The paper studies a new class of robust regression estimators based on the two-step least weighted squares (2S-LWS) estimator which employs data-adaptive weights determined from the empirical distribution or quantile functions of regression residuals obtained from an initial robust fit. Just like many existing two-step robust methods, the proposed 2S-LWS estimator preserves robust properties of the initial robust estimate. However, contrary to the existing methods, the first-order asymptotic behavior of 2S-LWS is fully independent of the initial estimate under mild conditions. We propose data-adaptive weighting schemes that perform well both in the cross-section and time-series data and prove the asymptotic normality and efficiency of the resulting procedure. A simulation study documents these theoretical properties in finite samples.
{"title":"Efficient robust estimation of time-series regression models","authors":"P. Čížek","doi":"10.2139/ssrn.1068624","DOIUrl":"https://doi.org/10.2139/ssrn.1068624","url":null,"abstract":"The paper studies a new class of robust regression estimators based on the two-step least weighted squares (2S-LWS) estimator which employs data-adaptive weights determined from the empirical distribution or quantile functions of regression residuals obtained from an initial robust fit. Just like many existing two-step robust methods, the proposed 2S-LWS estimator preserves robust properties of the initial robust estimate. However, contrary to the existing methods, the first-order asymptotic behavior of 2S-LWS is fully independent of the initial estimate under mild conditions. We propose data-adaptive weighting schemes that perform well both in the cross-section and time-series data and prove the asymptotic normality and efficiency of the resulting procedure. A simulation study documents these theoretical properties in finite samples.","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"7 1","pages":"267-279"},"PeriodicalIF":0.7,"publicationDate":"2007-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76390261","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"70th birthday of Vratislav Horálek","authors":"V. Beneš, I. Saxl","doi":"10.21136/am.1996.134323","DOIUrl":"https://doi.org/10.21136/am.1996.134323","url":null,"abstract":"","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"51 1 1","pages":"233-234"},"PeriodicalIF":0.7,"publicationDate":"1996-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90658065","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Summary. The preconditioned conjugate gradient method for solving the system of linear algebraic equations with a positive definite matrix is investigated . The initial approxima tion for conjugate gradient is constructed as a result o f a matrix iteration method after 77i steps . The behaviour o f the error vector for such a combined method is studied and special numerical tests and conclusions are made.
{"title":"Combining the preconditioned conjugate gradient method and a matrix iterative method","authors":"J. Zítko","doi":"10.21136/am.1996.134311","DOIUrl":"https://doi.org/10.21136/am.1996.134311","url":null,"abstract":"Summary. The preconditioned conjugate gradient method for solving the system of linear algebraic equations with a positive definite matrix is investigated . The initial approxima tion for conjugate gradient is constructed as a result o f a matrix iteration method after 77i steps . The behaviour o f the error vector for such a combined method is studied and special numerical tests and conclusions are made.","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"33 1","pages":"19-39"},"PeriodicalIF":0.7,"publicationDate":"1996-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73886114","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Hard clamped and hard simply supported elastic plate is considered. The mixed finite element analysis combined with some interpolation, proposed by Brezzi, Fortin and Stenberg, is extended to the case of variable thickness and anisotropic material.
{"title":"Reissner-Mindlin model for plates of variable thickness. Solution by mixed-interpolated elements","authors":"I. Hlavácek","doi":"10.21136/am.1996.134313","DOIUrl":"https://doi.org/10.21136/am.1996.134313","url":null,"abstract":"Hard clamped and hard simply supported elastic plate is considered. The mixed finite element analysis combined with some interpolation, proposed by Brezzi, Fortin and Stenberg, is extended to the case of variable thickness and anisotropic material.","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"123 1","pages":"57-78"},"PeriodicalIF":0.7,"publicationDate":"1996-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83441022","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper is devoted to the study of a class of hemivariational inequalities which was introduced by P. D. Panagiotopoulos [31] and later by Z. Naniewicz [22]. These variational formulations are natural nonconvex generalizations [15–17], [22–33] of the well-known variational inequalities. Several existence results are proved in [15]. In this paper, we are concerned with some related results and several applications.
