Comparisons among three estimation methods in linear models when observations are pairwise correlated

1998 ◽  
Vol 60 (3) ◽  
pp. 223-236 ◽  
Author(s):  
Yu-Sheng Hsu ◽  
Hong Mei
Keyword(s):  
Linear Models ◽  
Estimation Methods

Fuzzy C-Regression Models

2013 ◽  
Vol 278-280 ◽  
pp. 1323-1326
Author(s):  
Yan Hua Yu ◽  
Li Xia Song ◽  
Kun Lun Zhang
Keyword(s):  
Linear Regression ◽  
Least Squares ◽  
Linear Models ◽  
Least Squares Method ◽  
Least Square Method ◽  
Least Square ◽  
Estimation Methods ◽  
Statistical Regression ◽  
Fuzzy Linear Regression ◽  
Fuzzy Degree

Fuzzy linear regression has been extensively studied since its inception symbolized by the work of Tanaka et al. in 1982. As one of the main estimation methods, fuzzy least squares approach is appealing because it corresponds, to some extent, to the well known statistical regression analysis. In this article, a restricted least squares method is proposed to fit fuzzy linear models with crisp inputs and symmetric fuzzy output. The paper puts forward a kind of fuzzy linear regression model based on structured element, This model has precise input data and fuzzy output data, Gives the regression coefficient and the fuzzy degree function determination method by using the least square method, studies the imitation degree question between the observed value and the forecast value.

scholarly journals Autoregressive Models of the Random fields—A Survey

2020 ◽  
pp. 1-9
Keyword(s):  
Random Fields ◽  
Linear Models ◽  
Estimation Methods ◽  
Suitable Model ◽  
Main Mode ◽  
One Dimensional ◽  
Non Linear ◽  
The Status ◽  
Ar Models ◽  
Shed Light

Autoregressive (AR) random fields are widely use to describe changes in the status of real-physical objects and implemented for analyzing linear & non-linear models. AR models are Markov processes with a higher order dependence for one-dimensional time series. Actually, various estimation methods were used in order to evaluate the autoregression parameters. Although in many applications background knowledge can often shed light on the search for a suitable model, but other applications lack this knowledge and often require the type of trial errors to choose a model. This article presents a brief survey of the literatures related to the linear and non-linear autoregression models, including several extensions of the main mode models and the models developed. The use of autoregression to describe such system requires that they be of sufficiently high orders which leads to increase the computational costs.

Parameter Estimation of Linear Sensorimotor Synchronization Models: Phase Correction, Period Correction, and Ensemble Synchronization

2015 ◽  
Vol 3 (1-2) ◽  
pp. 52-87 ◽  
Author(s):  
Nori Jacoby ◽  
Naftali Tishby ◽  
Bruno H. Repp ◽  
Merav Ahissar ◽  
Peter E. Keller
Keyword(s):  
Experimental Data ◽  
Parameter Estimation ◽  
Linear Models ◽  
Estimation Error ◽  
Phase Correction ◽  
Sensorimotor Synchronization ◽  
Estimation Methods ◽  
Single Subject ◽  
Novel Method ◽  
Parameter Estimation Methods

Linear models have been used in several contexts to study the mechanisms that underpin sensorimotor synchronization. Given that their parameters are often linked to psychological processes such as phase correction and period correction, the fit of the parameters to experimental data is an important practical question. We present a unified method for parameter estimation of linear sensorimotor synchronization models that extends available techniques and enhances their usability. This method enables reliable and efficient analysis of experimental data for single subject and multi-person synchronization. In a previous paper (Jacoby et al., 2015), we showed how to significantly reduce the estimation error and eliminate the bias of parameter estimation methods by adding a simple and empirically justified constraint on the parameter space. By applying this constraint in conjunction with the tools of matrix algebra, we here develop a novel method for estimating the parameters of most linear models described in the literature. Through extensive simulations, we demonstrate that our method reliably and efficiently recovers the parameters of two influential linear models: Vorberg and Wing (1996), and Schulze et al. (2005), together with their multi-person generalization to ensemble synchronization. We discuss how our method can be applied to include the study of individual differences in sensorimotor synchronization ability, for example, in clinical populations and ensemble musicians.

