Related papers: Nonparametric inference in generalized functional …
Functional autoregressive (FAR) models provide a fundamental framework for analyzing temporally dependent functional data. However, the infinite-dimensional nature of the underlying Hilbert space introduces intrinsic ill-posedness, as the…
Statistical inference in high dimensional settings has recently attracted enormous attention within the literature. However, most published work focuses on the parametric linear regression problem. This paper considers an important…
We develop a general assumption-lean framework for constructing uniformly valid confidence sets for functionals defined by moment equalities, referred to as $Z$-functionals. Our approach combines self-normalized statistics with a test…
Generalized likelihood ratio statistics have been proposed in Fan, Zhang and Zhang [Ann. Statist. 29 (2001) 153-193] as a generally applicable method for testing nonparametric hypotheses about nonparametric functions. The likelihood ratio…
The existing Fr\'echet regression is actually defined within a linear framework, since the weight function in the Fr\'echet objective function is linearly defined, and the resulting Fr\'echet regression function is identified to be a linear…
We consider nonparametric regression in the context of functional data, that is, when a random sample of functions is observed on a fine grid. We obtain a functional asymptotic normality result allowing to build simultaneous confidence…
Rapid advancements in data science require us to have fundamentally new frameworks to tackle prevalent but highly non-trivial "irregular" inference problems, to which the large sample central limit theorem does not apply. Typical examples…
The validity of estimation and smoothing parameter selection for the wide class of generalized additive models for location, scale and shape (GAMLSS) relies on the correct specification of a likelihood function. Deviations from such…
Non-probability sampling is prevailing in survey sampling, but ignoring its selection bias leads to erroneous inferences. We offer a unified nonparametric calibration method to estimate the sampling weights for a non-probability sample by…
Statistical inference in the presence of nuisance functionals with complex survey data is an important topic in social and economic studies. The Gini index, Lorenz curves and quantile shares are among the commonly encountered examples. The…
Nonlinear regression analysis is a popular and important tool for scientists and engineers. In this article, we introduce theories and methods of nonlinear regression and its statistical inferences using the frequentist and Bayesian…
Functional linear regression is an important topic in functional data analysis. It is commonly assumed that samples of the functional predictor are independent realizations of an underlying stochastic process, and are observed over a grid…
We study a functional linear regression model that deals with functional responses and allows for both functional covariates and high-dimensional vector covariates. The proposed model is flexible and nests several functional regression…
We investigate the behavior of the Generalized Likelihood Ratio Test (GLRT) (Fan, Zhang and Zhang [Ann. Statist. 29 (2001) 153-193]) for time varying coefficient models where the regressors and errors are non-stationary time series and can…
Nonparametric series regression often involves specification search over the tuning parameter, i.e., evaluating estimates and confidence intervals with a different number of series terms. This paper develops pointwise and uniform inferences…
Estimating the score, i.e., the gradient of log density function, from a set of samples generated by an unknown distribution is a fundamental task in inference and learning of probabilistic models that involve flexible yet intractable…
With modern technology development, functional data are being observed frequently in many scientific fields. A popular method for analyzing such functional data is ``smoothing first, then estimation.'' That is, statistical inference such as…
We propose a novel procedure for estimating and conducting inference on average marginal effects in partially linear instrumental regressions using Reproducing Kernel Hilbert Space methods. Our procedure relies on a single regularization…
No matter the nature of the response and/or explanatory variables in a regression model, some basic issues such as the existence of an effect of the predictor on the response, or the assessment of a common shape across groups of…
A framework for estimation and hypothesis testing of functional restrictions against general alternatives is proposed. The parameter space is a reproducing kernel Hilbert space (RKHS). The null hypothesis does not necessarily define a…