We consider varying coefficient Cox models with high-dimensional covariates. We apply the group Lasso method to these models and propose a variable selection procedure. Our procedure copes with variable selection and structure identification from a high dimensional varying coefficient model to a semivarying coefficient model simultaneously. We derive an oracle inequality and closely examine restrictive eigenvalue conditions, too. In this paper, we give the details for Cox models with time-varying coefficients. The theoretical results on variable selection can be easily extended to some other important models and we briefly mention those models since those models can be treated in the same way. The models considered in this paper are the most popular models among structured nonparametric regression models. The results of a small numerical study are also given.
This paper derives the asymptotic distribution of Tanaka's score statistic under moderate deviation from a unit root in a moving average model of order one or MA(1). We classify the limiting distribution into three types depending on the order of deviation. In the fastest case, the convergence order of the asymptotic distribution continuously changes from the invertible process to the unit root. In the slowest case, the limiting distribution coincides with the invertible process in a distributional sense. This implies that these cases share an asymptotic property. The limiting distribution in the intermediate case provides the boundary property between the fastest and slowest cases.
This paper considers the conditional sum of squares estimator (CSSE) for the moderate deviation MA(1) process that has the parameter of the MA (1) with the distance between the parameter and unity being larger than O(T −1 ).We show that the asymptotic distribution of the CSSE is normal, even though the process belongs to the local-tounity class. The convergence rate continuously changes from an invertible order to a noninvertible one. In this sense, the moderate deviation process in MA(1) has a continuous bridge property like the AR process.
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