Linear least squares estimation of the first order moving average parameter

We propose an iterative procedure to minimize the sum of squares function which avoids the nonlinear nature of estimating the first order moving average parameter and provides a closed form of the estimator. The asymptotic properties of the method are discussed and the consistency of the linear least squares estimator is proved for the invertible case. We perform various Monte Carlo experiments in order to compare the sample properties of the linear least squares estimator with its nonlinear counterpart for the conditional and unconditional cases. Some examples are also discussed

Linear least squares estimation of the first order moving average parameter

We propose an iterative procedure to minimize the sum of squares function which avoids the nonlinear nature of estimating the first order moving average parameter and provides a closed form of the estimator. The asymptotic properties of the method are discussed and the consistency of the linear least squares estimator is proved for the invertible case. We perform various Monte Carlo experiments in order to compare the sample properties of the linear least squares estimator with its nonlinear counterpart for the conditional and unconditional cases. Some examples are also discussed

Second-order parameter estimation

This work provides a general framework for the design of second-order blind estimators without adopting anyapproximation about the observation statistics or the a prioridistribution of the parameters. The proposed solution is obtainedminimizing the estimator variance subject to some constraints onthe estimator bias. The resulting optimal estimator is found todepend on the observation fourth-order moments that can be calculatedanalytically from the known signal model. Unfortunately,in most cases, the performance of this estimator is severely limitedby the residual bias inherent to nonlinear estimation problems.To overcome this limitation, the second-order minimum varianceunbiased estimator is deduced from the general solution by assumingaccurate prior information on the vector of parameters.This small-error approximation is adopted to design iterativeestimators or trackers. It is shown that the associated varianceconstitutes the lower bound for the variance of any unbiasedestimator based on the sample covariance matrix.The paper formulation is then applied to track the angle-of-arrival(AoA) of multiple digitally-modulated sources by means ofa uniform linear array. The optimal second-order tracker is comparedwith the classical maximum likelihood (ML) blind methodsthat are shown to be quadratic in the observed data as well. Simulationshave confirmed that the discrete nature of the transmittedsymbols can be exploited to improve considerably the discriminationof near sources in medium-to-high SNR scenarios.

Model predictive control using dynamic integrated system optimisation and parameter estimation (DISOPE)

DISOPE is a technique for solving optimal control problems where there are differences in structure and parameter values between reality and the model employed in the computations. The model reality differences can also allow for deliberate simplification of model characteristics and performance indices in order to facilitate the solution of the optimal control problem. The technique was developed originally in continuous time and later extended to discrete time. The main property of the procedure is that by iterating on appropriately modified model based problems the correct optimal solution is achieved in spite of the model-reality differences. Algorithms have been developed in both continuous and discrete time for a general nonlinear optimal control problem with terminal weighting, bounded controls and terminal constraints. The aim of this paper is to show how the DISOPE technique can aid receding horizon optimal control computation in nonlinear model predictive control.

Likelihood-free estimation of model evidence

Statistical methods of inference typically require the likelihood function to be computable in a reasonable amount of time. The class of “likelihood-free” methods termed Approximate Bayesian Computation (ABC) is able to eliminate this requirement, replacing the evaluation of the likelihood with simulation from it. Likelihood-free methods have gained in efficiency and popularity in the past few years, following their integration with Markov Chain Monte Carlo (MCMC) and Sequential Monte Carlo (SMC) in order to better explore the parameter space. They have been applied primarily to estimating the parameters of a given model, but can also be used to compare models. Here we present novel likelihood-free approaches to model comparison, based upon the independent estimation of the evidence of each model under study. Key advantages of these approaches over previous techniques are that they allow the exploitation of MCMC or SMC algorithms for exploring the parameter space, and that they do not require a sampler able to mix between models. We validate the proposed methods using a simple exponential family problem before providing a realistic problem from human population genetics: the comparison of different demographic models based upon genetic data from the Y chromosome.

On estimation and influence diagnostics for the Grubbs` model under heavy-tailed distributions

The Grubbs` measurement model is frequently used to compare several measuring devices. It is common to assume that the random terms have a normal distribution. However, such assumption makes the inference vulnerable to outlying observations, whereas scale mixtures of normal distributions have been an interesting alternative to produce robust estimates, keeping the elegancy and simplicity of the maximum likelihood theory. The aim of this paper is to develop an EM-type algorithm for the parameter estimation, and to use the local influence method to assess the robustness aspects of these parameter estimates under some usual perturbation schemes, In order to identify outliers and to criticize the model building we use the local influence procedure in a Study to compare the precision of several thermocouples. (C) 2008 Elsevier B.V. All rights reserved.

