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.

scholarly journals SMALL BANDWIDTH ASYMPTOTICS FOR DENSITY-WEIGHTED AVERAGE DERIVATIVES

2013 ◽  
Vol 30 (1) ◽  
pp. 176-200 ◽  
Author(s):  
Matias D. Cattaneo ◽  
Richard K. Crump ◽  
Michael Jansson
Keyword(s):  
Weighted Average ◽  
Standard Errors ◽  
Monte Carlo Experiment ◽  
Finite Sample ◽  
Small Bandwidth ◽  
Nominal Coverage ◽  
Error Formulas ◽  
Coverage Rates ◽  
Asymptotic Validity ◽  
Average Derivative

This paper proposes (apparently) novel standard error formulas for the density-weighted average derivative estimator of Powell, Stock, and Stoker (Econometrica 57, 1989). Asymptotic validity of the standard errors developed in this paper does not require the use of higher-order kernels, and the standard errors are “robust” in the sense that they accommodate (but do not require) bandwidths that are smaller than those for which conventional standard errors are valid. Moreover, the results of a Monte Carlo experiment suggest that the finite sample coverage rates of confidence intervals constructed using the standard errors developed in this papercoincide (approximately) with the nominal coverage rates across a nontrivial range of bandwidths.

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.

scholarly journals Error Characteristic Analysis of Fluid Momentum Law Test Apparatus

2020 ◽  
Vol 11 (1) ◽  
pp. 90
Author(s):  
Song Yang ◽  
Xianyong Zhu ◽  
Hui Wang
Keyword(s):  
Measurement Error ◽  
Control Method ◽  
Theoretical Research ◽  
Structural Deformation ◽  
Error Characteristic ◽  
Characteristic Analysis ◽  
Jet Impact ◽  
Effect Theory ◽  
Characteristic Points ◽  
Periodic Error

The flat-plate momentum test bench is a widely used experimental device in the verification of the momentum law of fluid mechanics, and its error characteristics are of positive significance for theoretical research and engineering innovation and expansion. The SPH-FEM coupling algorithm and spectrum analysis method are used to calculate and analyze the displacement response and spectrum characteristics of the characteristic points of the sensor under different jet loads. Based on them, the cause, classification, law, scope, influence and control method of the measurement error of the system are discussed and analyzed with the application of the error theory and the lateral effect theory of strain gauges; combined with physical experiments, the relevant analysis methods and conclusions are verified. The results show that the measurement error of the system includes linear error and periodic error. Structural deformation in the direction of jet impact is the main source of linear error; linear error increases with the increase of jet loads. Meanwhile, periodic vibration in non-jet direction is the main cause of periodic error, and the periodic error decreases with the increase of jet loads.

Asymptotic properties of stereological estimators of volume fraction for stationary random sets

1982 ◽  
Vol 19 (1) ◽  
pp. 111-126 ◽  
Author(s):  
Shigeru Mase
Keyword(s):  
Volume Fraction ◽  
Asymptotic Variance ◽  
Asymptotic Properties ◽  
Parametric Estimation ◽  
Random Sets ◽  
Stationary Time Series ◽  
Boolean Models ◽  
Window Functions ◽  
Spectral Density Functions ◽  
Point Estimators

We shall discuss asymptotic properties of stereological estimators of volume (area) fraction for stationary random sets (in the sense of Matheron) under natural and general assumptions. Results obtained are strong consistency, asymptotic normality, and asymptotic unbiasedness and consistency of asymptotic variance estimators. The method is analogous to the non-parametric estimation of spectral density functions of stationary time series using window functions. Proofs are given for areal estimators, but they are also valid for lineal and point estimators with slight modifications. Finally we show that stationary Boolean models satisfy the relevant assumptions reasonably well.

On estimation of the integrals of certain functions of spectral density

1980 ◽  
Vol 17 (01) ◽  
pp. 73-83 ◽  
Author(s):  
Masanobu Taniguchi
Keyword(s):  
Continuous Function ◽  
Spectral Density ◽  
Stationary Process ◽  
Asymptotic Variance ◽  
Asymptotic Properties ◽  
Gaussian Stationary Process

Let g(x) be the spectral density of a Gaussian stationary process. Then, for each continuous function ψ (x) we shall give an estimator of whose asymptotic variance is O(n –1), where Φ(·) is an appropriate known function. Also we shall investigate the asymptotic properties of its estimator.

ADMISSIBLE, SIMILAR TESTS: A CHARACTERIZATION

2019 ◽  
Vol 36 (2) ◽  
pp. 347-366 ◽  
Author(s):  
José Luis Montiel Olea
Keyword(s):  
Weight Function ◽  
Instrumental Variables ◽  
Structural Parameters ◽  
Average Power ◽  
Nuisance Parameter ◽  
Weighted Average ◽  
Necessary Condition ◽  
Ratio Test ◽  
Finite Sample ◽  
Characterization Result