Lower Bound on the Accuracy of Parameter Estimation Methods for Linear Sensorimotor Synchronization Models

2015 ◽  
Vol 3 (1-2) ◽  
pp. 32-51 ◽  
Author(s):  
Nori Jacoby ◽  
Peter E. Keller ◽  
Bruno H. Repp ◽  
Merav Ahissar ◽  
Naftali Tishby
Keyword(s):  
Parameter Estimation ◽  
Lower Bound ◽  
Computational Models ◽  
Linear Models ◽  
Estimation Error ◽  
Explanatory Power ◽  
Estimation Method ◽  
Sensorimotor Synchronization ◽  
Estimation Methods ◽  
Unbiased Estimation

The mechanisms that support sensorimotor synchronization — that is, the temporal coordination of movement with an external rhythm — are often investigated using linear computational models. The main method used for estimating the parameters of this type of model was established in the seminal work of Vorberg and Schulze (2002), and is based on fitting the model to the observed auto-covariance function of asynchronies between movements and pacing events. Vorberg and Schulze also identified the problem of parameter interdependence, namely, that different sets of parameters might yield almost identical fits, and therefore the estimation method cannot determine the parameters uniquely. This problem results in a large estimation error and bias, thereby limiting the explanatory power of existing linear models of sensorimotor synchronization. We present a mathematical analysis of the parameter interdependence problem. By applying the Cramér–Rao lower bound, a general lower bound limiting the accuracy of any parameter estimation procedure, we prove that the mathematical structure of the linear models used in the literature determines that this problem cannot be resolved by any unbiased estimation method without adopting further assumptions. We then show that adding a simple and empirically justified constraint on the parameter space — assuming a relationship between the variances of the noise terms in the model — resolves the problem. In a follow-up paper in this volume, we present a novel estimation technique that uses this constraint in conjunction with matrix algebra to reliably estimate the parameters of almost all linear models used in the literature.

scholarly journals Flood frequency analysis using mean daily flows vs. instantaneous peak flows

2021 ◽  
Author(s):  
Anne Bartens ◽  
Uwe Haberlandt
Keyword(s):  
Frequency Analysis ◽  
Linear Models ◽  
Flood Frequency ◽  
Flood Frequency Analysis ◽  
Estimation Methods ◽  
Entire Study ◽  
Flood Peak ◽  
Flood Dynamics ◽  
Event Based ◽  
Available Information

Abstract. In many cases flood frequency analysis needs to be carried out on mean daily flow (MDF) series without any available information on the instantaneous peak flow (IPF). We analyze the error of using MDFs instead of IPFs for flood quantile estimation on a German dataset and assess spatial patterns and factors that influence the deviation of MDF floods from their IPF counterparts. The main dependence could be found for catchment area but also gauge elevation appeared to have some influence. Based on the findings we propose simple linear models to correct both MDF flood peaks of individual flood events and overall MDF flood statistics. Key predictor in the models is the event-based ratio of flood peak and flood volume obtained directly from the daily flow records. This correction approach requires a minimum of data input, is easily applied, valid for the entire study area and successfully estimates IPF peaks and flood statistics. The models perform particularly well in smaller catchments, where other IPF estimation methods fall short. Still, the limit of the approach is reached for catchment sizes below 100 km2, where the hydrograph information from the daily series is no longer capable of approximating instantaneous flood dynamics.

scholarly journals Bayes and Empirical Bayes Estimation for the Chain Ladder Model

