Estimating Nonlinear Dynamic Models Using Least Absolute Error Estimation

Least Absolute Relative Error Estimation.

Multiplicative regression model or accelerated failure time model, which becomes linear regression model after logarithmic transformation, is useful in analyzing data with positive responses, such as stock prices or life times, that are particularly common in economic/financial or biomedical studies. Least squares or least absolute deviation are among the most widely used criterions in statisti...

Estimation for Nonlinear Time Series Models Using Estimating Equations

Godambe's (1985) theorem on optimal estimating eq'uation for stochasti; processes is applied to nonlinear time series estimation problems. Examples are considered from the usual classes of nonlinear time series models. Recursive estimation procedure based on optimal estimating equation is provided. It is also shown that prefiltered estimates can be used to obtain the optimal estimate from a non...

Least Absolute Value vs. Least Squares Estimation and Inference Procedures in Regression Models with Asymmetric Error Distributions

Regression Model Estimation Using Least Absolute Deviations , Least Squares Deviations and Minimax Absolute Deviations Criteria

Regression models and their statistical analyses is the most important tool used by scientists in data analyses especially for modeling the relationship among random variables and making predictions with higher accuracy. A fundamental problem in the theory of errors, which has drawn attention of leading mathematicians and scientists since past few centuries, was that of fitting functions. For t...

Least Absolute Deviation Estimation for All-Pass Time Series Models

An autoregressive-moving average model in which all of the roots of the autoregressive polynomial are reciprocals of roots of the moving average polynomial and vice versa is called an all-pass time series model. All-pass models generate uncorrelated (white noise) time series, but these series are not independent in the non-Gaussian case. An approximation to the likelihood of the model in the ca...