{"title":"Noncoercive hemivariational inequality and its applications in nonconvex unilateral mechanics","authors":"D. Goeleven","doi":"10.21136/AM.1996.134321","DOIUrl":"https://doi.org/10.21136/AM.1996.134321","url":null,"abstract":"This paper is devoted to the study of a class of hemivariational inequalities which was introduced by P. D. Panagiotopoulos [31] and later by Z. Naniewicz [22]. These variational formulations are natural nonconvex generalizations [15–17], [22–33] of the well-known variational inequalities. Several existence results are proved in [15]. In this paper, we are concerned with some related results and several applications.","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"01 1","pages":"203-229"},"PeriodicalIF":0.7,"publicationDate":"1996-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88295563","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Till now the finite element analysis for semiregular finite elements has been restricted to interpolation theorems (see [2], [3], [5] and references there). In this paper a complete finite element analysis is presented briefly.
{"title":"Finite element variational crimes in the case of semiregular elements","authors":"A. Ženíšek","doi":"10.21136/am.1996.134332","DOIUrl":"https://doi.org/10.21136/am.1996.134332","url":null,"abstract":"Till now the finite element analysis for semiregular finite elements has been restricted to interpolation theorems (see [2], [3], [5] and references there). In this paper a complete finite element analysis is presented briefly.","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"44 1","pages":"367-398"},"PeriodicalIF":0.7,"publicationDate":"1996-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90126773","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In actuarial practice the credibility models must face the problem of outliers and missing observations. If using the $M$-estimation principle from robust statistics in combination with Kalman filtering one obtains the solution of this problem that is acceptable in the numerical framework of the practical actuarial credibility. The credibility models are classified as static and dynamic in this paper and the shrinkage is used for the final ratemaking.
{"title":"Dynamic credibility with outliers and missing observations","authors":"T. Cipra","doi":"10.21136/AM.1996.134318","DOIUrl":"https://doi.org/10.21136/AM.1996.134318","url":null,"abstract":"In actuarial practice the credibility models must face the problem of outliers and missing observations. If using the $M$-estimation principle from robust statistics in combination with Kalman filtering one obtains the solution of this problem that is acceptable in the numerical framework of the practical actuarial credibility. The credibility models are classified as static and dynamic in this paper and the shrinkage is used for the final ratemaking.","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"12 1","pages":"149-159"},"PeriodicalIF":0.7,"publicationDate":"1996-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81783660","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Seasonal time series with missing observations","authors":"T. Ratinger","doi":"10.21136/AM.1996.134312","DOIUrl":"https://doi.org/10.21136/AM.1996.134312","url":null,"abstract":"","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"47 1","pages":"41-55"},"PeriodicalIF":0.7,"publicationDate":"1996-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80603772","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Linear model with inaccurate variance components","authors":"L. Kubácek","doi":"10.21136/am.1996.134336","DOIUrl":"https://doi.org/10.21136/am.1996.134336","url":null,"abstract":"","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"46 1","pages":"433-445"},"PeriodicalIF":0.7,"publicationDate":"1996-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86518118","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We find conditions, in multi-objective convex programming with nonsmooth functions, when the sets of efficient (Pareto) and properly efficient solutions coincide. This occurs, in particular, when all functions have locally flat surfaces (LFS). In the absence of the LFS property the two sets are generally different and the characterizations of efficient solutions assume an asymptotic form for problems with three or more variables. The results are applied to a problem in highway construction, where the quantity of dirt to be removed and the uniform smoothness of the shape of a terrain are optimized simultaneously.
{"title":"LFS functions in multi-objective programming","authors":"L. Neralić, S. Zlobec","doi":"10.21136/AM.1996.134331","DOIUrl":"https://doi.org/10.21136/AM.1996.134331","url":null,"abstract":"We find conditions, in multi-objective convex programming with nonsmooth functions, when the sets of efficient (Pareto) and properly efficient solutions coincide. This occurs, in particular, when all functions have locally flat surfaces (LFS). In the absence of the LFS property the two sets are generally different and the characterizations of efficient solutions assume an asymptotic form for problems with three or more variables. The results are applied to a problem in highway construction, where the quantity of dirt to be removed and the uniform smoothness of the shape of a terrain are optimized simultaneously.","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"77 1","pages":"347-366"},"PeriodicalIF":0.7,"publicationDate":"1996-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81178948","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：