Improved maximum-likelihood estimation in a regression model with general parametrization

We analyse the finite-sample behaviour of two second-order bias-corrected alternatives to the maximum-likelihood estimator of the parameters in a multivariate normal regression model with general parametrization proposed by Patriota and Lemonte [A. G. Patriota and A. J. Lemonte, Bias correction in a multivariate regression model with genereal parameterization, Stat. Prob. Lett. 79 (2009), pp. 1655-1662]. The two finite-sample corrections we consider are the conventional second-order bias-corrected estimator and the bootstrap bias correction. We present the numerical results comparing the performance of these estimators. Our results reveal that analytical bias correction outperforms numerical bias corrections obtained from bootstrapping schemes.

A simple and non-destructive model for individual leaf area estimation in citrus

Introduction. Leaf area is often related to plant growth, development, physiology and yield. Many non-destructive models have been proposed for leaf area estimation of several plant genotypes, demonstrating that leaf length, leaf width and leaf area are closely correlated. Thus, the objective of our study was to develop a reliable model for leaf area estimation from linear measurements of leaf dimensions for citrus genotypes. Materials and methods. Leaves of citrus genotypes were harvested, and their dimensions (length, width and area) were measured. Values of leaf area were regressed against length, width, the square of length, the square of width and the product (length x width). The most accurate equations, either linear or second-order polynomial, were regressed again with a new data set; then the most reliable equation was defined. Results and discussion. The first analysis showed that the variables length, width and the square of length gave better results in second-order polynomial equations, while the linear equations were more suitable and accurate when the width and the product (length x width) were used. When these equations were regressed with the new data set, the coefficient of determination (R(2)) and the agreement index 'd' were higher for the one that used the variable product (length x width), while the Mean Absolute Percentage Error was lower. Conclusion. The product of the simple leaf dimensions (length x width) can provide a reliable and simple non-destructive model for leaf area estimation across citrus genotypes.

Motion-based wave estimation: Small-scale tests with a crane-barge model

This paper provides additional validation to the problem of estimating wave spectra based on the first-order motions of a moored vessel. Prior investigations conducted by the authors have attested that even a large-volume ship, such as an FPSO unit, could be adopted for on-board estimation of the wave field. The obvious limitation of the methodology concerns filtering of high-frequency wave components, for which the vessel has no significant response. As a result, the estimation range is directly dependent on the characteristics of the vessel response. In order to extend this analysis, further small-scale tests were performed with a model of a pipe-laying crane-barge. When compared to the FPSO case, the results attest that a broader range of typical sea states can be accurately estimated, including crossed-sea states with low peak periods. (C) 2012 Elsevier Ltd. All rights reserved.

Estimation Technique of International Input-Output Model by Non-survey Method

The Asian International Input-Output (IO) Table that is compiled by Institute of Developing Economies-JETRO (IDE), was constructed in Isard type form. Thus, it required a lot of time to publish. In order to avoid this time-lag problem and establish a more simple compilation technique, this paper concentrates on verifying the possibility of using the Chenery-Moses type estimation technique. If possible, applying the Chenery-Moses instead of the Isard type would be effective for both impact and linkage analysis (except for some countries such as Malaysia and Singapore and some primary sectors. Using Chenery-Moses estimation method, production of the Asian International IO table can be reduced by two years. And more, this method might have the possibilities to be applied for updating exercise of Asian IO table.

New methods for the estimation of Takagi-Sugeno model based extended Kalman filter and its applications to optimal control for nonlinear systems

This paper describes new approaches to improve the local and global approximation (matching) and modeling capability of Takagi–Sugeno (T-S) fuzzy model. The main aim is obtaining high function approximation accuracy and fast convergence. The main problem encountered is that T-S identification method cannot be applied when the membership functions are overlapped by pairs. This restricts the application of the T-S method because this type of membership function has been widely used during the last 2 decades in the stability, controller design of fuzzy systems and is popular in industrial control applications. The approach developed here can be considered as a generalized version of T-S identification method with optimized performance in approximating nonlinear functions. We propose a noniterative method through weighting of parameters approach and an iterative algorithm by applying the extended Kalman filter, based on the same idea of parameters’ weighting. We show that the Kalman filter is an effective tool in the identification of T-S fuzzy model. A fuzzy controller based linear quadratic regulator is proposed in order to show the effectiveness of the estimation method developed here in control applications. An illustrative example of an inverted pendulum is chosen to evaluate the robustness and remarkable performance of the proposed method locally and globally in comparison with the original T-S model. Simulation results indicate the potential, simplicity, and generality of the algorithm. An illustrative example is chosen to evaluate the robustness. In this paper, we prove that these algorithms converge very fast, thereby making them very practical to use.

