Further Results on a Modified EM Algorithm for Parameter Estimation in Linear Models with Time-Dependent Autoregressive and t-Distributed Errors

2018 ◽  
pp. 323-337 ◽  
Author(s):  
Boris Kargoll ◽  
Mohammad Omidalizarandi ◽  
Hamza Alkhatib ◽  
Wolf-Dieter Schuh
Keyword(s):  
Parameter Estimation ◽  
Em Algorithm ◽  
Linear Models ◽  
Time Dependent

scholarly journals Marginal quantile regression for longitudinal data analysis in the presence of time-dependent covariates

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
I-Chen Chen ◽  
Philip M. Westgate
Keyword(s):  
Parameter Estimation ◽  
Longitudinal Data ◽  
Quantile Regression ◽  
Mean Squared Error ◽  
Time Dependent ◽  
Regression Methods ◽  
Squared Error ◽  
Highly Correlated ◽  
Time Dependent Covariates ◽  
Independence Structure

AbstractWhen observations are correlated, modeling the within-subject correlation structure using quantile regression for longitudinal data can be difficult unless a working independence structure is utilized. Although this approach ensures consistent estimators of the regression coefficients, it may result in less efficient regression parameter estimation when data are highly correlated. Therefore, several marginal quantile regression methods have been proposed to improve parameter estimation. In a longitudinal study some of the covariates may change their values over time, and the topic of time-dependent covariate has not been explored in the marginal quantile literature. As a result, we propose an approach for marginal quantile regression in the presence of time-dependent covariates, which includes a strategy to select a working type of time-dependency. In this manuscript, we demonstrate that our proposed method has the potential to improve power relative to the independence estimating equations approach due to the reduction of mean squared error.

scholarly journals Efficient estimation of bounded gradient-drift diffusion models for affect on CPU and GPU

2021 ◽  
Author(s):  
Tim Loossens ◽  
Kristof Meers ◽  
Niels Vanhasbroeck ◽  
Nil Anarat ◽  
Stijn Verdonck ◽  
...  
Keyword(s):  
Parameter Estimation ◽  
Continuous Time ◽  
Graphics Processing Units ◽  
Linear Models ◽  
Likelihood Function ◽  
Efficient Estimation ◽  
Closed Form Expression ◽  
Central Processing ◽  
Research Fields ◽  
Non Linear

AbstractComputational modeling plays an important role in a gamut of research fields. In affect research, continuous-time stochastic models are becoming increasingly popular. Recently, a non-linear, continuous-time, stochastic model has been introduced for affect dynamics, called the Affective Ising Model (AIM). The drawback of non-linear models like the AIM is that they generally come with serious computational challenges for parameter estimation and related statistical analyses. The likelihood function of the AIM does not have a closed form expression. Consequently, simulation based or numerical methods have to be considered in order to evaluate the likelihood function. Additionally, the likelihood function can have multiple local minima. Consequently, a global optimization heuristic is required and such heuristics generally require a large number of likelihood function evaluations. In this paper, a Julia software package is introduced that is dedicated to fitting the AIM. The package includes an implementation of a numeric algorithm for fast computations of the likelihood function, which can be run both on graphics processing units (GPU) and central processing units (CPU). The numerical method introduced in this paper is compared to the more traditional Euler-Maruyama method for solving stochastic differential equations. Furthermore, the estimation software is tested by means of a recovery study and estimation times are reported for benchmarks that were run on several computing devices (two different GPUs and three different CPUs). According to these results, a single parameter estimation can be obtained in less than thirty seconds using a mainstream NVIDIA GPU.

scholarly journals Best linear unbiased estimation for varying probability with and without replacement sampling

2019 ◽  
Vol 7 (1) ◽  
pp. 78-91
Author(s):  
Stephen Haslett
Keyword(s):  
Parameter Estimation ◽  
Covariance Matrix ◽  
Linear Models ◽  
Unbiased Estimation ◽  
Error Covariance Matrix ◽  
Best Linear Unbiased Estimation ◽  
Error Covariance ◽  
Inclusion Probabilities ◽  
Best Linear Unbiased ◽  
Linear Unbiased Estimation

Abstract When sample survey data with complex design (stratification, clustering, unequal selection or inclusion probabilities, and weighting) are used for linear models, estimation of model parameters and their covariance matrices becomes complicated. Standard fitting techniques for sample surveys either model conditional on survey design variables, or use only design weights based on inclusion probabilities essentially assuming zero error covariance between all pairs of population elements. Design properties that link two units are not used. However, if population error structure is correlated, an unbiased estimate of the linear model error covariance matrix for the sample is needed for efficient parameter estimation. By making simultaneous use of sampling structure and design-unbiased estimates of the population error covariance matrix, the paper develops best linear unbiased estimation (BLUE) type extensions to standard design-based and joint design and model based estimation methods for linear models. The analysis covers both with and without replacement sample designs. It recognises that estimation for with replacement designs requires generalized inverses when any unit is selected more than once. This and the use of Hadamard products to link sampling and population error covariance matrix properties are central topics of the paper. Model-based linear model parameter estimation is also discussed.

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