scholarly journals Quantile Regression with Generated Regressors

Econometrics ◽  
2021 ◽  
Vol 9 (2) ◽  
pp. 16
Author(s):  
Liqiong Chen ◽  
Antonio F. Galvao ◽  
Suyong Song
Keyword(s):  
Quantile Regression ◽  
Estimation Error ◽  
Asymptotic Variance ◽  
Asymptotic Properties ◽  
Estimation Procedure ◽  
Finite Sample ◽  
Testing Procedures ◽  
Engel Curves ◽  
Generated Regressors ◽  
Two Step Estimation

This paper studies estimation and inference for linear quantile regression models with generated regressors. We suggest a practical two-step estimation procedure, where the generated regressors are computed in the first step. The asymptotic properties of the two-step estimator, namely, consistency and asymptotic normality are established. We show that the asymptotic variance-covariance matrix needs to be adjusted to account for the first-step estimation error. We propose a general estimator for the asymptotic variance-covariance, establish its consistency, and develop testing procedures for linear hypotheses in these models. Monte Carlo simulations to evaluate the finite-sample performance of the estimation and inference procedures are provided. Finally, we apply the proposed methods to study Engel curves for various commodities using data from the UK Family Expenditure Survey. We document strong heterogeneity in the estimated Engel curves along the conditional distribution of the budget share of each commodity. The empirical application also emphasizes that correctly estimating confidence intervals for the estimated Engel curves by the proposed estimator is of importance for inference.

QUASI-INDIRECT INFERENCE FOR DIFFUSION PROCESSES

1998 ◽  
Vol 14 (2) ◽  
pp. 161-186 ◽  
Author(s):  
Laurence Broze ◽  
Olivier Scaillet ◽  
Jean-Michel Zakoïan
Keyword(s):  
Diffusion Processes ◽  
Asymptotic Properties ◽  
Estimation Procedure ◽  
Indirect Inference ◽  
Sampled Data ◽  
Finite Sample ◽  
Inference Procedure ◽  
Monte Carlo Experiments ◽  
Simulation Step ◽  
Finite Sample Properties

We discuss an estimation procedure for continuous-time models based on discrete sampled data with a fixed unit of time between two consecutive observations. Because in general the conditional likelihood of the model cannot be derived, an indirect inference procedure following Gouriéroux, Monfort, and Renault (1993, Journal of Applied Econometrics 8, 85–118) is developed. It is based on simulations of a discretized model. We study the asymptotic properties of this “quasi”-indirect estimator and examine some particular cases. Because this method critically depends on simulations, we pay particular attention to the appropriate choice of the simulation step. Finally, finite-sample properties are studied through Monte Carlo experiments.

scholarly journals IDENTIFYING THE BROWNIAN COVARIATION FROM THE CO-JUMPS GIVEN DISCRETE OBSERVATIONS

2012 ◽  
Vol 28 (2) ◽  
pp. 249-273 ◽  
Author(s):  
Cecilia Mancini ◽  
Fabio Gobbi
Keyword(s):  
Risk Factors ◽  
Monte Carlo ◽  
Time Horizon ◽  
Limit Theorems ◽  
Estimation Error ◽  
Asymptotic Variance ◽  
Fixed Time ◽  
Finite Sample ◽  
Discrete Observations ◽  
Measures Of Dependence

When the covariance between the risk factors of asset prices is due to both Brownian and jump components, the realized covariation (RC) approaches the sum of the integrated covariation (IC) with the sum of the co-jumps, as the observation frequency increases to infinity, in a finite and fixed time horizon. In this paper the two components are consistently separately estimated within a semimartingale framework with possibly infinite activity jumps. The threshold (or truncated) estimator $I\hat C_n $ is used, which substantially excludes from RC all terms containing jumps. Unlike in Jacod (2007, Universite de Paris-6) and Jacod (2008, Stochastic Processes and Their Applications 118, 517–559), no assumptions on the volatilities’ dynamics are required. In the presence of only finite activity jumps: 1) central limit theorems (CLTs) for $I\hat C_n $ and for further measures of dependence between the two Brownian parts are obtained; the estimation error asymptotic variance is shown to be smaller than for the alternative estimators of IC in the literature; 2) by also selecting the observations as in Hayashi and Yoshida (2005, Bernoulli 11, 359–379), robustness to nonsynchronous data is obtained. The proposed estimators are shown to have good finite sample performances in Monte Carlo simulations even with an observation frequency low enough to make microstructure noises’ impact on data negligible.

