Approximation by randomly weighting method in censored regression model

Censored regression ("Tobit") models have been in common use, and their linear hypothesis testings have been widely studied. However, the critical values of these tests are usually related to quantities of an unknown error distribution and estimators of nuisance parameters. In this paper, we propose a randomly weighting test statistic and take its conditional distribution as an approximation to null distribution of the test statistic. It is shown that, under both the null and local alternative hypotheses, conditionally asymptotic distribution of the randomly weighting test statistic is the same as the null distribution of the test statistic. Therefore, the critical values of the test statistic can be obtained by randomly weighting method without estimating the nuisance parameters. At the same time, we also achieve the weak consistency and asymptotic normality of the randomly weighting least absolute deviation estimate in censored regression model. Simulation studies illustrate that the per-formance of our proposed resampling test method is better than that of central chi-square distribution under the null hypothesis.

Approximation by random weighting method for M-test in linear models

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.

Rank-Based Test for Partial Functional Linear Regression Models

This paper investigates the hypothesis test of the parametric component in partial functional linear regression models.Based on a rank score function,the authors develop a rank test using functional principal component analysis,and establish the asymptotic properties of the resulting test under null and local alternative hypotheses.A simulation study shows that the proposed test procedure has good size and power with finite sample sizes.The authors also present an illustration through fitting the Berkeley Growth Data and testing the effect of gender on the height of kids.

Asymptotic Distribution of the Jump Change-Point Estimator

The asymptotic distribution of the change-point estimator in a jump change- point model is considered. For the jump change-point model Xi - α ＋ θ{[nτ0] 〈 i ≤ n} ＋ εi, where εi （i = 1,…. , n） are independent identically distributed random variables with Eεi -= 0 and Var（εi） 〈 ∞, with the help of the slip window method, the asymptotic distribution of the jump change-point estimator τ is studied under the condition of the local alternative hypothesis.