When dealing with a regular (fixed-support) one-parameter distribution, the corresponding maximum-likelihood estimator (MLE) is, to a good approximation, normally distributed. But, when the support boundaries are func...When dealing with a regular (fixed-support) one-parameter distribution, the corresponding maximum-likelihood estimator (MLE) is, to a good approximation, normally distributed. But, when the support boundaries are functions of the parameter, finding good approximation for the sampling distribution of MLE (needed to construct an accurate confidence interval for the parameter’s true value) may get very challenging. We demonstrate the nature of this problem, and show how to deal with it, by a detailed study of a specific situation. We also indicate several possible ways to bypass MLE by proposing alternate estimators;these, having relatively simple sampling distributions, then make constructing a confidence interval rather routine. .展开更多
When dealing with a regular (fixed-support) one-parameter distribution, the corresponding maximum-likelihood estimator (MLE) is, to a good approximation, normally distributed. But, when the support boundaries are func...When dealing with a regular (fixed-support) one-parameter distribution, the corresponding maximum-likelihood estimator (MLE) is, to a good approximation, normally distributed. But, when the support boundaries are functions of the parameter, finding good approximation for the sampling distribution of MLE (needed to construct an accurate confidence interval for the parameter’s true value) may get very challenging. We demonstrate the nature of this problem, and show how to deal with it, by a detailed study of a specific situation. We also indicate several possible ways to bypass MLE by proposing alternate estimators;these, having relatively simple sampling distributions, then make constructing a confidence interval rather routine. .展开更多
Deficiencies of the performance-based iterative learning control （ILC） for the non-regular systems are investigated in detail, then a faster control input updating and lifting technique is introduced in the design o...Deficiencies of the performance-based iterative learning control （ILC） for the non-regular systems are investigated in detail, then a faster control input updating and lifting technique is introduced in the design of performance index based ILCs for the partial non-regular systems. Two ldnds of optimal ILCs based on different performance indices are considered. Finally, simulation examples are given to illustrate the feasibility of the proposed learning controls.展开更多
A λ harmonic graph G, a λ-Hgraph G for short, means that there exists a constant λ such that the equality λd（vi） = Σ（vi,vj）∈E（G） d（vj） holds for all i = 1, 2,..., ｜V（G）｜, where d（vi） denotes the d...A λ harmonic graph G, a λ-Hgraph G for short, means that there exists a constant λ such that the equality λd（vi） = Σ（vi,vj）∈E（G） d（vj） holds for all i = 1, 2,..., ｜V（G）｜, where d（vi） denotes the degree of vertex vi. Let ni denote the number of vertices with degree i. This paper deals with the 3-Hgraphs and determines their degree series. Moreover, the 3-Hgraphs with bounded ni （1 ≤ i ≤ 7） are studied and some interesting results are obtained.展开更多
For any given 0 〈α 〈 β 〈 ∞, we construct a tree such that under tree metric, the Hausdorff dimension of the corresponding boundary is α, but both the Packing dimension and the boxing dimension are β. Applying ...For any given 0 〈α 〈 β 〈 ∞, we construct a tree such that under tree metric, the Hausdorff dimension of the corresponding boundary is α, but both the Packing dimension and the boxing dimension are β. Applying the connection between tree and iterated functions system, non- regular fractal sets on real line are constructed. Moreover, the method adopted in our paper is different from those which have been used before for constructing non-regular fractal set in general metric space.展开更多
文摘When dealing with a regular (fixed-support) one-parameter distribution, the corresponding maximum-likelihood estimator (MLE) is, to a good approximation, normally distributed. But, when the support boundaries are functions of the parameter, finding good approximation for the sampling distribution of MLE (needed to construct an accurate confidence interval for the parameter’s true value) may get very challenging. We demonstrate the nature of this problem, and show how to deal with it, by a detailed study of a specific situation. We also indicate several possible ways to bypass MLE by proposing alternate estimators;these, having relatively simple sampling distributions, then make constructing a confidence interval rather routine. .
文摘When dealing with a regular (fixed-support) one-parameter distribution, the corresponding maximum-likelihood estimator (MLE) is, to a good approximation, normally distributed. But, when the support boundaries are functions of the parameter, finding good approximation for the sampling distribution of MLE (needed to construct an accurate confidence interval for the parameter’s true value) may get very challenging. We demonstrate the nature of this problem, and show how to deal with it, by a detailed study of a specific situation. We also indicate several possible ways to bypass MLE by proposing alternate estimators;these, having relatively simple sampling distributions, then make constructing a confidence interval rather routine. .
基金supported by the National Natural Science Foundation of China (No.60774023)Hunan Provincial Natural Science Foundation (No.06JJ50141)
文摘Deficiencies of the performance-based iterative learning control （ILC） for the non-regular systems are investigated in detail, then a faster control input updating and lifting technique is introduced in the design of performance index based ILCs for the partial non-regular systems. Two ldnds of optimal ILCs based on different performance indices are considered. Finally, simulation examples are given to illustrate the feasibility of the proposed learning controls.
基金supported by the National Natural Science Foundation of China (10771080)the Specialized Research Fund for the Doctoral Program of Higher Eduction (20070574006)
文摘A λ harmonic graph G, a λ-Hgraph G for short, means that there exists a constant λ such that the equality λd（vi） = Σ（vi,vj）∈E（G） d（vj） holds for all i = 1, 2,..., ｜V（G）｜, where d（vi） denotes the degree of vertex vi. Let ni denote the number of vertices with degree i. This paper deals with the 3-Hgraphs and determines their degree series. Moreover, the 3-Hgraphs with bounded ni （1 ≤ i ≤ 7） are studied and some interesting results are obtained.
文摘For any given 0 〈α 〈 β 〈 ∞, we construct a tree such that under tree metric, the Hausdorff dimension of the corresponding boundary is α, but both the Packing dimension and the boxing dimension are β. Applying the connection between tree and iterated functions system, non- regular fractal sets on real line are constructed. Moreover, the method adopted in our paper is different from those which have been used before for constructing non-regular fractal set in general metric space.