A new approach to fuzzy estimation of Takagi-Sugeno model and its applications to optimal control for nonlinear systems

An efficient approach is presented to improve the local and global approximation and modelling capability of Takagi-Sugeno (T-S) fuzzy model. The main aim is obtaining high function approximation accuracy. The main problem is that T-S identification method cannot be applied when the membership functions are overlapped by pairs. This restricts the use of the T-S method because this type of membership function has been widely used during the last two decades in the stability, controller design and are popular in industrial control applications. The approach developed here can be considered as a generalized version of T-S method with optimized performance in approximating nonlinear functions. A simple approach with few computational effort, based on the well known parameters' weighting method is suggested for tuning T-S parameters to improve the choice of the performance index and minimize it. A global fuzzy controller (FC) based Linear Quadratic Regulator (LQR) is proposed in order to show the effectiveness of the estimation method developed here in control applications. Illustrative examples of an inverted pendulum and Van der Pol system are chosen to evaluate the robustness and remarkable performance of the proposed method and the high accuracy obtained in approximating nonlinear and unstable systems locally and globally in comparison with the original T-S model. Simulation results indicate the potential, simplicity and generality of the algorithm.

Spatially-Explicit Testing of a General Aboveground Carbon Density Estimation Model in aWestern Amazonian Forest Using Airborne LiDAR

Mapping aboveground carbon density in tropical forests can support CO2 emissionmonitoring and provide benefits for national resource management. Although LiDAR technology has been shown to be useful for assessing carbon density patterns, the accuracy and generality of calibrations of LiDAR-based aboveground carbon density (ACD) predictions with those obtained from field inventory techniques should be intensified in order to advance tropical forest carbon mapping. Here we present results from the application of a general ACD estimation model applied with small-footprint LiDAR data and field-based estimates of a 50-ha forest plot in Ecuador?s Yasuní National Park. Subplots used for calibration and validation of the general LiDAR equation were selected based on analysis of topographic position and spatial distribution of aboveground carbon stocks. The results showed that stratification of plot locations based on topography can improve the calibration and application of ACD estimation using airborne LiDAR (R2 = 0.94, RMSE = 5.81 Mg?C? ha?1, BIAS = 0.59). These results strongly suggest that a general LiDAR-based approach can be used for mapping aboveground carbon stocks in western lowland Amazonian forests.

Three-dimensional planar model estimation using multi-constraint knowledge based on k-means and RANSAC

Plane model extraction from three-dimensional point clouds is a necessary step in many different applications such as planar object reconstruction, indoor mapping and indoor localization. Different RANdom SAmple Consensus (RANSAC)-based methods have been proposed for this purpose in recent years. In this study, we propose a novel method-based on RANSAC called Multiplane Model Estimation, which can estimate multiple plane models simultaneously from a noisy point cloud using the knowledge extracted from a scene (or an object) in order to reconstruct it accurately. This method comprises two steps: first, it clusters the data into planar faces that preserve some constraints defined by knowledge related to the object (e.g., the angles between faces); and second, the models of the planes are estimated based on these data using a novel multi-constraint RANSAC. We performed experiments in the clustering and RANSAC stages, which showed that the proposed method performed better than state-of-the-art methods.

Estimation of productivity in Korean electric power plants:a semiparametric smooth coefficient model

This paper analyzes the impact of load factor, facility and generator types on the productivity of Korean electric power plants. In order to capture important differences in the effect of load policy on power output, we use a semiparametric smooth coefficient (SPSC) model that allows us to model heterogeneous performances across power plants and over time by allowing underlying technologies to be heterogeneous. The SPSC model accommodates both continuous and discrete covariates. Various specification tests are conducted to compare performance of the SPSC model. Using a unique generator level panel dataset spanning the period 1995-2006, we find that the impact of load factor, generator and facility types on power generation varies substantially in terms of magnitude and significance across different plant characteristics. The results have strong implication for generation policy in Korea as outlined in this study.