A weighted Fama-MacBeth two-step panel regression procedure: asymptotic properties, finite-sample adjustment, and performance

2020 ◽  
Vol 37 (2) ◽  
pp. 347-360
Author(s):  
Kyuseok Lee
Keyword(s):  
Asymptotic Distribution ◽  
Standard Error ◽  
Asymptotic Properties ◽  
Formal Proof ◽  
Error Estimator ◽  
Panel Regression ◽  
Finite Sample ◽  
Asymptotic Results ◽  
Content Type ◽  
Regression Procedure

Purpose In a recent paper, Yoon and Lee (2019) (YL hereafter) propose a weighted Fama and MacBeth (FMB hereafter) two-step panel regression procedure and provide evidence that their weighted FMB procedure produces more efficient coefficient estimators than the usual unweighted FMB procedure. The purpose of this study is to supplement and improve their weighted FMB procedure, as they provide neither asymptotic results (i.e. consistency and asymptotic distribution) nor evidence on how close their standard error estimator is to the true standard error. Design/methodology/approach First, asymptotic results for the weighted FMB coefficient estimator are provided. Second, a finite-sample-adjusted standard error estimator is provided. Finally, the performance of the adjusted standard error estimator compared to the true standard error is assessed. Findings It is found that the standard error estimator proposed by Yoon and Lee (2019) is asymptotically consistent, although the finite-sample-adjusted standard error estimator proposed in this study works better and helps to reduce bias. The findings of Yoon and Lee (2019) are confirmed even when the average R2 over time is very small with about 1% or 0.1%. Originality/value The findings of this study strongly suggest that the weighted FMB regression procedure, in particular the finite-sample-adjusted procedure proposed here, is a computationally simple but more powerful alternative to the usual unweighted FMB procedure. In addition, to the best of the authors’ knowledge, this is the first study that presents a formal proof of the asymptotic distribution for the FMB coefficient estimator.

THE NONSTATIONARY FRACTIONAL UNIT ROOT

1999 ◽  
Vol 15 (4) ◽  
pp. 549-582 ◽  
Author(s):  
Katsuto Tanaka
Keyword(s):  
Unit Root ◽  
Asymptotic Properties ◽  
Test Statistics ◽  
Finite Sample ◽  
Asymptotic Results ◽  
Simulation Experiments ◽  
Normality Assumption ◽  
Asymptotically Efficient ◽  
Uniformly Most Powerful ◽  
Fractional Unit

This paper deals with a scalar I(d) process {yj}, where the integration order d is any real number. Under this setting, we first explore asymptotic properties of various statistics associated with {yj}, assuming that d is known and is greater than or equal to ½. Note that {yj} becomes stationary when d < ½, whose case is not our concern here. It turns out that the case of d = ½ needs a separate treatment from d > ½. We then consider, under the normality assumption, testing and estimation for d, allowing for any value of d. The tests suggested here are asymptotically uniformly most powerful invariant, whereas the maximum likelihood estimator is asymptotically efficient. The asymptotic theory for these results will not assume normality. Unlike in the usual unit root problem based on autoregressive models, standard asymptotic results hold for test statistics and estimators, where d need not be restricted to d ≥ ½. Simulation experiments are conducted to examine the finite sample performance of both the tests and estimators.

Estimation Uncertainty in the Determination of the Master Curve Reference Temperature

2010 ◽  
Author(s):  
T.-L. Sam Sham ◽  
Daniel R. Eno
Keyword(s):  
Standard Error ◽  
Master Curve ◽  
Asymptotic Properties ◽  
Test Methods ◽  
Reference Temperature ◽  
Finite Sample ◽  
Estimation Uncertainty ◽  
Single Temperature ◽  
Rigorous Treatment ◽  
Temperature Test

The Master Curve Reference Temperature, T0, characterizes the fracture performance of structural steels in the ductile-to-brittle transition region. For a given material, this reference temperature is estimated via fracture toughness testing. A methodology is presented to compute the standard error of an estimated T0 value from a finite sample of toughness data, in a unified manner for both single temperature and multiple temperature test methods. Using the asymptotic properties of maximum likelihood estimators, closed-form expressions for the standard error of the estimate of T0 are presented for both test methods. This methodology includes statistically rigorous treatment of censored data, which represents an advance over the current ASTM E1921 methodology. Through Monte Carlo simulations of realistic single temperature and multiple temperature test plans, the recommended likelihood-based procedure is shown to provide better statistical performance than the methods in the ASTM E1921 standard.

