In robust regression we often have to decide how many are the unusualobservations, which should be removed from the sample in order to obtain better fitting for the restof the observations. Generally, we use the basic...In robust regression we often have to decide how many are the unusualobservations, which should be removed from the sample in order to obtain better fitting for the restof the observations. Generally, we use the basic principle of LTS, which is to fit the majority ofthe data, identifying as outliers those points that cause the biggest damage to the robust fit.However, in the LTS regression method the choice of default values for high break down-point affectsseriously the efficiency of the estimator. In the proposed approach we introduce penalty cost fordiscarding an outlier, consequently, the best fit for the majority of the data is obtained bydiscarding only catastrophic observations. This penalty cost is based on robust design weights andhigh break down-point residual scale taken from the LTS estimator. The robust estimation is obtainedby solving a convex quadratic mixed integer programming problem, where in the objective functionthe sum of the squared residuals and penalties for discarding observations is minimized. Theproposed mathematical programming formula is suitable for small-sample data. Moreover, we conduct asimulation study to compare other robust estimators with our approach in terms of their efficiencyand robustness.展开更多
We present two recent methods,called UTAGMS and GRIP,from the viewpoint of robust ranking of multi-criteria alternatives.In these methods,the preference information provided by a single or multiple Decision Makers(DMs...We present two recent methods,called UTAGMS and GRIP,from the viewpoint of robust ranking of multi-criteria alternatives.In these methods,the preference information provided by a single or multiple Decision Makers(DMs)is composed of holistic judgements of some selected alternatives,called reference alternatives.The judgements express pairwise comparisons of some reference alternatives(in UTAGMS),and comparisons of selected pairs of reference alternatives from the viewpoint of intensity of preference(in GRIP).Ordinal regression is used to find additive value functions compatible with this preference information.The whole set of compatible value functions is then used in Linear Programming(LP)to calculate a necessary and possible weak preference relations in the set of all alternatives,and in the set of all pairs of alternatives.While the necessary relation is true for all compatible value functions,the possible relation is true for at least one compatible value function.The necessary relation is a partial preorder and the possible relation is a complete and negatively transitive relation.The necessary relations show consequences of the given preference information which are robust because "always true".We illustrate this methodology with an example.展开更多
We propose a subsampling method for robust estimation of regression models which is built on classical methods such as the least squares method. It makes use of the non-robust nature of the underlying classical method...We propose a subsampling method for robust estimation of regression models which is built on classical methods such as the least squares method. It makes use of the non-robust nature of the underlying classical method to find a good sample from regression data contaminated with outliers, and then applies the classical method to the good sample to produce robust estimates of the regression model parameters. The subsampling method is a computational method rooted in the bootstrap methodology which trades analytical treatment for intensive computation;it finds the good sample through repeated fitting of the regression model to many random subsamples of the contaminated data instead of through an analytical treatment of the outliers. The subsampling method can be applied to all regression models for which non-robust classical methods are available. In the present paper, we focus on the basic formulation and robustness property of the subsampling method that are valid for all regression models. We also discuss variations of the method and apply it to three examples involving three different regression models.展开更多
Logistic regression is the most important tool for data analysis in various fields. The classical approach for estimating parameters is the maximum likelihood estimation, a disadvantage of this method is high sensitiv...Logistic regression is the most important tool for data analysis in various fields. The classical approach for estimating parameters is the maximum likelihood estimation, a disadvantage of this method is high sensitivity to outlying observations. Robust estimators for logistic regression are alternative techniques due to their robustness. This paper presents a new class of robust techniques for logistic regression. They are weighted maximum likelihood estimators which are considered as Mallows-type estimator. Moreover, we compare the performance of these techniques with classical maximum likelihood and some existing robust estimators. The results are illustrated depending on a simulation study and real datasets.?The new estimators showed the best performance relative to other estimators.展开更多
Portfolio theory is used to measure the expected return and risk on the basis of the return ratio, but in fact there is always excessively high or low return ratio caused by some short-term fundamental good or bad new...Portfolio theory is used to measure the expected return and risk on the basis of the return ratio, but in fact there is always excessively high or low return ratio caused by some short-term fundamental good or bad news in the history data of return ratio. We introduce the robust statistic idea into the portfolio theory in this paper, thus reduce outliers’ influence on portfolio decision in the history data of return ratios, and bring back the portfolio on its long-term investment value track. We focused on the robust estimate method and apply them to solution processing in the portfolio model and obtained good results.展开更多
Due to the direct statistical interpretation,censored linear regression offers a valuable complement to the Cox proportional hazards regression in survival analysis.We propose a rank-based high-dimensional inference f...Due to the direct statistical interpretation,censored linear regression offers a valuable complement to the Cox proportional hazards regression in survival analysis.We propose a rank-based high-dimensional inference for censored linear regression without imposing any moment condition on the model error.We develop a theory of the high-dimensional U-statistic,circumvent challenges stemming from the non-smoothness of the loss function,and establish the convergence rate of the regularized estimator and the asymptotic normality of the resulting de-biased estimator as well as the consistency of the asymptotic variance estimation.As censoring can be viewed as a way of trimming,it strengthens the robustness of the rank-based high-dimensional inference,particularly for the heavy-tailed model error or the outlier in the presence of the response.We evaluate the finite-sample performance of the proposed method via extensive simulation studies and demonstrate its utility by applying it to a subcohort study from The Cancer Genome Atlas(TCGA).展开更多
文摘In robust regression we often have to decide how many are the unusualobservations, which should be removed from the sample in order to obtain better fitting for the restof the observations. Generally, we use the basic principle of LTS, which is to fit the majority ofthe data, identifying as outliers those points that cause the biggest damage to the robust fit.However, in the LTS regression method the choice of default values for high break down-point affectsseriously the efficiency of the estimator. In the proposed approach we introduce penalty cost fordiscarding an outlier, consequently, the best fit for the majority of the data is obtained bydiscarding only catastrophic observations. This penalty cost is based on robust design weights andhigh break down-point residual scale taken from the LTS estimator. The robust estimation is obtainedby solving a convex quadratic mixed integer programming problem, where in the objective functionthe sum of the squared residuals and penalties for discarding observations is minimized. Theproposed mathematical programming formula is suitable for small-sample data. Moreover, we conduct asimulation study to compare other robust estimators with our approach in terms of their efficiencyand robustness.
