Three essays in econometric theory

This thesis consists of three essays in econometric theory. In the first essay, he considers a prediction problem with a large number of predictors. He improves the prediction precision of the standard factor model by allowing some variables to have idiosyncratic factors that are relevant for prediction. He selects idiosyncratic factors using a new model selection approach. In the second essay he studies two related tests of bivariate central symmetry. The asymptotic distributions of the two test statistics are established under rather weak conditions. He compares the finite sample performance of the test procedures with alternative tests by simulation. In the third and final essay, Zhuojiong proposes a pooled least-squares break point estimator for panel data. The estimator is shown to be consistent when the number of cross-sectional observations tends to infinity. Based on this break point estimator, he further proposes three consistent and asymptotically normally distributed slope estimators. The asymptotic variances of the three estimators are compared under a few simplifying assumptions.