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Full-Text Articles in Social and Behavioral Sciences
Glivenko-Cantelli Theorems For Integrated Functionals Of Stochastic Processes, Jia Li, Congshan Zhang, Yunxiao Liu
Glivenko-Cantelli Theorems For Integrated Functionals Of Stochastic Processes, Jia Li, Congshan Zhang, Yunxiao Liu
Research Collection School Of Economics
We prove a Glivenko-Cantelli theorem for integrated functionals of latent continuous-time stochastic processes. Based on a bracketing condition via random brackets, the theorem establishes the uniform convergence of a sequence of empirical occupation measures towards the occupation measure induced by underlying processes over large classes of test functions, including indicator functions, bounded monotone functions, Lipschitz-in-parameter functions, and Hölder classes as special cases. The general Glivenko-Cantelli theorem is then applied in more concrete high-frequency statistical settings to establish uniform convergence results for general integrated functionals of the volatility of efficient price and local moments of microstructure noise.
Determining The Number Of Communities In Degree-Corrected Stochastic Block Models, Shujie Ma, Liangjun Su, Yichong Zhang
Determining The Number Of Communities In Degree-Corrected Stochastic Block Models, Shujie Ma, Liangjun Su, Yichong Zhang
Research Collection School Of Economics
We propose to estimate the number of communities in degree-corrected stochastic block models based on a pseudo likelihood ratio. For estimation, we consider a spectral clustering together with binary segmentation method. This approach guarantees an upper bound for the pseudo likelihood ratio statistic when the model is over-fitted. We also derive its limiting distribution when the model is under-fitted. Based on these properties, we establish the consistency of our estimator for the true number of communities. Developing these theoretical properties require a mild condition on the average degree: growing at a rate faster than log(n), where n is the number …