文摘We present two recent methods,called UTAGMS and GRIP,from the viewpoint of robust ranking of multi-criteria alternatives.In these methods,the preference information provided by a single or multiple Decision Makers(DMs)is composed of holistic judgements of some selected alternatives,called reference alternatives.The judgements express pairwise comparisons of some reference alternatives(in UTAGMS),and comparisons of selected pairs of reference alternatives from the viewpoint of intensity of preference(in GRIP).Ordinal regression is used to find additive value functions compatible with this preference information.The whole set of compatible value functions is then used in Linear Programming(LP)to calculate a necessary and possible weak preference relations in the set of all alternatives,and in the set of all pairs of alternatives.While the necessary relation is true for all compatible value functions,the possible relation is true for at least one compatible value function.The necessary relation is a partial preorder and the possible relation is a complete and negatively transitive relation.The necessary relations show consequences of the given preference information which are robust because "always true".We illustrate this methodology with an example.
文摘We propose a subsampling method for robust estimation of regression models which is built on classical methods such as the least squares method. It makes use of the non-robust nature of the underlying classical method to find a good sample from regression data contaminated with outliers, and then applies the classical method to the good sample to produce robust estimates of the regression model parameters. The subsampling method is a computational method rooted in the bootstrap methodology which trades analytical treatment for intensive computation;it finds the good sample through repeated fitting of the regression model to many random subsamples of the contaminated data instead of through an analytical treatment of the outliers. The subsampling method can be applied to all regression models for which non-robust classical methods are available. In the present paper, we focus on the basic formulation and robustness property of the subsampling method that are valid for all regression models. We also discuss variations of the method and apply it to three examples involving three different regression models.
文摘Logistic regression is the most important tool for data analysis in various fields. The classical approach for estimating parameters is the maximum likelihood estimation, a disadvantage of this method is high sensitivity to outlying observations. Robust estimators for logistic regression are alternative techniques due to their robustness. This paper presents a new class of robust techniques for logistic regression. They are weighted maximum likelihood estimators which are considered as Mallows-type estimator. Moreover, we compare the performance of these techniques with classical maximum likelihood and some existing robust estimators. The results are illustrated depending on a simulation study and real datasets.?The new estimators showed the best performance relative to other estimators.
文摘Portfolio theory is used to measure the expected return and risk on the basis of the return ratio, but in fact there is always excessively high or low return ratio caused by some short-term fundamental good or bad news in the history data of return ratio. We introduce the robust statistic idea into the portfolio theory in this paper, thus reduce outliers’ influence on portfolio decision in the history data of return ratios, and bring back the portfolio on its long-term investment value track. We focused on the robust estimate method and apply them to solution processing in the portfolio model and obtained good results.
基金supported by National Natural Science Foundation of China(Grant No.12071483)。
文摘Due to the direct statistical interpretation,censored linear regression offers a valuable complement to the Cox proportional hazards regression in survival analysis.We propose a rank-based high-dimensional inference for censored linear regression without imposing any moment condition on the model error.We develop a theory of the high-dimensional U-statistic,circumvent challenges stemming from the non-smoothness of the loss function,and establish the convergence rate of the regularized estimator and the asymptotic normality of the resulting de-biased estimator as well as the consistency of the asymptotic variance estimation.As censoring can be viewed as a way of trimming,it strengthens the robustness of the rank-based high-dimensional inference,particularly for the heavy-tailed model error or the outlier in the presence of the response.We evaluate the finite-sample performance of the proposed method via extensive simulation studies and demonstrate its utility by applying it to a subcohort study from The Cancer Genome Atlas(TCGA).