scholarly journals Communication-Efficient Modeling with Penalized Quantile Regression for Distributed Data

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
Aijun Hu ◽  
Chujin Li ◽  
Jing Wu
Keyword(s):  
Quantile Regression ◽  
Estimation Error ◽  
Asymptotic Properties ◽  
High Dimensional ◽  
Distributed Data ◽  
Local Data ◽  
High Dimensional Case ◽  
Alternating Direction ◽  
Admm Algorithm ◽  
Resistance Data

In order to deal with high-dimensional distributed data, this article develops a novel and communication-efficient approach for sparse and high-dimensional data with the penalized quantile regression. In each round, the proposed method only requires the master machine to deal with a sparse penalized quantile regression which could be realized fastly by proximal alternating direction method of multipliers (ADMM) algorithm and the other worker machines to compute the subgradient on local data. The advantage of the proximal ADMM algorithm is that it could make every parameter of iteration to have closed formula even in high-dimensional case, which greatly improves the speed of calculation. As for the communication efficiency, the proposed method does not sacrifice any statistical accuracy and provably improves the estimation error obtained by centralized method, provided the penalty levels are chosen properly. Moreover, the asymptotic properties of the proposed estimation and the convergence of the algorithm are convincible. Especially, it presents extensive experiments on both the numerical simulations and the HIV drug resistance data analysis, which all confirm the significant efficiency of our proposed method in quantile regression for distributed data by comparative and empirical analysis.

scholarly journals AVERAGE DERIVATIVE ESTIMATION UNDER MEASUREMENT ERROR

2020 ◽  
pp. 1-30 ◽  
Author(s):  
Hao Dong ◽  
Taisuke Otsu ◽  
Luke Taylor
Keyword(s):  
Measurement Error ◽  
Asymptotic Variance ◽  
Asymptotic Properties ◽  
Weighted Average ◽  
Error Characteristic ◽  
Finite Sample ◽  
Gaussian Density ◽  
Error Distributions ◽  
Error Density ◽  
Average Derivative

Abstract In this paper, we derive the asymptotic properties of the density-weighted average derivative estimator when a regressor is contaminated with classical measurement error and the density of this error must be estimated. Average derivatives of conditional mean functions are used extensively in economics and statistics, most notably in semiparametric index models. As well as ordinary smooth measurement error, we provide results for supersmooth error distributions. This is a particularly important class of error distribution as it includes the Gaussian density. We show that under either type of measurement error, despite using nonparametric deconvolution techniques and an estimated error characteristic function, we are able to achieve a $\sqrt {n}$ -rate of convergence for the average derivative estimator. Interestingly, if the measurement error density is symmetric, the asymptotic variance of the average derivative estimator is the same irrespective of whether the error density is estimated or not. The promising finite sample performance of the estimator is shown through a Monte Carlo simulation.

Asymmetric Laplace Regression: Maximum Likelihood, Maximum Entropy and Quantile Regression

2016 ◽  
Vol 5 (1) ◽  
Author(s):  
Anil K. Bera ◽  
Antonio F. Galvao ◽  
Gabriel V. Montes-Rojas ◽  
Sung Y. Park
Keyword(s):  
Maximum Likelihood ◽  
Quantile Regression ◽  
Maximum Entropy ◽  
Asymptotic Properties ◽  
Likelihood Estimation ◽  
Finite Sample ◽  
Score Functions ◽  
Finite Sample Properties ◽  
Quasi Maximum Likelihood ◽  
Joint Consideration

AbstractThis paper studies the connections among the asymmetric Laplace probability density (ALPD), maximum likelihood, maximum entropy and quantile regression. We show that the maximum likelihood problem is equivalent to the solution of a maximum entropy problem where we impose moment constraints given by the joint consideration of the mean and median. The ALPD score functions lead to joint estimating equations that delivers estimates for the slope parameters together with a representative quantile. Asymptotic properties of the estimator are derived under the framework of the quasi maximum likelihood estimation. With a limited simulation experiment we evaluate the finite sample properties of our estimator. Finally, we illustrate the use of the estimator with an application to the US wage data to evaluate the effect of training on wages.