Procedure for Uncertainty Estimation in Determining the Master Curve Reference Temperature1

2013 ◽  
Vol 135 (5) ◽  
Author(s):  
T.-L. Sham ◽  
Daniel R. Eno
Keyword(s):  
Standard Error ◽  
Master Curve ◽  
Asymptotic Properties ◽  
Test Methods ◽  
Test Method ◽  
Reference Temperature ◽  
Finite Sample ◽  
Transition Range ◽  
Single Temperature ◽  
Temperature Test

The master curve reference temperature, T0, characterizes the fracture performance of structural steels in the ductile-to-brittle transition region. For a given material, this reference temperature is estimated via fracture toughness testing. A methodology is presented to compute the standard error of an estimated T0 value from a finite sample of toughness data, in a unified manner for both single temperature and multiple temperature test methods. Using the asymptotic properties of maximum likelihood estimators, closed-form expressions for the standard error of the estimate of T0 are presented for both test methods. This methodology includes statistically rigorous treatment of censored data, which represents an advance over the current ASTM E1921 methodology (“E1921-10, Standard Test Method for Determination of Reference Temperature, T0, for Ferritic Steels in the Transition Range,” ASTM International, West Conshohocken, PA, 2010). Through Monte Carlo simulations of realistic single temperature and multiple temperature test plans, the recommended likelihood-based procedure is shown to provide better statistical performance than the methods in the ASTM E1921 standard.

The Korteweg-de Vries equation and water waves. Solutions of the equation. Part 1

1973 ◽  
Vol 59 (4) ◽  
pp. 721-736 ◽  
Author(s):  
Harvey Segur
Keyword(s):  
Water Waves ◽  
Large Time ◽  
Vries Equation ◽  
Asymptotic Properties ◽  
Series Representation ◽  
Convergent Series ◽  
Asymptotic Results ◽  
De Vries ◽  
Method Of Solution

The method of solution of the Korteweg–de Vries equation outlined by Gardneret al.(1967) is exploited to solve the equation. A convergent series representation of the solution is obtained, and previously known aspects of the solution are related to this general form. Asymptotic properties of the solution, valid for large time, are examined. Several simple methods of obtaining approximate asymptotic results are considered.

Estimation of P(X

2017 ◽  
Vol 34 (7) ◽  
pp. 1111-1122 ◽  
Author(s):  
Soumya Roy ◽  
Biswabrata Pradhan ◽  
E.V. Gijo
Keyword(s):  
Maximum Likelihood ◽  
Censored Data ◽  
Quality Characteristic ◽  
Logistic Distribution ◽  
Type Ii ◽  
Finite Sample ◽  
Data Set ◽  
Content Type ◽  
Type Ii Censored Data ◽  
Interval Estimators

Purpose The purpose of this paper is to compare various methods of estimation of P(X<Y) based on Type-II censored data, where X and Y represent a quality characteristic of interest for two groups. Design/methodology/approach This paper assumes that both X and Y are independently distributed generalized half logistic random variables. The maximum likelihood estimator and the uniformly minimum variance unbiased estimator of R are obtained based on Type-II censored data. An exact 95 percent maximum likelihood estimate-based confidence interval for R is also provided. Next, various Bayesian point and interval estimators are obtained using both the subjective and non-informative priors. A real life data set is analyzed for illustration. Findings The performance of various point and interval estimators is judged through a detailed simulation study. The finite sample properties of the estimators are found to be satisfactory. It is observed that the posterior mean marginally outperform other estimators with respect to the mean squared error even under the non-informative prior. Originality/value The proposed methodology can be used for comparing two groups with respect to a suitable quality characteristic of interest. It can also be applied for estimation of the stress-strength reliability, which is of particular interest to the reliability engineers.

