W. NIEMIRO (Warszawa) ESTIMATION OF NUISANCE PARAMETERS FOR INFERENCE BASED ON LEAST ABSOLUTE DEVIATIONS

Linear Hypothesis Testing in Censored Regression Models

For testing a linear hypothesis in a censored regression (or censored “Tobit”) model, three test criteria and four test statistics based on least absolute deviations estimates of parameters are proposed and their limiting chi-square distributions are established. Some consistent estimates of nuisance parameters are obtained for use in computing the test statistics. A simulation study for small ...

Weighted Least Absolute Deviations Estimation for Arma Models with Infinite Variance

For autoregressive and moving-average (ARMA) models with infinite variance innovations, quasi-likelihood based estimators (such as Whittle’s estimators ) suffer from complex asymptotic distributions depending on unknown tail indices. This makes the statistical inference for such models difficult. In contrast, the least absolute deviations estimators (LADE) are more appealing in dealing with hea...

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

Inference for Tail Index of GARCH(1,1) Model and AR(1) Model with ARCH(1) Errors

For a GARCH(1,1) sequence or an AR(1) model with ARCH(1) errors, it is known that the observations have a heavy tail and the tail index is determined by an estimating equation. Therefore, one can estimate the tail index by solving the estimating equation with unknown parameters replaced by quasi maximum likelihood estimation (QMLE), and profile empirical likelihood method can be employed to eff...

Analysis of least absolute deviation

The least absolute deviation or L1 method is a widely known alternative to the classical least squares or L2 method for statistical analysis of linear regression models. Instead of minimizing the sum of squared errors, it minimizes the sum of absolute values of errors. Despite its long history and many ground-breaking works (cf. Portnoy and Koenker (1997) and references therein), the former has...