1990 ◽  
Vol 20 (2) ◽  
pp. 217-243 ◽  
Author(s):  
R.J. Verrall
Keyword(s):  
Empirical Bayes ◽  
Linear Models ◽  
Bayes Estimation ◽  
Estimation Methods ◽  
Empirical Bayes Estimation ◽  
Collateral Information ◽  
Classical Formulation ◽  
The Subject ◽  
Modelling Assumptions ◽  
Chain Ladder

AbstractThe subject of predicting outstanding claims on a porfolio of general insurance policies is approached via the theory of hierarchical Bayesian linear models. This is particularly appropriate since the chain ladder technique can be expressed in the form of a linear model. The statistical methods which are applied allow the practitioner to use different modelling assumptions from those implied by a classical formulation, and to arrive at forecasts which have a greater degree of inherent stability. The results can also be used for other linear models. By using a statistical structure, a sound approach to the chain ladder technique can be derived. The Bayesian results allow the input of collateral information in a formal manner. Empirical Bayes results are derived which can be interpreted as credibility estimates. The statistical assumptions which are made in the modelling procedure are clearly set out and can be tested by the practitioner. The results based on the statistical theory form one part of the reserving procedure, and should be followed by expert interpretation and analysis. An illustration of the use of Bayesian and empirical Bayes estimation methods is given.

scholarly journals Using Social Network Information for Survey Estimation

2018 ◽  
Vol 34 (1) ◽  
pp. 181-209 ◽  
Author(s):  
Thomas Suesse ◽  
Ray Chambers
Keyword(s):  
Linear Models ◽  
Mean Squared Error ◽  
Contextual Information ◽  
Auxiliary Information ◽  
Adaptive Strategy ◽  
Estimation Methods ◽  
Population Total ◽  
Network Information ◽  
Model Based ◽  
Best Linear Unbiased

Abstract Model-based and model-assisted methods of survey estimation aim to improve the precision of estimators of the population total or mean relative to methods based on the nonparametric Horvitz-Thompson estimator. These methods often use a linear regression model defined in terms of auxiliary variables whose values are assumed known for all population units. Information on networks represents another form of auxiliary information that might increase the precision of these estimators, particularly if it is reasonable to assume that networked population units have similar values of the survey variable. Linear models that use networks as a source of auxiliary information include autocorrelation, disturbance, and contextual models. In this article we focus on social networks, and investigate how much of the population structure of the network needs to be known for estimation methods based on these models to be useful. In particular, we use simulation to compare the performance of the best linear unbiased predictor under a model that ignores the network with model-based estimators that incorporate network information. Our results show that incorporating network information via a contextual model seems to be the most appropriate approach. We also show that one does not need to know the full population network, but that knowledge of the partial network linking the sampled population units to the non-sampled population units is necessary. Finally, we also provide an estimator for the mean-squared error to make an informed decision about using the contextual information, as well as the results showing that this adaptive strategy leads to higher precision.

THE ACCURATE ESTIMATION OF METEOROLOGICAL PROFILES EMPLOYING ANNs

2002 ◽  
Vol 12 (03n04) ◽  
pp. 319-337 ◽  
Author(s):  
TATIANA TAMBOURATZIS ◽  
MYRSINI GAZELA
Keyword(s):  
Linear Models ◽  
Target Location ◽  
Weather Forecasting ◽  
Energy System ◽  
Estimation Methods ◽  
Accurate Estimation ◽  
Neural Network Approach ◽  
Reference Location ◽  
Energy Applications ◽  
Artificial Neural

The lack of meteorological measurements at a location of interest (target location) constitutes a problem that is crucial for the purposes of both weather forecasting and energy system design/validation. This paper constitutes a pilot study for the accurate estimation of meteorological values at a target location employing the meteorological measurements collected at a nearby (reference) location. Artificial neural networks are investigated and compared with traditional estimation methods such as linear models of first and higher orders and the non-linear model. The significance of the improvement obtained via the estimation — and especially the artificial neural network approach — over simply considering the measurements at the reference location is demonstrated in a number of energy applications.

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