On copula moment: empirical likelihood based estimation method

PurposeIn this paper, the authors applied the empirical likelihood method, which was originally proposed by Owen, to the copula moment based estimation methods to take advantage of its properties, effectiveness, flexibility and reliability of the nonparametric methods, which have limiting chi-square distributions and may be used to obtain tests or confidence intervals. The authors derive an asymptotically normal estimator of the empirical likelihood based on copula moment estimation methods (ELCM). Finally numerical performance with a simulation experiment of ELCM estimator is studied and compared to the CM estimator, with a good result.Design/methodology/approachIn this paper we applied the empirical likelihood method which originally proposed by Owen, to the copula moment based estimation methods.FindingsWe derive an asymptotically normal estimator of the empirical likelihood based on copula moment estimation methods (ELCM). Finally numerical performance with a simulation experiment of ELCM estimator is studied and compared to the CM estimator, with a good result.Originality/valueIn this paper we applied the empirical likelihood method which originally proposed by Owen 1988, to the copula moment based estimation methods given by Brahimi and Necir 2012. We derive an new estimator of copula parameters and the asymptotic normality of the empirical likelihood based on copula moment estimation methods.

Positive Solutions of the Fractional SDEs with Non-Lipschitz Diffusion Coefficient

We study a class of fractional stochastic differential equations (FSDEs) with coefficients that may not satisfy the linear growth condition and non-Lipschitz diffusion coefficient. Using the Lamperti transform, we obtain conditions for positivity of solutions of such equations. We show that the trajectories of the fractional CKLS model with β>1 are not necessarily positive. We obtain the almost sure convergence rate of the backward Euler approximation scheme for solutions of the considered SDEs. We also obtain a strongly consistent and asymptotically normal estimator of the Hurst index H>1/2 for positive solutions of FSDEs.

Quantiles on Stream: An Application to Monte Carlo Simulation

Monte Carlo simulation is an efficient method to estimate quantile. However, it becomes a serious problem when a huge sample size is required but the memory is insufficient. In this paper, we apply the stream quantile algorithm to Monte Carlo simulation in order to estimate quantile with limited memory. A rigorous theoretical analysis on the properties of theϵn-approximate quantile is proposed in this paper. We prove that ifϵn=o(n-1/2), then theϵn-approximateα-quantile computed by any deterministic stream quantile algorithm is a consistent and asymptotically normal estimator of the true quantileqα. We suggest settingϵn= 1/(n1/2log10n) in practice. Two deterministic stream quantile algorithms, including of GK algorithm and ZW algorithm, are employed to illustrate the performance of theϵn-approximate quantile. The numerical example shows that the deterministic stream quantile algorithm can provide desired estimator of the true quantile with less memory.

A STUDY ON A TWO UNIT STANDBY SYSTEM WITH ERLANGIAN REPAIR TIME

A two-unit cold standby system is considered. The failure rate of a unit is a constant and the repair time distribution is a two-stage Erlang distribution. Measures of system performance such as reliability, mean time before failure, system availability, and steady-state availability are derived. Also, a consistent asymptotically normal estimator and a 100(1-α)% asymptotic confidence interval for the steady-state availability of the system are obtained.

Robustness of the Ewens sampling formula

Under the assumptions of the neutral infinite alleles model, K (the total number of alleles present in a sample) is sufficient for estimating θ (the mutation rate). This is a direct result of the Ewens sampling formula, which gives a consistent, asymptotically normal estimator for θ based on K. It is shown that the same estimator used to estimate θ under neutrality is consistent and asymptotically normal, even when the assumption of selective neutrality is violated.

Robustness of the Ewens sampling formula

Under the assumptions of the neutral infinite alleles model, K (the total number of alleles present in a sample) is sufficient for estimating θ (the mutation rate). This is a direct result of the Ewens sampling formula, which gives a consistent, asymptotically normal estimator for θ based on K. It is shown that the same estimator used to estimate θ under neutrality is consistent and asymptotically normal, even when the assumption of selective neutrality is violated.