Robust linear regression is one of the most popular problems in the robust statistics community. The parameters of this method are often estimated via least trimmed squares, which minimizes the sum of the k smallest squared residuals. So, the estimation method in contrast to the common least squares estimation method is very computationally expensive. The main idea of this paper is to propose a new estimation method in partial linear models based on minimizing the sum of the k smallest squared residuals which determines the set of outlier point and provides robust estimators. In this regard, first, difference based method in estimation parameters of partial linear models is introduced. Then the method of obtaining robust difference based estimators in partial linear models is introduced which is based on solving an optimization problem minimizing the sum of the k smallest squared residuals. This method can identify outliers. The simulated example and applied numerical example with real data found the proposed robust difference based estimators in the paper produce highly accurate results in compare to the common difference based estimators in partial linear models.

In this paper a method has been given to detect the shocks in structural time series using Kalman filter algorithm. As the Kalman filter algorithm is used for state space forms which include ARMA models as an especial case, the suggested method can be used for more general time series than linear models. Five shocks; additive outlier, level change, seasonal change, periodic change and slope change have been reviewed with this method. The performance of suggested method has been shown via a simulation study. The marriage data set from England has been considered as a real data set to study.

The presence of outliers in data set may affect structure of analysis of variance test so that test results led to wrong acceptance or rejection of null hypothesis. In this paper the method of robust permutation distribution of F statistic based on trimmed mean is proposed. This method by permutation distribution of a function of trimmed mean, reduces the sensitivity to classical assumptions such as normality and presence of outlier and it guarantees the reliability of result. The proposed method is compared with robust analysis of variance based of forward search approach. The proposed method, unlike the forward search-based approach is free of restricted parametric assumptions and computationally spend less time. Numerically assessment results on type I error and power of test, demonstrate good performance of this robust method in comparison with competitor method.

The study of regression diagnostic, including identification of the influential observations and outliers, is of particular importance. The sensitivity of least squares estimators to the outliers and influential observations lead to extending the regression diagnostic in order to provide criteria to assess the anomalous observations. Detecting influential observations and outliers in the presence of collinearity is a complicated task, in the sense that collinearity may cover some of the unusual data. One of the considerable methods to identify outliers is the mean shift outliers method. In this article, we extend the mean shift outliers method to the ridge estimates under linear stochastic restrictions, which is used to reduce the effect of collinearity, and to provide the test statistic to identify the outliers in these estimators. Finally, we show the ability of our proposed method using a practical example of real data.

‎In many fields such as econometrics‎, ‎psychology‎, ‎social sciences‎, ‎medical sciences‎, ‎engineering‎, ‎etc.‎, ‎we face with multicollinearity among the explanatory variables and the existence of outliers in data‎. ‎In such situations‎, ‎the ordinary least-squares estimator leads to an inaccurate estimate‎. ‎The robust methods are used to handle the outliers‎. ‎Also‎, ‎to overcome multicollinearity ridge estimators are suggested‎. ‎On the other hand‎, ‎when the error terms are heteroscedastic or correlated‎, ‎the generalized least squares method is used‎. ‎In this paper‎, ‎a fast algorithm for computation of the feasible generalized least trimmed squares ridge estimator in a semiparametric regression model is proposed and then‎, ‎the performance of the proposed estimators is examined through a Monte Carlo simulation study and a real data set.

This paper discusses stochastic comparisons of the parallel and series systems comprising multiple-outlier scale components. Under uncertain conditions on the baseline reversed hazard rate, hazard rate functions and scale parameters, the likelihood ratio, dispersive and mean residual life orders between parallel and series systems are established. We then apply the results for two exceptional cases of the multiple-outlier scale model: gamma and Pareto multiple-outlier components to illustrate the found results.

This paper discusses the hazard rate order of the fail-safe systems arising from two sets of independent multiple-outlier scale distributed components. Under certain conditions on scale parameters in the scale model and the submajorization order between the sample size vectors, the hazard rate ordering between the corresponding fail-safe systems from multiple-outlier scale random variables is established. Under certain conditions on the Archimedean copula and scale parameters, we also discuss the usual stochastic order of these systems with dependent components.

Paying attention to the copula function in order to model the structure of data dependence has become very common in recent decades. Three methods of estimation, moment method, mixture method, and copula moment, are considered to estimate the dependence parameter of copula function in the presence of outlier data. Although the moment method is an old method, sometimes this method leads to inaccurate estimation. Thus, two other moment-based methods are intended to improve that old method. The simulation study results showed that when we use copula moment and mixture moment for estimating the dependence parameter of copula function in the presence of outlier data, the obtained MSEs are smaller. Also, the copula moment method is the best estimate based on MSE. Finally, the obtained numerical results are used in a practical example.