Asymptotic properties of a nonparametric conditional density estimator in the local linear estimation for functional data via a functional single-index model

This paper deals with the conditional density estimator of a real response variable given a functional random variable(i.e.,takes values in an infinite-dimensional space).Specifically,we focus on the functional index model,and this approach represents a good compromise between nonparametric and parametric models.Then we give under general conditions and when the variables are independent,the quadratic error and asymptotic normality of estimator by local linear method,based on the single-index structure.Finally,wecomplete these theoretical advances by some simulation studies showing both the practical result of the local linear method and the good behaviour for finite sample sizes of the estimator and of the Monte Carlo methods to create functional pseudo-confidence area.

Local Linear Estimation by TSLS with Variable Bandwidth for Semi-parametric Simultaneous Equation Models in Econometrics

Econometric simultaneous equation models play an important role in making economic policies, analyzing economic structure and economic forecasting. This paper presents local linear estimators by TSLS with variable bandwidth for every structural equation in semi-parametric simultaneous equation models in econometrics. The properties under large sample size were studied by using the asymptotic theory when all variables were random. The results show that the estimators of the parameters have consistency and asymptotic normality, and their convergence rates are equal to n^-1/2. And the estimator of the nonparametric function has the consistency and asymptotic normality in interior points and its rate of convergence is equal to the optimal convergence rate of the nonparametric function estimation.

Local Hybrid Linear State Estimation for Electric Power Systems Using Stream Processing

The increasing penetration of renewable energy resources with highly fluctuating outputs has placed increasing concern on the accuracy and timeliness of electric power system state estimation(SE).Meanwhile,we note that only a fraction of system states fluctuate at the millisecond level and require to be updated.As such,refreshing only those states with significant variation would enhance the computational efficiency of SE and make fast-continuous update of states possible.However,this is difficult to achieve with conventional SE methods,which generally refresh states of the entire system every 4–5 s.In this context,we propose a local hybrid linear SE framework using stream processing,in which synchronized measurements received from phasor measurement units(PMUs),and trigger/timingmode measurements received from remote terminal units(RTUs)are used to update the associated local states.Moreover,the measurement update process efficiency and timeliness are enhanced by proposing a trigger measurement-based fast dynamic partitioning algorithm for determining the areas of the system with states requiring recalculation.In particular,non-iterative hybrid linear formulations with both RTUs and PMUs are employed to solve the local SE problem.The timeliness,accuracy,and computational efficiency of the proposed method are demonstrated by extensive simulations based on IEEE 118-,300-,and 2383-bus systems.

Asymptotic Confidence Bands for Copulas Based on the Local Linear Kernel Estimator

In this paper, we establish asymptotically optimal simultaneous confidence bands for the copula function based on the local linear kernel estimator proposed by Chen and Huang [1]. For this, we prove under smoothness conditions on the derivatives of the copula a uniform in bandwidth law of the iterated logarithm for the maximal deviation of this estimator from its expectation. We also show that the bias term converges uniformly to zero with a precise rate. The performance of these bands is illustrated by a simulation study. An application based on pseudo-panel data is also provided for modeling the dependence structure of Senegalese households’ expense data in 2001 and 2006.

Testing Linearity of Nonparametric Component in Partially Linear Model

In this paper, we propose the test statistic to check whether the nonparametric function in partially linear models is linear or not. We estimate the nonparametric function in alternative by using the local linear method, and then estimate the parameters by the two stage method. The test statistic under the null hypothesis is calculated, and it is shown to be asymptotically normal.

Testing Equality of Nonparametric Functions in Two Partially Linear Models

We propose the test statistic to check whether the nonpararnetric functions in two partially linear models are equality or not in this paper. We estimate the nonparametric function both in null hypothesis and the alternative by the local linear method, where we ignore the parametric components, and then estimate the parameters by the two stage method. The test statistic is derived, and it is shown to be asymptotically normal under the null hypothesis.

Local linear estimator for stochastic diferential equations driven by α-stable Lvy motions

We study tile local linear estimator for tile drift coefficient of stochastic differential equations driven by α-stable Levy motions observed at discrete instants. Under regular conditions, we derive the weak consis- tency and central limit theorem of the estimator. Compared with Nadaraya-Watson estimator, the local linear estimator has a bias reduction whether the kernel function is symmetric or not under different schemes. A silnu- lation study demonstrates that the local linear estimator performs better than Nadaraya-Watson estimator, especially on the boundary.

OPTIMAL INTERIOR AND LOCAL ERROR ESTIMATES OF A RECOVERED GRADIENT OF LINEAR ELEMENTS ON NONUNIFORM TRIANGULATIONS

We examine a simple averaging formula for the gradieni of linear finite elemelitsin Rd whose interpolation order in the Lq-norm is O(h2) for d < 2q and nonuniformtriangulations. For elliptic problems in R2 we derive an interior superconvergencefor the averaged gradient over quasiuniform triangulations. Local error estimatesup to a regular part of the boundary and the effect of numerical integration arealso investigated.

Innovation,financial permeation,and income inequality:From a dynamicperspective in China

Innovation is a driving force of wealth distribution.To explore its time-varying effect on income inequality,we propose a nonparametric model using the local linear dummy variable estimation(LLDVE)method.Based on province-level panel data from China spanning from 2006 to 2020,we find that innovation initially reduces income disparity until 2009,then exacerbates it from 2013 to 2016,and alleviates inequality again over 2018-2020.We further verify that financial permeation serves as a catalyst in the inequitable income distribution driven by innovation.However,this moderating effect reverses the relationship between green innovation and income inequality.This suggests that we should enhance the financial service towards all aspects of innovation beyond its support of green innovation.

ASYMPTOTIC NORMALITY OF THE NONPARAMETRIC KERNEL ESTIMATION OF THE CONDITIONAL HAZARD FUNCTION FOR LEFT-TRUNCATED AND DEPENDENT DATA

Under some mild conditions, we derive the asymptotic normality of the Nadaraya-Watson and local linear estimators of the conditional hazard function for left-truncated and dependent data. The estimators were proposed by Liang and Ould-Sa?d [1]. The results confirm the guess in Liang and Ould-Sa?d [1].

The nonparametric estimation of long memory spatio-temporal random field models

This paper considers the local linear estimation of a multivariate regression function and its derivatives for a stationary long memory(long range dependent) nonparametric spatio-temporal regression model.Under some mild regularity assumptions, the pointwise strong convergence, the uniform weak consistency with convergence rates and the joint asymptotic distribution of the estimators are established. A simulation study is carried out to illustrate the performance of the proposed estimators.

Mixtures of Semiparametric Varying Coefficient Models for Longitudinal Data with Nonignorable Dropout

Informative dropout often arise in longitudinal data. In this paper we propose a mixture model in which the responses follow a semiparametric varying coefficient random effects model and some of the regression coefficients depend on the dropout time in a non-parametric way. The local linear version of the profile-kernel method is used to estimate the parameters of the model. The proposed estimators are shown to be consistent and asymptotically normal, and the finite performance of the estimators is evaluated by numerical simulation.