We assume T1,..., Tn are i.i.d. data sampled from distribution function F with density function f and C1,...,Cn are i.i.d. data sampled from distribution function G. Observed data consists of pairs （Xi, δi）, em= 1,...We assume T1,..., Tn are i.i.d. data sampled from distribution function F with density function f and C1,...,Cn are i.i.d. data sampled from distribution function G. Observed data consists of pairs （Xi, δi）, em= 1,..., n, where Xi = min{Ti,Ci}, δi = I（Ti 6 Ci）, I（A） denotes the indicator function of the set A. Based on the right censored data {Xi, δi}, em=1,..., n, we consider the problem of estimating the level set {f 〉 c} of an unknown one-dimensional density function f and study the asymptotic behavior of the plug-in level set estimators. Under some regularity conditions, we establish the asymptotic normality and the exact convergence rate of the λg-measure of the symmetric difference between the level set {f ≥ c} and its plug-in estimator {fn ≥ c}, where f is the density function of F, and fn is a kernel-type density estimator of f. Simulation studies demonstrate that the proposed method is feasible. Illustration with a real data example is also provided.展开更多
Stars are born in dense cores of molecular clouds. The core mass function （CMF）, which is the mass distribution of dense cores, is important for understanding the stellar initial mass function （IMF）. We obtained ...Stars are born in dense cores of molecular clouds. The core mass function （CMF）, which is the mass distribution of dense cores, is important for understanding the stellar initial mass function （IMF）. We obtained 350μm dust continuum data using the SHARC-II camera at the Caltech Submillimeter Observatory （CSO） telescope. A 350μm map covering 0.25 deg2 of the Ophiuchus molecular cloud was created by mosaicing 56 separate scans. The CSO telescope had an angular resolution of 9＂, corresponding to 1.2 ×103 AU at the distance of the Ophiuchus molecular cloud （131 pc）. The data was reduced using the Comprehensive Reduction Utility for SHARC-II （CRUSH）. The flux density map was analyzed using the GaussClumps algorithm, within which 75 cores has been identified. We used the Spitzer c2d catalogs to separate the cores into 63 starless cores and 12 protostellar cores. By locating Jeans instabilities, 55 prestellar cores （a subcategory of starless cores） were also identified. The excitation temperatures, which were derived from FCRAO 12CO data, help to improve the accuracy of the masses of the cores. We adopted a Monte Carlo approach to analyze the CMF with two types of functional forms; power law and log-normal. The whole and prestellar CMF are both well fitted by a log-normal distribution, with p = -1. 18 ±0.10, σ = 0.58 ± 0.05 and μ= 1.40 ＋ 0.10, σ= 0.50 ＋ 0.05 respectively. This finding suggests that turbulence influences the evolution of the Ophiuchus molecular cloud.展开更多
基金supposed by National Natural Science Foundation of China (Grant Nos. 11071137 and 11371215)Tsinghua Yue-Yuen Medical Science Fund
文摘We assume T1,..., Tn are i.i.d. data sampled from distribution function F with density function f and C1,...,Cn are i.i.d. data sampled from distribution function G. Observed data consists of pairs （Xi, δi）, em= 1,..., n, where Xi = min{Ti,Ci}, δi = I（Ti 6 Ci）, I（A） denotes the indicator function of the set A. Based on the right censored data {Xi, δi}, em=1,..., n, we consider the problem of estimating the level set {f 〉 c} of an unknown one-dimensional density function f and study the asymptotic behavior of the plug-in level set estimators. Under some regularity conditions, we establish the asymptotic normality and the exact convergence rate of the λg-measure of the symmetric difference between the level set {f ≥ c} and its plug-in estimator {fn ≥ c}, where f is the density function of F, and fn is a kernel-type density estimator of f. Simulation studies demonstrate that the proposed method is feasible. Illustration with a real data example is also provided.
基金by the California Institute of Technology under cooperative agreement with the National Science Foundation (Grant No. AST0838261)supported by National Basic Research Program of China (Grant No. 2012CB821800)+2 种基金National Aeronautics and Space Administration Undergraduate Student Research Program of USANational Natural Science Foundation of China (Grant Nos. 11373038 and 11163002)Graduate Innovative Fund of Gui Zhou University (Grant Nos. 2013024)
文摘Stars are born in dense cores of molecular clouds. The core mass function （CMF）, which is the mass distribution of dense cores, is important for understanding the stellar initial mass function （IMF）. We obtained 350μm dust continuum data using the SHARC-II camera at the Caltech Submillimeter Observatory （CSO） telescope. A 350μm map covering 0.25 deg2 of the Ophiuchus molecular cloud was created by mosaicing 56 separate scans. The CSO telescope had an angular resolution of 9＂, corresponding to 1.2 ×103 AU at the distance of the Ophiuchus molecular cloud （131 pc）. The data was reduced using the Comprehensive Reduction Utility for SHARC-II （CRUSH）. The flux density map was analyzed using the GaussClumps algorithm, within which 75 cores has been identified. We used the Spitzer c2d catalogs to separate the cores into 63 starless cores and 12 protostellar cores. By locating Jeans instabilities, 55 prestellar cores （a subcategory of starless cores） were also identified. The excitation temperatures, which were derived from FCRAO 12CO data, help to improve the accuracy of the masses of the cores. We adopted a Monte Carlo approach to analyze the CMF with two types of functional forms; power law and log-normal. The whole and prestellar CMF are both well fitted by a log-normal distribution, with p = -1. 18 ±0.10, σ = 0.58 ± 0.05 and μ= 1.40 ＋ 0.10, σ= 0.50 ＋ 0.05 respectively. This finding suggests that turbulence influences the evolution of the Ophiuchus molecular cloud.
