Boosted Beta regression.

Regression analysis with a bounded outcome is a common problem in applied statistics. Typical examples include regression models for percentage outcomes and the analysis of ratings that are measured on a bounded scale. In this paper, we consider beta regression, which is a generalization of logit models to situations where the response is continuous on the interval (0,1). Consequently, beta regression is a convenient tool for analyzing percentage responses. The classical approach to fit a beta regression model is to use maximum likelihood estimation with subsequent AIC-based variable selection. As an alternative to this established - yet unstable - approach, we propose a new estimation technique called boosted beta regression. With boosted beta regression estimation and variable selection can be carried out simultaneously in a highly efficient way. Additionally, both the mean and the variance of a percentage response can be modeled using flexible nonlinear covariate effects. As a consequence, the new method accounts for common problems such as overdispersion and non-binomial variance structures

A unified approach to nonlinearity, structural change and outliers

This paper demonstrates that the class of conditionally linear and Gaussianstate-space models offers a general and convenient framework for simultaneouslyhandling nonlinearity, structural change and outliers in time series. Manypopular nonlinear time series models, including threshold, smooth transitionand Markov-Switching models, can be written in state-space form. It is thenstraightforward to add components that capture parameter instability andintervention effects. We advocate a Bayesian approach to estimation andinference, using an efficient implementation of Markov Chain Monte Carlosampling schemes for such linear dynamic mixture models. The general modellingframework and the Bayesian methodology are illustrated by means of severalexamples. An application to quarterly industrial production growth rates forthe G7 countries demonstrates the empirical usefulness of the approach.Bayesian inference;threshold models;Markov-switching models;business cycle asymmetry;state-space models

A unified approach to nonlinearity, structural change and outliers

This paper demonstrates that the class of conditionally linear and Gaussian state-space models offers a general and convenient framework for simultaneously handling nonlinearity, structural change and outliers in time series. Many popular nonlinear time series models, including threshold, smooth transition and Markov-Switching models, can be written in state-space form. It is then straightforward to add components that capture parameter instability and intervention effects. We advocate a Bayesian approach to estimation and inference, using an efficient implementation of Markov Chain Monte Carlo sampling schemes for such linear dynamic mixture models. The general modelling framework and the Bayesian methodology are illustrated by means of several examples. An application to quarterly industrial production growth rates for the G7 countries demonstrates the empirical usefulness of the approach

Identification of nonlinear time-varying systems using an online sliding-window and common model structure selection (CMSS) approach with applications to EEG

The identification of nonlinear time-varying systems using linear-in-the-parameter models is investigated. A new efficient Common Model Structure Selection (CMSS) algorithm is proposed to select a common model structure. The main idea and key procedure is: First, generate K 1 data sets (the first K data sets are used for training, and theK 1 th one is used for testing) using an online sliding window method; then detect significant model terms to form a common model structure which fits over all the K training data sets using the new proposed CMSS approach. Finally, estimate and refine the time-varying parameters for the identified common-structured model using a Recursive Least Squares (RLS) parameter estimation method. The new method can effectively detect and adaptively track the transient variation of nonstationary signals. Two examples are presented to illustrate the effectiveness of the new approach including an application to an EEG data set

Linear Model Estimation of Nonlinear Systems Using Least-Squares Algorithm5

This paper presents utilizes Least-Squares Algorithm to obtain more accurate linear models of nonlinear systems using parameter estimation. This approach generates an optimal linear model which is valid over a wide range of trajectories and converges to the desired steady-state value with no errors unlike the existing techniques. The proposed technique is very efficient and does not require storing the data. Therefore, it can easily be used and implemented with limited resources for undergraduate curriculum especially in underdeveloped countries. Most available techniques for linearization of nonlinear system are only valid about the operating point; furthermore, the knowledge of the operating point is required. The advantage of proposed technique is that the linearized model is not sensitive to the operating point; the estimation only requires the order of the system not the operating point. A physical example will be giving to illustrate the linear model of jet engines nonlinear system

Matching Function Equilibria with Partial Assignment: Existence, Uniqueness and Estimation

In this paper, we argue that models coming from a variety of fields share a common structure that we call matching function equilibria with partial assignment. This structure revolves around an aggregate matching function and a system of nonlinear equations. This encompasses search and matching models, matching models with transferable, non-transferable and imperfectly transferable utility, and matching with peer effects. We provide a proof of existence and uniqueness of an equilibrium as well as an efficient algorithm to compute it. We show how to estimate parametric versions of these models by maximum likelihood. We also propose an approach to construct counterfactuals without estimating the matching functions for a subclass of models. We illustrate our estimation approach by analyzing the impact of the elimination of the Social Security Student Benefit Program in 1982 on the marriage market in the United States

Nonlinear Evolutionary PDE-Based Refinement of Optical Flow

The goal of this paper is to propose two nonlinear variational models for obtaining a refined motion estimation from an image sequence. Both the proposed models can be considered as a part of a generalized framework for an accurate estimation of physics-based flow fields such as rotational and fluid flow. The first model is novel in the sense that it is divided into two phases: the first phase obtains a crude estimate of the optical flow and then the second phase refines this estimate using additional constraints. The correctness of this model is proved using an Evolutionary PDE approach. The second model achieves the same refinement as the first model, but in a standard manner, using a single functional. A special feature of our models is that they permit us to provide efficient numerical implementations through the first-order primaldual Chambolle-Pock scheme. Both the models are compared in the context of accurate estimation of angle by performing an anisotropic regularization of the divergence and curl of the flow respectively. We observe that, although both the models obtain the same level of accuracy, the two-phase model is more efficient. In fact, we empirically demonstrate that the single-phase and the two-phase models have convergence rates of order $O(1/N^2)$ and $O(1/N)$ respectively

MULTIVARIABLE SYSTEM IDENTIFICATION OF A CONTINUOUS BINARY DISTILLATION COLUMN

Distillation is a process that is commonly used in industries for separation purpose. A distillation column is a multivariable system which shows nonlinear dynamic behavior due to its nonlinear vapor-liquid equilibrium. In order to gain better product quality and lower energy consumption of the distillation column, an effective model based control system is needed to allow the process to be operated over a certain operating range. In control engineering, System Identification is considered as a well suited approach for developing an approximate model for the nonlinear system. In this study, System Identification technique is applied to predict the top and bottom product composition by focusing the temperature of the distillation column. The process in the column is based on the distillation of a binary mixture of Isopropyl Alcohol and Acetone. The experimental data obtained from the distillation column was used for estimation and validation of simulated models. During analysis, different types of linear and nonlinear models were developed and are compared to predict the best model which can be effectively used for designing the control system of the distillation column. Among the linear models such as; Autoregressive with Exogenous Input (ARX), Autoregressive Moving Average with Exogenous inputs (ARMAX), Linear State Space (LSS) model and Continuous Process Model were developed and compared with each other. The results of this comparison reveals that the performance of LSS model is efficient and hence it was further used to improve the modeling approach and compared with other nonlinear models. A Nonlinear State Space (NSS) model was developed by the combination of LSS and Neural Network (NN) and is compared solely with NN and ANFIS identification model. The simulation results show that the developed NSS model is well capable of defining the dynamics of the plant based on the best fit criteria and residual performance. In addition to this, NSS model predicted the best statistical measurement of the nonlinear system. This approach is helpful for designing the efficient control system for online separation process of the plant