Statistical Papers最新文献

Abstract

In the paper, we propose a functional dimension reduction method for functional predictors and a scalar response. In the past study, the most popular functional dimension reduction method is the functional sliced inverse regression (FSIR) and people usually use a fixed slicing scheme to implement the estimation of FSIR. However, in practical, there are two main questions for the fixed slicing scheme: how many slices should be chosen and how to divide all samples into different slices. To solve these problems, we first expand the functional predictor and functional regression parameters on the functional principal component basis or a given basis such as B-spline basis. Then the functional regression parameters will be estimated by using the adaptive slicing for FSIR approach. Simulation results and real data analysis are presented to show the merit of the new proposed method.

We address the semiparametric challenge of identifying and estimating generalized additive partial linear models with nonignorable missingness in the response. Identifiability is ensured under instrumental variable assumption that there is an instrumental covariate related to the prospensity but unrelated to the response variable, or the assumption that the conditional score function is linear in the response variable. We propose a new estimating equation for the prospensity by taking expectation of the unobservable part on a linear combination of all covariates rather than the covariates themselves. This estimating equation does not suffer from the typical curse of dimensionality. Then the unknown nonparametric function is approximated by polynomial spline basis functions and we construct estimating equations for mean of response based on the inverse probability weighting. Under some regular conditions, we establish asymptotic normality of the proposed estimators for parametric components and consistency of the estimators of nonparametric functions. Simulation studies demonstrate that the proposed inference procedure performs well in many settings. The proposed method is applied to analyze the household income dataset from the Chinese Household Income Project Survey 2013.

Abstract

Solving semiparametric models can be computationally challenging because the dimension of parameter space may grow large with increasing sample size. Classical Newton’s method becomes quite slow and unstable with an intensive calculation of the large Hessian matrix and its inverse. Iterative methods separately updating parameters for the finite dimensional component and the infinite dimensional component have been developed to speed up single iterations, but they often take more steps until convergence or even sometimes sacrifice estimation precision due to sub-optimal update direction. We propose a computationally efficient implicit profiling algorithm that achieves simultaneously the fast iteration step in iterative methods and the optimal update direction in Newton’s method by profiling out the infinite dimensional component as the function of the finite-dimensional component. We devise a first-order approximation when the profiling function has no explicit analytical form. We show that our implicit profiling method always solves any local quadratic programming problem in two steps. In two numerical experiments under semiparametric transformation models and GARCH-M models, as well as a real application using NTP data, we demonstrated the computational efficiency and statistical precision of our implicit profiling method. Finally, we implement the proposed implicit profiling method in the R package SemiEstimate

Abstract

Response functions that link regression predictors to properties of the response distribution are fundamental components in many statistical models. However, the choice of these functions is typically based on the domain of the modeled quantities and is usually not further scrutinized. For example, the exponential response function is often assumed for parameters restricted to be positive, although it implies a multiplicative model, which is not necessarily desirable or adequate. Consequently, applied researchers might face misleading results when relying on such defaults. For parameters restricted to be positive, we propose to construct alternative response functions based on the softplus function. These response functions are differentiable and correspond closely to the identity function for positive values of the regression predictor implying a quasi-additive model. Consequently, the proposed response functions allow for an additive interpretation of the estimated effects by practitioners and can be a better fit in certain data situations. We study the properties of the newly constructed response functions and demonstrate the applicability in the context of count data regression and Bayesian distributional regression. We contrast our approach to the commonly used exponential response function.

Based on a progressive first-failure censoring (PFFC) sample, we discuss the statistical inferences of the entropy of a Rayleigh distribution. In particular, the Maximum likelihood and the different Bayes estimates for entropy are derived and compared via a Monte Carlo simulation study. Bayes estimators are developed using both symmetric and asymmetric loss functions. Approximate confidence intervals (CIs) and credible intervals (CrIs) of the entropy of the model are also performed. Numerical examples and a real data set are given to illustrate the proposed estimators.

From a continuous-time long memory stochastic process, a discrete-time randomly sampled one is drawn using a renewal sampling process. We establish the existence of the spectral density of the sampled process, and we give its expression in terms of that of the initial process. We also investigate different aspects of the statistical inference on the sampled process. In particular, we obtain asymptotic results for the periodogram, the local Whittle estimator of the memory parameter and the long run variance of partial sums. We mainly focus on Gaussian continuous-time process. The challenge being that the randomly sampled process will no longer be jointly Gaussian.

A procedure is outlined aiming at testing the bias due to omitted variables in vector autoregressions. The procedure consists first of filtering a vector of omitted variables and then testing the bias. The test does not rely on the availability of the omitted variables, and is based on a comparison between maximum-likelihood with Kalman filter vector autoregression and linear vector autoregression estimates. The empirical part considers two illustrative examples: a univariate regression analysis, based on the rational expectation-augmented Phillips curve; and a VAR with output, inflation and interest rates where a “price puzzle” arises.

In this paper, we propose a novel varying coefficient partially nonlinear multiplicative model (VCPNLMM) to handle positive response data in a flexible way. The unknown parameters and functions arising in the model are estimated by a local least product relative error (LLPRE) algorithm which is developed based on the technique of the local kernel smoothing. With the help of quadratic approximation lemma and Lyapunov’s central limit theorem, the convergence properties of the proposed estimators are established. A new goodness-of-fit test is proposed to check whether the coefficient functions are constants or not. Experiments and the real data analysis are conducted to illustrate the performance of the new estimators and testing procedures.