Non-ergodic martingale estimating functions and related asymptotics

作者：Hwang S Y^*; Basawa I V; Choi M S; Lee S D

来源：Statistics, 2014, 48(3): 487-507.

DOI：10.1080/02331888.2012.748772

• non-ergodic process
• martingale estimating functions
• branching process
• asymptotic optimality
• explosive autoregressive model
• Primary 62M10

Well-known estimation methods such as conditional least squares, quasilikelihood and maximum likelihood (ML) can be unified via a single framework of martingale estimating functions (MEFs). Asymptotic distributions of estimates for ergodic processes use constant norm (e.g. square root of the sample size) for asymptotic normality. For certain non-ergodic-type applications, however, such as explosive autoregression and super-critical branching processes, one needs a random norm in order to get normal limit distributions. In this paper, we are concerned with non-ergodic processes and investigate limit distributions for a broad class of MEFs. Asymptotic optimality (within a certain class of non-ergodic MEFs) of the ML estimate is deduced via establishing a convolution theorem using a random norm. Applications to non-ergodic autoregressive processes, generalized autoregressive conditional heteroscedastic-type processes, and super-critical branching processes are discussed. Asymptotic optimality in terms of the maximum random limiting power regarding large sample tests is briefly discussed.

• 出版日期2014-5-4