Partial Functional Linear Regression Model Research Articles

Robust estimation for partial functional linear regression models based on FPCA and weighted composite quantile regression

Abstract In this paper, we consider a novel estimation for partial functional linear regression models. The functional principal component analysis method is employed to estimate the slope function and the functional predictive variable, respectively. An efficient estimation based on principal component basis function approximation is used for minimizing the proposed weighted composite quantile regression (WCQR) objective function. Since the proposed WCQR involves a vector of weights, we develop a computational strategy for data-driven selection of the optimal weights. Under some mild conditions, the theoretical properties of the proposed WCQR method are obtained. The simulation study and a real data analysis are provided to illustrate the numerical performance of the resulting estimators.

Composite Quantile Estimation in Partial Functional Linear Regression Model Based on Polynomial Spline

Composite Quantile Estimation in Partial Functional Linear Regression Model Based on Polynomial Spline

Extreme quantile estimation for partial functional linear regression models with heavy-tailed distributions.

In this article, we propose a novel estimator of extreme conditional quantiles in partial functional linear regression models with heavy-tailed distributions. The conventional quantile regression estimators are often unstable at the extreme tails due to data sparsity, especially for heavy-tailed distributions. We first estimate the slope function and the partially linear coefficient using a functional quantile regression based on functional principal component analysis, which is a robust alternative to the ordinary least squares regression. The extreme conditional quantiles are then estimated by using a new extrapolation technique from extreme value theory. We establish the asymptotic normality of the proposed estimator and illustrate its finite sample performance by simulation studies and an empirical analysis of diffusion tensor imaging data from a cognitive disorder study.

Rank method for partial functional linear regression models

In this paper, we consider rank estimation for partial functional linear regression models based on functional principal component analysis. The proposed rank-based method is robust to outliers in the errors and highly efficient under a wide range of error distributions. The asymptotic properties of the resulting estimators are established under some regularity conditions. A simulation study conducted to investigate the finite sample performance of the proposed estimators shows that the proposed rank method performs well. Furthermore, the proposed methodology is illustrated by means of an analysis of the Berkeley growth data.

Rank-Based Test for Partial Functional Linear Regression Models

This paper investigates the hypothesis test of the parametric component in partial functional linear regression models. Based on a rank score function, the authors develop a rank test using functional principal component analysis, and establish the asymptotic properties of the resulting test under null and local alternative hypotheses. A simulation study shows that the proposed test procedure has good size and power with finite sample sizes. The authors also present an illustration through fitting the Berkeley Growth Data and testing the effect of gender on the height of kids.

Test for the parametric part in partial functional linear regression based on B-spline

In this paper, we investigate the hypothesis test of the parametric component in partial functional linear regression model based on B-spline. The test statistic is constructed by using the residual sums of squares under the null and alternative hypothesis. We show that the limiting distribution of the test statistic under the null hypothesis is the chi-square distribution. Besides, as the sample size goes to infinity, we prove that the power of the proposed test approaches 1. The finite sample performance of our test is evaluated by a simulation study. Also, we compare our method with existing method.

Composite quantile estimation in partial functional linear regression model with dependent errors

In this paper, we consider composite quantile estimation for the partial functional linear regression model with errors from a short-range dependent and strictly stationary linear processes. The functional principal component analysis method is employed to estimate the slope function and the functional predictive variable, respectively. Under some regularity conditions, we obtain the optimal convergence rate of the slope function, and the asymptotic normality of the parameter vector. Simulation studies demonstrate that the proposed new estimation method is robust and works much better than the least squares based method when there are outliers in the dataset or the autoregressive error distribution follows a heavy-tailed distribution. Finally, we apply the proposed methodology to electricity consumption data.

Empirical Likelihood Inference for Partial Functional Linear Regression Models Based on B-spline

In this paper, we apply empirical likelihood method to infer for the regression parameters in the partial functional linear regression models based on B-spline. We prove that the empirical log-likelihood ratio for the regression parameters converges in law to a weighted sum of independent chi-square distributions. Our simulation shows that the proposed empirical likelihood method produces more accurate confidence regions in terms of coverage probability than the asymptotic normality method.

Parameter regimes in partial functional panel regression

A new partial functional linear regression model for panel data with time varying parameters is introduced. The parameter vector of the multivariate model component is allowed to be completely time varying while the function-valued parameter of the functional model component is assumed to change over K unknown parameter regimes. Consistency is derived for the suggested estimators and for the classification procedure used to detect the K unknown parameter regimes. Additionally, the convergence rates of the estimators are derived under a double asymptotic differentiating between asymptotic scenarios depending on the relative order of the panel dimensions n and T. The statistical model is motivated by a real data application considering the so-called “idiosyncratic volatility puzzle” using high frequency data from the S&P500.

A test of linearity in partial functional linear regression

This paper investigates the hypothesis test of the parametric component in partial functional linear regression. We propose a test procedure based on the residual sums of squares under the null and alternative hypothesis, and establish the asymptotic properties of the resulting test. A simulation study shows that the proposed test procedure has good size and power with finite sample sizes. Finally, we present an illustration through fitting the Berkeley growth data with a partial functional linear regression model and testing the effect of gender on the height of kids.

One-day-ahead daily power forecasting of photovoltaic systems based on partial functional linear regression models

The intra-day time-varying pattern of solar data is more informative than the aggregated mean daily data. However, most of the traditional forecasting models often construct the 1-day ahead daily power forecast based on its historical daily averages but ignore the information from its intra-day dynamic pattern. Intuitively, the use of aggregated data could cause certain loss of information in forecasting, which in turn adversely affects forecasting accuracy. In order to make use of the valuable trajectory information of the power output within a day, this paper suggests a partial functional linear regression model (PFLRM) for forecasting the daily power output of PV systems. The PFLRM is a generalization of the traditional multiple linear regression model but enables to model nonlinearity structure. Compared to the neural network models that are often criticized by the requirements of past experience and reliable knowledge in the design of network architecture, the suggested method only involves a few parameter estimates. A regularized algorithm was used to estimate the PFLRM parameters. It is shown that the regularized PFLRM improves the forecast accuracy of power output over the traditional multiple linear regression and neural network models. The results were validated based on a 2.1 kW grid connected PV system.

Polynomial spline estimation for partial functional linear regression models

Because of its orthogonality, interpretability and best representation, functional principal component analysis approach has been extensively used to estimate the slope function in the functional linear model. However, as a very popular smooth technique in nonparametric/semiparametric regression, polynomial spline method has received little attention in the functional data case. In this paper, we propose the polynomial spline method to estimate a partial functional linear model. Some asymptotic results are established, including asymptotic normality for the parameter vector and the global rate of convergence for the slope function. Finally, we evaluate the performance of our estimation method by some simulation studies.

Varying coefficient partially functional linear regression models

By relaxing the linearity assumption in partial functional linear regression models, we propose a varying coefficient partially functional linear regression model (VCPFLM), which includes varying coefficient regression models and functional linear regression models as its special cases. We study the problem of functional parameter estimation in a VCPFLM. The functional parameter is approximated by a polynomial spline, and the spline coefficients are estimated by the ordinary least squares method. Under some regular conditions, we obtain asymptotic properties of functional parameter estimators, including the global convergence rates and uniform convergence rates. Simulation studies are conducted to investigate the performance of the proposed methodologies.