The paper deals with an analysis of how to use certain measures of location in analysis of salaries. One of the traditional measures of location, the mean should offer typical value of variable, representing all its v...The paper deals with an analysis of how to use certain measures of location in analysis of salaries. One of the traditional measures of location, the mean should offer typical value of variable, representing all its values by the best way. Sometimes, the mean is located in the tail of the distribution and gives a very biased idea about the location of the distribution. In these cases, using different measures of location could be useful. Trimmed mean is described. The trimmed mean refers to a situation where a certain proportion of the largest and smallest observations are removed and the remaining observations are averaged. The construction of some measures of location is based on the analysis of outliers. Outliers are characterized. Then the possibilities of the detection of outliers are analyzed. Computing of one-step M-estimator and modified one-step M-estimator of location is described. A comparison of the trimmed means and M-estimators of location is presented. Finally, the paper focuses on the application of the trimmed mean and M-estimators of location in analysis of salaries. The analysis of salaries of employers of the big Slovak companies in second half of the year 2009 is realized. The data from the census are used in the analysis. The median, 20% trimmed mean and the characteristics, based on the one-step M-estimator of location and modified one step M-estimator, are calculated.展开更多
Semiparametric regression models and estimating covariance functions are very useful for longitudinal study. To heed the positive-definiteness constraint, we adopt the modified Cholesky decomposition approach to decom...Semiparametric regression models and estimating covariance functions are very useful for longitudinal study. To heed the positive-definiteness constraint, we adopt the modified Cholesky decomposition approach to decompose the covariance structure. Then the covariance structure is fitted by a semiparametric model by imposing parametric within-subject correlation while allowing the nonparametric variation function. We estimate regression functions by using the local linear technique and propose generalized estimating equations for the mean and correlation parameter. Kernel estimators are developed for the estimation of the nonparametric variation function. Asymptotic normality of the the resulting estimators is established. Finally, the simulation study and the real data analysis are used to illustrate the proposed approach.展开更多
文摘The paper deals with an analysis of how to use certain measures of location in analysis of salaries. One of the traditional measures of location, the mean should offer typical value of variable, representing all its values by the best way. Sometimes, the mean is located in the tail of the distribution and gives a very biased idea about the location of the distribution. In these cases, using different measures of location could be useful. Trimmed mean is described. The trimmed mean refers to a situation where a certain proportion of the largest and smallest observations are removed and the remaining observations are averaged. The construction of some measures of location is based on the analysis of outliers. Outliers are characterized. Then the possibilities of the detection of outliers are analyzed. Computing of one-step M-estimator and modified one-step M-estimator of location is described. A comparison of the trimmed means and M-estimators of location is presented. Finally, the paper focuses on the application of the trimmed mean and M-estimators of location in analysis of salaries. The analysis of salaries of employers of the big Slovak companies in second half of the year 2009 is realized. The data from the census are used in the analysis. The median, 20% trimmed mean and the characteristics, based on the one-step M-estimator of location and modified one step M-estimator, are calculated.
基金supported by National Natural Science Foundation of China (GrantNos.10931002,10911120386)
文摘Semiparametric regression models and estimating covariance functions are very useful for longitudinal study. To heed the positive-definiteness constraint, we adopt the modified Cholesky decomposition approach to decompose the covariance structure. Then the covariance structure is fitted by a semiparametric model by imposing parametric within-subject correlation while allowing the nonparametric variation function. We estimate regression functions by using the local linear technique and propose generalized estimating equations for the mean and correlation parameter. Kernel estimators are developed for the estimation of the nonparametric variation function. Asymptotic normality of the the resulting estimators is established. Finally, the simulation study and the real data analysis are used to illustrate the proposed approach.
