A0471
Title: Partial penalized quasi-likelihood with covariance matrix misspecification
Authors: Jing Zhou - University of East Anglia (United Kingdom) [presenting]
Zhe Zhang - University of Pennsylvania (United States)
Abstract: In the past twenty years, hypothesis testing for regularized estimators has been researched and proposed in various frameworks, including partial penalization. These inference frameworks typically rely on specifying a complete data-generating model. The scenarios are handled where specifying the full marginal density of the response is challenging, such as in longitudinal data where correlation exists between the measurements or over(under)-dispersion in the generalized linear models. Under the assumption that the conditional mean function is correctly specified, a $\sqrt{n}$-consistent estimation of the unknown parameter vector is obtained via the fixed point solutions of the regularized estimating equations. The consistency holds even if the working covariance matrix is misspecified. Further, test statistics are constructed via partial penalized estimating equations, of which the test statistic converges to a chi-squared distribution. It is demonstrated that the power of the test depends on the variance specification and working correlation matrix.