Quantile regression models for survival data with missing censoring indicators

2021 ◽  
pp. 096228022199598
Author(s):  
Zhiping Qiu ◽  
Huijuan Ma ◽  
Jianwei Chen ◽  
Gregg E Dinse
Keyword(s):  
Quantile Regression ◽  
Regression Model ◽  
Survival Data ◽  
Asymptotic Properties ◽  
Estimating Equations ◽  
Real Data ◽  
Finite Sample ◽  
Dynamic Relationship ◽  
Quantile Regression Model ◽  
Missing Censoring Indicators

The quantile regression model has increasingly become a useful approach for analyzing survival data due to its easy interpretation and flexibility in exploring the dynamic relationship between a time-to-event outcome and the covariates. In this paper, we consider the quantile regression model for survival data with missing censoring indicators. Based on the augmented inverse probability weighting technique, two weighted estimating equations are developed and corresponding easily implemented algorithms are suggested to solve the estimating equations. Asymptotic properties of the resultant estimators and the resampling-based inference procedures are established. Finally, the finite sample performances of the proposed approaches are investigated in simulation studies and a real data application.

scholarly journals ESTIMATION FOR THE PREDICTION OF POINT PROCESSES WITH MANY COVARIATES

2017 ◽  
Vol 34 (3) ◽  
pp. 598-627 ◽  
Author(s):  
Alessio Sancetta
Keyword(s):  
Linear Combination ◽  
Point Processes ◽  
Estimation Error ◽  
Asymptotic Properties ◽  
Additive Model ◽  
Rates Of Convergence ◽  
Finite Sample ◽  
Intensity Measure ◽  
Variable Screening ◽  
The Impact

Estimation of the intensity of a point process is considered within a nonparametric framework. The intensity measure is unknown and depends on covariates, possibly many more than the observed number of jumps. Only a single trajectory of the counting process is observed. Interest lies in estimating the intensity conditional on the covariates. The impact of the covariates is modelled by an additive model where each component can be written as a linear combination of possibly unknown functions. The focus is on prediction as opposed to variable screening. Conditions are imposed on the coefficients of this linear combination in order to control the estimation error. The rates of convergence are optimal when the number of active covariates is large. As an application, the intensity of the buy and sell trades of the New Zealand Dollar futures is estimated and a test for forecast evaluation is presented. A simulation is included to provide some finite sample intuition on the model and asymptotic properties.

scholarly journals Asymmetric vector moving average models: estimation and testing

2021 ◽  
Author(s):  
Jan G. De Gooijer
Keyword(s):  
Moving Average ◽  
Likelihood Estimation ◽  
Estimation Procedure ◽  
Finite Sample ◽  
Test Statistic ◽  
Multivariate Test ◽  
Testing Procedures ◽  
Proposed Model ◽  
Moving Average Models ◽  
Global Invertibility

AbstractWe propose the class of asymmetric vector moving average (asVMA) models. The asymmetry of these models is characterized by different MA filters applied to the components of vectors of lagged positive and negative innovations. This allows for a detailed investigation of the interrelationships among past model innovations of different sign. We derive some covariance matrix properties of an asVMA model under the assumption of Gaussianity. Related to this, we investigate the global invertibility condition of the proposed model. The paper also introduces a maximum likelihood estimation procedure and a multivariate Wald-type test statistic for symmetry versus the alternative of asymmetry. The finite-sample performance of the proposed multivariate test is studied by simulation. Furthermore, we devise an exploratory test statistic based on lagged sample cross-bicovariance estimates. The estimation and testing procedures are used to uncover asymmetric effects in two US growth rates, and in three US industrial prices.

scholarly journals An autoregressive model for irregular time series of variable stars

2016 ◽  
Vol 12 (S325) ◽  
pp. 259-262
Author(s):  
Susana Eyheramendy ◽  
Felipe Elorrieta ◽  
Wilfredo Palma
Keyword(s):  
Time Series ◽  
Gravitational Lensing ◽  
Autoregressive Model ◽  
Likelihood Estimation ◽  
Estimation Procedure ◽  
Variable Stars ◽  
Light Curves ◽  
Finite Sample ◽  
Harmonic Model ◽  
Dependency Structure

AbstractThis paper discusses an autoregressive model for the analysis of irregularly observed time series. The properties of this model are studied and a maximum likelihood estimation procedure is proposed. The finite sample performance of this estimator is assessed by Monte Carlo simulations, showing accurate estimators. We implement this model to the residuals after fitting an harmonic model to light-curves from periodic variable stars from the Optical Gravitational Lensing Experiment (OGLE) and Hipparcos surveys, showing that the model can identify time dependency structure that remains in the residuals when, for example, the period of the light-curves was not properly estimated.

Sign in / Sign up

Export Citation Format

Share Document