Limit Distributions Of Estimators Research Articles

On limit distributions of estimators in irregular statistical models and a new representation of fractional Brownian motion

We provide new results concerning the limit distributions of Bayesian estimators (BE) and maximum likelihood estimators (MLE) of location parameters of cusp-type signals in “signal plus white noise” models. The limit distributions of BE and MLE are expressed in terms of fractional Brownian motion (fBm) with the Hurst parameter H, 0<H<1 as the noise intensity tends to zero. A new representation of fBm is given in terms of cusp functions. Simulation results for the densities and variances of the limit distributions of BE and MLE are also discussed.

Non-stationary quasi-likelihood and asymptotic optimality

This 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.

Gaussian and non-Gaussian limit distributions of estimates of the regression coefficients of a long-memory time series

We obtain Gaussian and non-Gaussian distributions of estimates of regression coefficients of a long-memory time series.

On Limit Distributions of Estimates for Two-Sided Censored Samples with a Discontinuous Density

On Limit Distributions of Estimates for Two-Sided Censored Samples with a Discontinuous Density