scholarly journals Realized Multi-Power Variation Process for Jump Detection in the Nigerian All Share Index

2021 ◽  
Vol 52 (3) ◽  
pp. 397-412
Author(s):  
Mabel Adeosun ◽  
Olabisi Ugbebor
Keyword(s):  
Stochastic Volatility ◽  
Stochastic Models ◽  
Asymptotic Properties ◽  
Higher Order ◽  
Asymptotic Results ◽  
Jump Detection ◽  
Limit Distributions ◽  
Price Process ◽  
Variation Process ◽  
Asymptotic Variances

In this paper, we studied the particular cases of higher-order realized multipower variation process, their asymptotic properties comprising the probability limits and limit distributions were highlighted. The respective asymptotic variances of the limit distributions were obtained and jump detection models were developed from the asymptotic results. The models were obtained from the particular cases of the higher-order of the realized multipower variation process, in a class of continuous stochastic volatility semimartingale process. These are extensions of the method of jump detection by Barndorff-Nielsen and Shephard (2006), for large discrete data. An Empirical Application of the models to the Nigerian All Share Index (NASI) data shows that the models are robust to jumps and suggest that stochastic models with added jump components will give a better representation of the NASI price process.

scholarly journals Profile Inferences on Restricted Additive Partially Linear EV Models

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Xiuli Wang
Keyword(s):  
Least Squares ◽  
Asymptotic Distribution ◽  
The Other ◽  
Finite Sample ◽  
Test Statistic ◽  
Two Stage ◽  
Chi Square ◽  
Partially Linear ◽  
Profile Least Squares ◽  
Restricted Estimator

We consider the testing problem for the parameter and restricted estimator for the nonparametric component in the additive partially linear errors-in-variables (EV) models under additional restricted condition. We propose a profile Lagrange multiplier test statistic based on modified profile least-squares method and two-stage restricted estimator for the nonparametric component. We derive two important results. One is that, without requiring the undersmoothing of the nonparametric components, the proposed test statistic is proved asymptotically to be a standard chi-square distribution under the null hypothesis and a noncentral chi-square distribution under the alternative hypothesis. These results are the same as the results derived by Wei and Wang (2012) for their adjusted test statistic. But our method does not need an adjustment and is easier to implement especially for the unknown covariance of measurement error. The other is that asymptotic distribution of proposed two-stage restricted estimator of the nonparametric component is asymptotically normal and has an oracle property in the sense that, though the other component is unknown, the estimator performs well as if it was known. Some simulation studies are carried out to illustrate relevant performances with a finite sample. The asymptotic distribution of the restricted corrected-profile least-squares estimator, which has not been considered by Wei and Wang (2012), is also investigated.

The asymptotic distribution of the Net Benefit estimator in presence of right-censoring

2021 ◽  
pp. 096228022110370
Author(s):  
Brice Ozenne ◽  
Esben Budtz-Jørgensen ◽  
Julien Péron
Keyword(s):  
Asymptotic Distribution ◽  
Nuisance Parameter ◽  
Real Data ◽  
R Package ◽  
Right Censoring ◽  
Drop Out ◽  
Net Benefit ◽  
Asymptotic Results ◽  
Finite Samples ◽  
Benefit Risk Assessment

The benefit–risk balance is a critical information when evaluating a new treatment. The Net Benefit has been proposed as a metric for the benefit–risk assessment, and applied in oncology to simultaneously consider gains in survival and possible side effects of chemotherapies. With complete data, one can construct a U-statistic estimator for the Net Benefit and obtain its asymptotic distribution using standard results of the U-statistic theory. However, real data is often subject to right-censoring, e.g. patient drop-out in clinical trials. It is then possible to estimate the Net Benefit using a modified U-statistic, which involves the survival time. The latter can be seen as a nuisance parameter affecting the asymptotic distribution of the Net Benefit estimator. We present here how existing asymptotic results on U-statistics can be applied to estimate the distribution of the net benefit estimator, and assess their validity in finite samples. The methodology generalizes to other statistics obtained using generalized pairwise comparisons, such as the win ratio. It is implemented in the R package BuyseTest (version 2.3.0 and later) available on Comprehensive R Archive Network.

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.

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