Journal of Data Science

Abstract: The null distribution of the likelihood ratio test (LRT) of a onecomponent normal model versus two-component normal mixture model is

Abstract: We consider the Autoregressive Conditional Marked Duration (ACMD) model and apply it to 16 stocks traded in Hong Kong Stock Ex change (SEHK). By examining the orderings of appropriate sets of model parameters, market microstructure phenomena can be explained. To sub stantiate these conclusions, likelihood ratio test is used for testing the sig nificance of the parameter orderings of the ACMD model. While some of our results resolve a few controversial market microstructure hypotheses and echo some of the existing empirical evidence, we discover some interesting market microstructure phenomena that may be characteristic to SEHK.

Cognitive Diagnosis Models (CDMs) are a special family of discrete latent variable models widely used in educational, psychological and social sciences. In many applications of CDMs, certain hierarchical structures among the latent attributes are assumed by researchers to characterize their dependence structure. Specifically, a directed acyclic graph is used to specify hierarchical constraints on the allowable configurations of the discrete latent attributes. In this paper, we consider the important yet unaddressed problem of testing the existence of latent hierarchical structures in CDMs. We first introduce the concept of testability of hierarchical structures in CDMs and present sufficient conditions. Then we study the asymptotic behaviors of the likelihood ratio test (LRT) statistic, which is widely used for testing nested models. Due to the irregularity of the problem, the asymptotic distribution of LRT becomes nonstandard and tends to provide unsatisfactory finite sample performance under practical conditions. We provide statistical insights on such failures, and propose to use parametric bootstrap to perform the testing. We also demonstrate the effectiveness and superiority of parametric bootstrap for testing the latent hierarchies over non-parametric bootstrap and the naïve Chi-squared test through comprehensive simulations and an educational assessment dataset.