This article investigates the testing for serial correlation in partially linear models with validation data and applies the empirical likelihood methods to construct serial tests statistics, and then we derive the asymptotic distribution of the test statistics under null hypothesis. Simulation results show that our method performs well.

In this paper, we investigate the testing for serial correlation in a linear model with validation data, then we apply the empirical likelihood method to construct the test statistic and derive the asymptotic distribution of the test statistic under null hypothesis. Simulation results show that our method performs well both in size and power with finite same size.

In this paper, we study the hypothesis test for regression coefficients of partially linear models when the number of covariates in the linear part diverges. We propose a U-type test statistic. Asymptotic properties of the proposed test statistic are derived under null and local alternative on mild conditions. Extensive numerical examples are presented to demonstrate the advantages of the proposed test statistic for finite sample size.

1. In the current era of big data, the scope of data types has extended far beyond mere numerical data. A wide range of both structured and unstructured data, including text, images, audio, and vid...