimation theory is presented, using time slice data. This involves the use of third order cumulant spectra to identify and estimate the parameters.     

Iterative parameter identification methods for nonlinear functions

This paper considers identification problems of nonlinear functions fitting or nonlinear systems modelling. A gradient based iterative algorithm and a Newton iterative algorithm are presented to determine the parameters of a nonlinear system by using the negative gradient search method and Newton method. Furthermore, two model transformation based iterative methods are proposed in order to enhance computational efficiencies. By means of the model transformation, a simpler nonlinear model is achieved to simplify the computation. Finally, the proposed approaches are analyzed using a numerical example.     

A parametric lifetime model for a multicomponents system with spatial interactions

In this paper, we consider a system made of n components displayed on a structure (eg, a steel plate). We define a parametric model for the hazard function, which includes covariates and spatial interaction between components. The state (nonfailed or failed) of each component is observed at some inspection times. From these data, we consider the problem of model parameter estimation. To achieve this, we suggest to use the SEM algorithm based on a pseudo‐likelihood function. A definition for the time‐to‐failure of the system is given, generalizing the classical cases. A study based on numerical simulations is provided to illustrate the proposed approach.     

Determination of precession and dissipation parameters in micromagnetism

The precession β and the dissipation parameter α of a ferromagnetic material can be considered microscopically space dependent. Their space distribution is difficult to obtain by direct measurements. In this article we consider an inverse problem, where we aim at recovering α and β from space measurements of the magnetization. The evolution of the magnetization in micromagnetism is governed by the Landau-Lifshitz (LL) equation. We first study the sensitivity of the LL equation. We derive the existence, uniqueness and stability results for the LL equation and the corresponding sensitivity equations. On the basis of the results we analyze the inverse problem. We employ the energy method and we minimize the underlying cost functional by means of the steepest descent method. We derive a convergence result for the proposed algorithm. The presented numerical examples support the theoretical results.     

Comparison of adaptive filters for gas turbine performance monitoring

Kalman filters are widely used in the turbine engine community for health monitoring purpose. This algorithm has proven its capability to track gradual deterioration with a good accuracy. On the other hand, its response to rapid deterioration is either a long delay in recognising the fault, and/or a spread of the estimated fault in several components. The main reason of this deficiency lies in the transition model of the parameters that assumes a smooth evolution of the engine’s condition. The aim of this contribution is to compare two adaptive diagnosis tools that combine a Kalman filter and a secondary system that monitors the residuals. This auxiliary component implements on one hand a covariance matching scheme and on the other hand a generalised likelihood ratio test to improve the behaviour of the diagnosis tool with respect to abrupt faults.     

Maximin efficiency robust test for multiple nuisance parameters and its statistical properties

We propose the maximin efficiency robust test (MERT) for multiple nuisance parameters based on theories about the maximin efficiency robust test for only one nuisance parameter and investigate some theoretical properties about this robust test. We explore some theoretical properties about the power of the MERT for multiple nuisance parameters in a specified scenario intuitively further more. We also propose a meaningful example from statistical genetic field to which the MERT for multiple nuisance parameters can be well applied. Extensive simulation studies are conducted to testify the robustness of the MERT for multiple nuisance parameters.     

FFT-Based Fast Computation of Multivariate Kernel Density Estimators With Unconstrained Bandwidth Matrices

The problem of fast computation of multivariate kernel density estimation (KDE) is still an open research problem. In our view, the existing solutions do not resolve this matter in a satisfactory way. One of the most elegant and efficient approach uses the fast Fourier transform. Unfortunately, the existing FFT-based solution suffers from a serious limitation, as it can accurately operate only with the constrained (i.e., diagonal) multivariate bandwidth matrices. In this article, we describe the problem and give a satisfactory solution. The proposed solution may be successfully used also in other research problems, for example, for the fast computation of the optimal bandwidth for KDE. Supplementary materials for this article are available online.     

A robust and efficient estimation method for single-index varying-coefficient models

A new estimation procedure based on modal regression is proposed for single-index varying-coefficient models. The proposed method achieves better robustness and efficiency than that of Xue and Pang (2013). We establish the asymptotic normalities of proposed estimators and evaluate the performance of the proposed method by a numerical simulation.