Confidence bands in a Normal Q-Q Plot allow us to detect non-normality of a data set rigorously, and in such a way that the conclusion does not depend on the subjectivity of the observer of the graph. In the construct...Confidence bands in a Normal Q-Q Plot allow us to detect non-normality of a data set rigorously, and in such a way that the conclusion does not depend on the subjectivity of the observer of the graph. In the construction of the graph, it is usual to fit a straight line to the plotted points, which serves both to check the hypothesis of normality (linear configuration of the plotted points) and to produce estimates of the parameters of the distribution. We can opt for dif-ferent types of lines. In this paper, we study the influence of five types of fitted straight lines in a Normal Q-Q Plot used for construction the confidence bands based on the exact distribution of the order statistics.展开更多
In this paper, we establish asymptotically optimal simultaneous confidence bands for the copula function based on the local linear kernel estimator proposed by Chen and Huang [1]. For this, we prove under smoothness c...In this paper, we establish asymptotically optimal simultaneous confidence bands for the copula function based on the local linear kernel estimator proposed by Chen and Huang [1]. For this, we prove under smoothness conditions on the derivatives of the copula a uniform in bandwidth law of the iterated logarithm for the maximal deviation of this estimator from its expectation. We also show that the bias term converges uniformly to zero with a precise rate. The performance of these bands is illustrated by a simulation study. An application based on pseudo-panel data is also provided for modeling the dependence structure of Senegalese households’ expense data in 2001 and 2006.展开更多
We define a class of confidence bands for distribution functions,named simple confidence bands.The class of bands includes the common step bands and continuous bands,some of which may perform better than the smoothed ...We define a class of confidence bands for distribution functions,named simple confidence bands.The class of bands includes the common step bands and continuous bands,some of which may perform better than the smoothed bands not belonging to the class,e.g.,the kernel smoothed bands.It is shown that under some mild assumptions,the simple bands with exact coverage for continuous distribution functions are all step bands.The unbiasedness problem of the step bands is also investigated.It is proved that most of two-sided step bands are biased and one-sided step bands are unbiased.展开更多
In this paper an asymptotic distribution is obtained for the maximaldeviation between the kernel quantile density estimator and the quantile density when the data aresubject to random left truncation and right censors...In this paper an asymptotic distribution is obtained for the maximaldeviation between the kernel quantile density estimator and the quantile density when the data aresubject to random left truncation and right censorship. Based on this result we propose a fullysequential procedure for constructing a fixed-width confidence band for the quantile density on afinite interval and show that the procedure has the desired coverage probability asymptotically asthe width of the band approaches zero.展开更多
文摘Confidence bands in a Normal Q-Q Plot allow us to detect non-normality of a data set rigorously, and in such a way that the conclusion does not depend on the subjectivity of the observer of the graph. In the construction of the graph, it is usual to fit a straight line to the plotted points, which serves both to check the hypothesis of normality (linear configuration of the plotted points) and to produce estimates of the parameters of the distribution. We can opt for dif-ferent types of lines. In this paper, we study the influence of five types of fitted straight lines in a Normal Q-Q Plot used for construction the confidence bands based on the exact distribution of the order statistics.
文摘In this paper, we establish asymptotically optimal simultaneous confidence bands for the copula function based on the local linear kernel estimator proposed by Chen and Huang [1]. For this, we prove under smoothness conditions on the derivatives of the copula a uniform in bandwidth law of the iterated logarithm for the maximal deviation of this estimator from its expectation. We also show that the bias term converges uniformly to zero with a precise rate. The performance of these bands is illustrated by a simulation study. An application based on pseudo-panel data is also provided for modeling the dependence structure of Senegalese households’ expense data in 2001 and 2006.
基金supported by National Science Foundation for Post-doctoral Scientists of China(Grant No.20090450603)National Natural Science Foundation of China(Grant No.10771015)
文摘We define a class of confidence bands for distribution functions,named simple confidence bands.The class of bands includes the common step bands and continuous bands,some of which may perform better than the smoothed bands not belonging to the class,e.g.,the kernel smoothed bands.It is shown that under some mild assumptions,the simple bands with exact coverage for continuous distribution functions are all step bands.The unbiasedness problem of the step bands is also investigated.It is proved that most of two-sided step bands are biased and one-sided step bands are unbiased.
基金Supported by the National Natural Science Foundation of China (No.10471140)
文摘In this paper an asymptotic distribution is obtained for the maximaldeviation between the kernel quantile density estimator and the quantile density when the data aresubject to random left truncation and right censorship. Based on this result we propose a fullysequential procedure for constructing a fixed-width confidence band for the quantile density on afinite interval and show that the procedure has the desired coverage probability asymptotically asthe width of the band approaches zero.
