Martingale Estimating Functions for Stochastic Processes: A Review Toward a Unifying Tool

Hwang, Sun Young; Basawa, I. V.

doi:10.1007/978-3-319-02651-0_2

Cited by 4 publications

(3 citation statements)

References 24 publications

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“…This example is taken and modified from Hwang and Basawa (2014). Recall the BAR(1) formulation (4.2) given by…”

Section: Quasi Likelihood (Ql)mentioning

confidence: 99%

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Contemporary review on the bifurcating autoregressive models : Overview and perspectives

Hwang¹

2014

Journal of the Korean Data and Information Science Society

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Since the bifurcating autoregressive (BAR) model was developed by Cowan and Staudte (1986) to analyze cell lineage data, a lot of research has been directed to BAR and its generalizations. Based mainly on the author's works, this paper is concerned with a contemporary review on the BAR in terms of an overview and perspectives. Specifically, bifurcating structure is extended to multi-cast tree and to branching tree structure. The AR(1) time series model of Cowan and Staudte (1986) is generalized to tree structured random processes. Branching correlations between individuals sharing the same parent are introduced and discussed. Various methods for estimating parameters and related asymptotics are also reviewed. Consequently, the paper aims to give a contemporary overview on the BAR model, providing some perspectives to the future works in this area.

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“…This example is taken and modified from Hwang and Basawa (2014). Recall the BAR(1) formulation (4.2) given by…”

Section: Quasi Likelihood (Ql)mentioning

confidence: 99%

“…Readers may refer to recent reference of Hwang and Basawa (2014) for unifying various estimation methods via martingale estimating functions. For conditional least squares estimation for higher order MAR processes, see Mao (2014) and references therein.…”

Section: Quasi Likelihood (Ql)mentioning

confidence: 99%

Contemporary review on the bifurcating autoregressive models : Overview and perspectives

Hwang¹

2014

Journal of the Korean Data and Information Science Society

View full text Add to dashboard Cite

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“…Suppose that {ε t } in (3.17) is mis-specified as heteroscedastic (rather than homoscedastic) in such a way that Var(ε t |F t−1 ) = h t (cf. Hwang & Basawa, 2014). A stationary GARCH(1,1) model defined by h t = α 0 + α 1 ε 2 t−1 + β 1 h t−1 may be useful for modeling h t .…”

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confidence: 99%

Non-stationary quasi-likelihood and asymptotic optimality

Hwang

Kim

2014

Journal of the Korean Statistical Society

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a b s t r a c tThis article is concerned with non-stationary time series which does not require the full knowledge of the likelihood function. Consequently, a quasi-likelihood is employed for estimating parameters instead of the maximum (exact) likelihood. For stationary cases, Wefelmeyer (1996) and Hwang and Basawa (2011a,b), among others, discussed the issue of asymptotic optimality of the quasi-likelihood within a restricted class of estimators. For non-stationary cases, however, the asymptotic optimality property of the quasi-likelihood has not yet been adequately addressed in the literature. This article presents the asymptotic optimal property of the non-stationary quasi-likelihood within certain estimating functions. We use a random norm instead of a constant norm to get limit distributions of estimates. To illustrate main results, the non-stationary ARCH model, branching Markov process, and non-stationary random-coefficient AR process are discussed.

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On the threshold innovation in quasi-likelihood for conditionally heteroscedastic time series

Yoon

Hwang

2019

Communications in Statistics - Simulation and Computation

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Martingale Estimating Functions for Stochastic Processes: A Review Toward a Unifying Tool

Cited by 4 publications

References 24 publications

Contemporary review on the bifurcating autoregressive models : Overview and perspectives

Contemporary review on the bifurcating autoregressive models : Overview and perspectives

Non-stationary quasi-likelihood and asymptotic optimality

On the threshold innovation in quasi-likelihood for conditionally heteroscedastic time series

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