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We consider conditional distribution and conditional density functionals in the space of generalized functions. The approach follows Phillips (1985, 1991, 1995) who employed generalized functions to overcome non-differentiability in order to develop expansions. We obtain the limit of the kernel estimators for weakly dependent data, even under non-differentiability of the distribution function; the limit Gaussian process is characterized as a stochastic random functional (random generalized function) on the suitable function space. An alternative simple to compute estimator based on the empirical distribution function is proposed for the generalized random functional. For test statistics based on this estimator, limit properties are established. A Monte Carlo experiment demonstrates good finite sample performance of the statistics for testing logit and probit specification in binary choice models.

This chapter studies a snowball sampling method for social networks with endogenous peer selection. Snowball sampling is a sampling design which preserves the dependence structure of the network. It sequentially collects the information of vertices linked to the vertices collected in the previous iteration. The snowball samples suffer from a sample selection problem because of the endogenous peer selection. The author proposes a new estimation method that uses the relationship between samples in different iterations to correct selection. The author uses the snowball samples collected from Facebook to estimate the proportion of users who support the Umbrella Movement in Hong Kong.

Vector Autoregression (VAR) has been a standard empirical tool used in macroeconomics and finance. In this paper we discuss how to compare alternative VAR models after they are estimated by Bayesian MCMC methods. In particular we apply a robust version of deviance information criterion (RDIC) recently developed in Li, Zeng, and Yu (2014b) to determine the best candidate model. RDIC is a better information criterion than the widely used deviance information criterion (DIC) when latent variables are involved in candidate models. Empirical analysis using US data shows that the optimal model selected by RDIC can be different from that by DIC.