In this paper, we propose a new estimation method for a nonparametric hidden Markov model(HMM), in which both the emission model and the transition matrix are nonparametric, and a semiparametric HMM, in which the tran...In this paper, we propose a new estimation method for a nonparametric hidden Markov model(HMM), in which both the emission model and the transition matrix are nonparametric, and a semiparametric HMM, in which the transition matrix is parametric while emission models are nonparametric. The estimation is based on a novel composite likelihood method, where the pairs of consecutive observations are treated as independent bivariate random variables. Therefore, the model is transformed into a mixture model, and a modified expectation-maximization(EM) algorithm is developed to compute the maximum composite likelihood.We systematically study asymptotic properties for both the nonparametric HMM and the semiparametric HMM. We also propose a generalized likelihood ratio test to choose between the nonparametric HMM and the semiparametric HMM. We derive the asymptotic distribution and prove the Wilk’s phenomenon of the proposed test statistics. Simulation studies and an application in volatility clustering analysis of the volatility index in the Chicago Board Options Exchange(CBOE) are conducted to demonstrate the effectiveness of the proposed methods.展开更多
In this paper,a theory on sieve likelihood ratio inference on general parameterspaces(including infinite dimensional)is studied.Under fairly general regularity conditions,the sieve log-likelihood ratio statistic is pr...In this paper,a theory on sieve likelihood ratio inference on general parameterspaces(including infinite dimensional)is studied.Under fairly general regularity conditions,the sieve log-likelihood ratio statistic is proved to be asymptotically X^2 distributed,whichcan be viewed as a generalization of the well-known Wilks' theorem.As an example,asemiparametric partial linear model is investigated.展开更多
基金supported by Shanghai Young Talent Development Program and Innovative Research Team of Shanghai University of Finance and Economics(Grant No.2020110930)supported by the Department of Energy of USA(Grant No.DE-EE0008574)。
文摘In this paper, we propose a new estimation method for a nonparametric hidden Markov model(HMM), in which both the emission model and the transition matrix are nonparametric, and a semiparametric HMM, in which the transition matrix is parametric while emission models are nonparametric. The estimation is based on a novel composite likelihood method, where the pairs of consecutive observations are treated as independent bivariate random variables. Therefore, the model is transformed into a mixture model, and a modified expectation-maximization(EM) algorithm is developed to compute the maximum composite likelihood.We systematically study asymptotic properties for both the nonparametric HMM and the semiparametric HMM. We also propose a generalized likelihood ratio test to choose between the nonparametric HMM and the semiparametric HMM. We derive the asymptotic distribution and prove the Wilk’s phenomenon of the proposed test statistics. Simulation studies and an application in volatility clustering analysis of the volatility index in the Chicago Board Options Exchange(CBOE) are conducted to demonstrate the effectiveness of the proposed methods.
基金supported in part by National Science Foundation of the USA(Grant IIS-0328802,Grant DMS-0072635)the National Natural Science Foundation of China(Grant.No.10071090 and 10231030).
文摘In this paper,a theory on sieve likelihood ratio inference on general parameterspaces(including infinite dimensional)is studied.Under fairly general regularity conditions,the sieve log-likelihood ratio statistic is proved to be asymptotically X^2 distributed,whichcan be viewed as a generalization of the well-known Wilks' theorem.As an example,asemiparametric partial linear model is investigated.
