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AbstractIn this paper, we develop two procedures for identifying the dynamic trends in the parameters of length-biased lognormal distribution based on likelihood ratio and modified information criterion. These methods mainly consider the test of the existence of the change point and provide the maximum likelihood estimation of the change point when the change point exists. In addition, the asymptotic distribution of test statistic based on likelihood ratio is derived as an extreme value distribution, while the asymptotic distribution of test statistic based on modified information criterion is derived as a chi-square distribution. And the consistency of parameter estimation is proved. Simulations are conducted to study the performance of the proposed method in terms of power, coverage probabilities and average sizes of confidence sets. The proposed methods are applied to a real data to illustrate the detecting procedures. [ABSTRACT FROM AUTHOR]

The mean residual life (MRL) function is one of the basic parameters of interest in survival analysis. In this paper, we develop three procedures based on modified versions of empirical likelihood (EL) to construct confidence intervals of the MRL function with length-biased data. The asymptotic results corresponding to the procedures have been established. The proposed methods exhibit better finite sample performance over other existing procedures, especially in small sample sizes. Simulations are conducted to compare coverage probabilities and the mean lengths of confidence intervals under different scenarios for the proposed methods and some existing methods. Two real data applications are provided to illustrate the methods of constructing confidence intervals. [ABSTRACT FROM AUTHOR]

In this paper, we propose a change point detection procedure based on the modified information criterion in a generalized lambda distribution (GLD) model. Simulations are conducted to obtain empirical critical values of the proposed test statistic. We have also conducted simulations to evaluate the performance of the proposed methods comparing to the log-likelihood method in terms of power, coverage probability, and confidence sets. Our results indicate that, under various conditions, the proposed method modified information criterion (MIC) approach shows good finite sample properties. Furthermore, we propose a new goodness-of-fit testing procedure based on the energy distance to evaluate the asymptotic null distribution of our test statistic. Two real data applications are provided to illustrate the use of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, a sequential change point detection method is developed to monitor structural change in smoothly clipped absolute deviation (SCAD) penalized quantile regression (SPQR) models. The asymptotic properties of the test statistic are derived from the null and alternative hypotheses. In order to improve the performance of the SPQR method, we propose a post‐SCAD penalized quantile regression estimator (P‐SPQR) for high‐dimensional data. We examined the finite sample properties of the proposed methods via Monte Carlo studies under different scenarios. A real data application is provided to demonstrate the effectiveness of the method. [ABSTRACT FROM AUTHOR]