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Empirical likelihood method has been applied to short-memory time series models by Monti (1997) through the Whittle's estimation method. Yau (2012) extended this idea to long-memory time series models. Asymptotic distributions of the empirical likelihood ratio statistic for short and long-memory time series have been derived to construct confidence regions for the corresponding model parameters. However, computing profile empirical likelihood function involving constrained maximization does not always have a solution which leads to several drawbacks. In this paper, we propose an adjusted empirical likelihood procedure to modify the one proposed by Yau (2012) for autoregressive fractionally integrated moving average (ARFIMA) model. It guarantees the existence of a solution to the required maximization problem as well as maintains same asymptotic properties obtained by Yau (2012). Simulations have been carried out to illustrate that the adjusted empirical likelihood method for different long-time series models provides better confidence regions and coverage probabilities than the unadjusted ones, especially for small sample sizes.

One common challenge in nonmanufacturing control chart applications is that many of the nonmanufacturing quality characteristics are not normally distributed. In these applications, normal transformation of the observations is certainly feasible; however, it will be done at the expense of the interpretability of the analysis that is particularly important to control chart users in nonmanufacturing industries.Most of the existing nonparametric control charts are designed for Phase II monitoring. Little has been done in developing nonparametric Phase I control charts especially for individual observations that are prevalent in nonmanufacturing applications. In this work, we propose a new nonparametric Phase I control chart for monitoring the location parameter whose construction is essentially based on the empirical likelihood ratio test. The performance of the proposed chart, in terms of the signal probability, compares favorably with the recently developed charts for individual observations. A nonmanufacturing example is included in which the proposed chart and the other competing charts are applied and compared.

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To cite this article: Wei Ning (2012) Empirical likelihood ratio test for a mean change point model with a linear trend followed by an abrupt change, Journal of Applied Statistics, 39:5, 947-961, In this paper, a change point model with the mean being constant up to some unknown point, and increasing linearly to another unknown point, then dropping back to the original level is studied. A nonparametric method based on the empirical likelihood test is proposed to detect and estimate the locations of change points. Under some mild conditions, the asymptotic null distribution of an empirical likelihood ratio test statistic is shown to have the extreme distribution. The consistency of the test is also proved. Simulations of the powers of the test indicate that it performs well under different assumptions of the data distribution. The test is applied to the aircraft arrival time data set and the Stanford heart transplant data set.