In this paper, we consider a change point model allowing at most one change, X($\tfrac{i}{n}$\tfrac{i}{n}) = f($\tfrac{i}{n}$\tfrac{i}{n}) + e($\tfrac{i}{n}$\tfrac{i}{n}), where f(t) = α + θ $I_{(t_0 ,1)} $I_{(t_0 ,1)} (t), 0 ≤ t ≤ 1, {e($\tfrac{1}{n}$\tfrac{1}{n}), ..., e($\tfrac{n}{n}$\tfrac{n}{n})} is a sequence of i.i.d. random variables distributed as e with 0 being the median of e. For this change point model, hypothesis test problem about the change-point t0 is studied and a test statistic is constructed. Furthermore, a nonparametric estimator of t0 is proposed and shown to be strongly consistent. Finally, we give an estimator of jump θ and obtain it’s asymptotic property. Performance of the proposed approach is investigated by extensive simulation studies.
In a generalized linear model with q x 1 responses, the bounded and fixed (or adaptive) p × q regressors Zi and the general link function, under the most general assumption on the minimum eigenvalue of ZiZ'i,the moment condition on responses as weak as possible and the other mild regular conditions, we prove that the maximum quasi-likelihood estimates for the regression parameter vector are asymptotically normal and strongly consistent.
YIN Changming, ZHAO Lincheng & WEI Chengdong School of Mathematics and Information Science, Guangxi University, Manning 530004, China
This paper studies the large sample properties of the change point estimates in binary response models. The estimate is obtained by maximizing the smoothed score function when the median of the latent error variable is assumed to be zero. An exponential convergence rate of the change point estimate is also established.
In this paper, we consider the change-point estimation in the censored regression model assuming that there exists one change point. A nonparametric estimate of the change-point is proposed and is shown to be strongly consistent. Furthermore, its convergence rate is also obtained.
The M-test has been in common use and widely studied in testing the linear hypotheses in linear models. However, the critical value for the test is usually related to the quantities of the unknown error distribution and the estimate of the nuisance parameters may be rather involved, not only for the M-test method but also for the existing bootstrap methods. In this paper we suggest a random weighting resampling method for approximating the null distribution of the M-test statistic. It is shown that, under both the null and the local alternatives, the random weighting statistic has the same asymptotic distribution as the null distribution of the M-test. The critical values of the M-test can therefore be obtained by the random weighting method without estimating the nuisance parameters. A distinguished feature of the proposed method is that the approximation is valid even the null hypothesis is not true and the power evaluation is possible under the local alternatives.