This article studies a classical problem in statistical decision theory: a hypothesis test of a sharp null in the presence of a nuisance parameter. The main contribution of this article is a characterization of two finite-sample properties often deemed reasonable in this environment: admissibility and similarity. Admissibility means that a test cannot be improved uniformly over the parameter space. Similarity requires the null rejection probability to be unaffected by the nuisance parameter.The characterization result has two parts. The first part—established by Chernozhukov, Hansen, and Jansson (2009, Econometric Theory 25, 806–818)—states that maximizing weighted average power (WAP) subject to a similarity constraint suffices to generate admissible, similar tests. The second part—hereby established—states that constrained WAP maximization is (essentially) a necessary condition for a test to be admissible and similar. The characterization result shows that choosing an admissible, similar test is tantamount to selecting a particular weight function to report weighted average power. This result applies to full vector inference with a nuisance parameter, not to subvector inference.The article also revisits the theory of testing in the instrumental variables model. Specifically—and in light of the relevance of the weighted average power criterion in the main theoretical result—the article suggests a weight function for the structural parameters of the homoskedastic instrumental variables model, based on the priors proposed by Chamberlain (2007). The corresponding test is, by construction, admissible and similar. In addition, the test is shown to have finite- and large-sample properties comparable to those of the conditional likelihood ratio test.

scholarly journals Gradient and Likelihood Ratio Tests in Cure Rate Models

2016 ◽  
Vol 5 (4) ◽  
pp. 9 ◽  
Author(s):  
Hérica P. A. Carneiro ◽  
Dione M. Valença
Keyword(s):  
Likelihood Ratio ◽  
Asymptotic Properties ◽  
Information Matrix ◽  
Survival Models ◽  
Finite Sample ◽  
Cure Rate ◽  
Time Model ◽  
Cure Rate Models ◽  
Large Sample ◽  
Finite Samples

In some survival studies part of the population may be no longer subject to the event of interest. The called cure rate models take this fact into account. They have been extensively studied for several authors who have proposed extensions and applications in real lifetime data. Classic large sample tests are usually considered in these applications, especially the likelihood ratio. Recently  a new test called \textit{gradient test} has been proposed. The gradient statistic shares the same asymptotic properties with the classic likelihood ratio and does not involve knowledge of the information matrix, which can be an advantage in survival models. Some simulation studies have been carried out to explore the behavior of the gradient test in finite samples and compare it with the classic tests in different models. However little is known about the properties of these large sample tests in finite sample for cure rate models. In this work we  performed a simulation study based on the promotion time model with Weibull distribution, to assess the performance of likelihood ratio and gradient tests in finite samples. An application is presented to illustrate the results.

scholarly journals Heterogeneous individual risk modelling of recurrent events

Biometrika ◽  
2020 ◽  
Author(s):  
Huijuan Ma ◽  
Limin Peng ◽  
Chiung-Yu Huang ◽  
Haoda Fu
Keyword(s):  
Recurrent Events ◽  
Asymptotic Properties ◽  
Dynamic Modelling ◽  
Individual Risk ◽  
Simulation Studies ◽  
Finite Sample ◽  
Risk Modelling ◽  
Modelling Framework ◽  
Proposed Model

Summary Progression of chronic disease is often manifested by repeated occurrences of disease-related events over time. Delineating the heterogeneity in the risk of such recurrent events can provide valuable scientific insight for guiding customized disease management. We propose a new sensible measure of individual risk of recurrent events and present a dynamic modelling framework thereof, which accounts for both observed covariates and unobservable frailty. The proposed modelling requires no distributional specification of the unobservable frailty, while permitting exploration of the dynamic effects of the observed covariates. We develop estimation and inference procedures for the proposed model through a novel adaptation of the principle of conditional score. The asymptotic properties of the proposed estimator, including the uniform consistency and weak convergence, are established. Extensive simulation studies demonstrate satisfactory finite-sample performance of the proposed method. We illustrate the practical utility of the new method via an application to a diabetes clinical trial that explores the risk patterns of hypoglycemia in type 2 diabetes patients.

scholarly journals SEMIPARAMETRIC ESTIMATION WITH GENERATED COVARIATES

2015 ◽  
Vol 32 (5) ◽  
pp. 1140-1177 ◽  
Author(s):  
Enno Mammen ◽  
Christoph Rothe ◽  
Melanie Schienle
Keyword(s):  
Nonlinear Models ◽  
Asymptotic Variance ◽  
Asymptotic Properties ◽  
Control Variable ◽  
Semiparametric Estimation ◽  
Nuisance Parameters ◽  
Infinite Dimensional ◽  
Asymptotically Normal ◽  
Endogenous Covariates ◽  
Nonstandard Problem

We study a general class of semiparametric estimators when the infinite-dimensional nuisance parameters include a conditional expectation function that has been estimated nonparametrically using generated covariates. Such estimators are used frequently to e.g., estimate nonlinear models with endogenous covariates when identification is achieved using control variable techniques. We study the asymptotic properties of estimators in this class, which is a nonstandard problem due to the presence of generated covariates. We give conditions under which estimators are root-nconsistent and asymptotically normal, derive a general formula for the asymptotic variance, and show how to establish validity of the bootstrap.

On estimation of the integrals of certain functions of spectral density

1980 ◽  
Vol 17 (1) ◽  
pp. 73-83 ◽  
Author(s):  
Masanobu Taniguchi
Keyword(s):  
Continuous Function ◽  
Spectral Density ◽  
Stationary Process ◽  
Asymptotic Variance ◽  
Asymptotic Properties ◽  
Gaussian Stationary Process

Let g(x) be the spectral density of a Gaussian stationary process. Then, for each continuous function ψ (x) we shall give an estimator of whose asymptotic variance is O(n–1), where Φ(·) is an appropriate known function. Also we shall investigate the asymptotic properties of its estimator.

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