50 research outputs found
Asymptotic tests of composite hypotheses for non-ergodic type stochastic processes
AbstractLimiting distributions of a score statistic and the likelihood ratio statistic for testing a composite hypothesis involving several parameters in non-ergodic type stochastic processes are obtained. It is shown that, unlike in the usual theory (ergodic type processes), the limiting distributions of these statistics are different both under the null and a contiguous sequence of alternative hypotheses. The results are applied to a regression model with explosive autoregressive Gaussian errors. In the discussion of this example a modified score statistic is suggested where the limiting null and non-null distributions are the same as those of the likelihood ratio statistic
Branching Markov processes and related asymptotics
AbstractModels for Markov processes indexed by a branching process are presented. The new class of models is referred to as the branching Markov process (BMP). The law of large numbers and a central limit theorem for the BMP are established. Bifurcating autoregressive processes (BAR) are special cases of the general BMP model discussed in the paper. Applications to parameter estimation are also presented
Large sample estimation in nonstationary autoregressive processes with multiple observations
AbstractThe asymptotic distributions of the least-squares estimators of the parameters in autoregressive processes with multiple observations are derived for the two nonstationary cases, viz., (a) the explosive case and (b) the unstable case. It is shown that nonstandard limit distributions are obtained
Asymptotically minimax tests of composite hypotheses for nonergodic type processes
AbstractAsymptotically efficient tests satisfying a minimax type criterion are derived for testing composite hypotheses involving several parameters in nonergodic type stochastic processes. It is shown, in particular, that the analogue of the usual Neyman's C (α) type test (i.e., the score test) is not efficient for the nonergodic case. Moreover, the likelihood-ratio statistic is not fully efficient for the model discussed in the paper. The efficient statistic derived here is a modified version of the score-statistic discussed previously by Basawa and Koul (1979)
Observation-driven generalized state space models for categorical time series
Observation-driven state space models are presented for categorical time series as an alternative to the regression type models which are commonly used in the literature. As an application to multi-categorical time series, we present a DNA data analysis and demonstrate the advantages of using state space models.
Godambe estimating functions and asymptotic optimal inference
Godambe (1985) introduced a class of optimum estimating functions which can be regarded as a generalization of quasilikelihood score functions. The "optimality" established by Godambe (1985) within a certain class is for estimating functions and it is based on finite samples. The question that arises naturally is what (if any) asymptotic optimality properties do the estimators and tests based on optimum estimating functions possess. In this paper, we establish, via presenting a convolution theorem, asymptotic optimality of estimators and tests obtained from Godambe optimum estimating functions. It is noted that we do not require the knowledge of the likelihood function.Asymptotic optimality Godambe estimating functions Large sample tests Quasilikelihood estimation