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We propose statistical inferential procedures for panel data models with interactive fixed effects in a kernel ridge regression framework.Compared with traditional sieve methods, our method is automatic in the sense that it does not require the choice of basis functions and truncation parameters.Model complexity is controlled by a continuous regularization parameter which can be automatically selected by generalized cross validation. Based on empirical processes theory and functional analysis tools, we derive joint asymptotic distributions for the estimators in the heterogeneous setting. These joint asymptotic results are then used to construct confidence intervals for the regression means and prediction intervals for the future observations, both being the first provably valid intervals in literature. Marginal asymptotic normality of the functional estimators in homogeneous setting is also obtained. Simulation and real data analysis demonstrate the advantages of our method.
In this work, we investigate Gaussian process regression used to recover a function based on noisy observations. We derive upper and lower error bounds for Gaussian process regression with possibly misspecified correlation functions. The optimal conv
Kernel ridge regression is an important nonparametric method for estimating smooth functions. We introduce a new set of conditions, under which the actual rates of convergence of the kernel ridge regression estimator under both the L_2 norm and the n
In this paper, we survey some recent results on statistical inference (parametric and nonparametric statistical estimation, hypotheses testing) about the spectrum of stationary models with tapered data, as well as, a question concerning robustness of
In this paper we study multi-task kernel ridge regression and try to understand when the multi-task procedure performs better than the single-task one, in terms of averaged quadratic risk. In order to do so, we compare the risks of the estimators wit
Regularization is an essential element of virtually all kernel methods for nonparametric regression problems. A critical factor in the effectiveness of a given kernel method is the type of regularization that is employed. This article compares and co