Modal regression for fixed effects panel data

Ullah, Aman; Wang, Tao; Yao, Weixin

doi:10.1007/s00181-020-01999-w

Cited by 16 publications

(45 citation statements)

References 37 publications

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“…For Theorem 1, the first term

{false(n h^{3} false)}^{- 1 false/ 2}

in the convergence rates characterizes the magnitude of the estimation variance, while the second term

h^{2}

characterizes the magnitude of the estimation bias. It is necessary to emphasize that these results are consistent with those in Yao and Li (2014) and Ullah et al (2021) for the i.i.d. data.…”

Section: Nonlinear Modal Regressionsupporting

confidence: 89%

“…DGP 1 We generate the dependent data from the following model

Y_{t} = X_{1, t} + \exp (2 X_{2, t}) + X_{1, t} ϵ_{t},

where

X_{1, t} = - 0.3 X_{1, t - 1} + u_{1, t}

u_{1, t} \tilde{overset} scriptN (0, 0 . 8^{2})

X_{2, t} = 0.4 X_{2, t - 1} + u_{2, t}

u_{2, t} \tilde{overset} scriptN (0, 0 . 5^{2})

, and

ϵ_{t} \tilde{overset} 0.5 scriptN (- 1, 2 . 5^{2}) + 0.5 scriptN (1, 0 . 5^{2})

with

double-struckE false(ϵ_{t} false) = 0

and

M o d e false(ϵ_{t} false) = 1

(Ullah et al, 2021; Yao & Li, 2014). We then have

({, \begin{matrix} lmatrix \\ left Mean Regression: double-struckE (Y_{t} | X_{1, t}, X_{2, t}) = X_{1, t} + \exp (2 X_{2, t}), \\ left Modal Regression: M o ... \end{matrix})

…”

Section: Nonlinear Modal Regressionmentioning

confidence: 99%

“…} T converges in probability to a negative definite matrix. Kemp and Santos Silva (2012), Yao and Li (2014) and Ullah et al (2021). Condition C1 is a common condition and can be easily satisfied in practice, as there are no constraints on 𝛽.…”

Section: Asymptotic Propertymentioning

confidence: 99%

“…In addition, due to the computation burden, we do not compute the confidence interval for predictions. This should be easily carried out based on the bootstrapped modal regression method introduced in Ullah et al (2021), where we independently draw bootstrapped pseudo samples of residuals from the estimated regression, use the pseudo residual to minus the corresponding mode value to ensure the mode of residual is zero, and then follow the standard procedure as in mean regression to get the modal confidence interval. Future studies could fruitfully explore these issues further.…”

Section: Nonlinear Modal Regression For Covid‐19 Datamentioning

confidence: 99%

“…There is emerging literature on studying modal regression. Due to space limitations, we refer the interested readers to Yao and Li (2014), Chen (2018), Ullah et al (2021), and the references therein for a comprehensive review of modal regression. Notice that Khardani and Yao (2017) extended the results in Kemp and Santos Silva (2012) to put forward a nonlinear modal regression for the independent samples.…”

Section: Introductionmentioning

confidence: 99%

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Nonlinear Modal Regression for Dependent Data with Application for Predicting Covid-19

Ullah

Wang

Yao

2022

Journal of the Royal Statistical Society Series A: Statistics in Society

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In this paper, under the stationary α‐mixing dependent samples, we develop a novel nonlinear modal regression for time series sequences and establish the consistency and asymptotic property of the proposed nonlinear modal estimator with a shrinking bandwidth h under certain regularity conditions. The asymptotic distribution is shown to be identical to the one derived from the independent observations, whereas the convergence rate (nh3 in which n is the sample size) is slower than that in the nonlinear mean regression. We numerically estimate the proposed nonlinear modal regression model by the use of a modified modal expectation–maximization (MEM) algorithm in conjunction with Taylor expansion. Monte Carlo simulations are presented to demonstrate the good finite sample (prediction) performance of the newly proposed model. We also construct a specified nonlinear modal regression to match the available daily new cases and new deaths data of the COVID‐19 outbreak at the state/region level in the United States, and provide forward predictions up to 130 days ahead (from 24 August 2020 to 31 December 2020). In comparison to the traditional nonlinear regressions, the suggested model can fit the COVID‐19 data better and produce more precise predictions. The prediction results indicate that there are systematic differences in spreading distributions among states/regions. For most western and eastern states, they have many serious COVID‐19 burdens compared to Midwest. We hope that the built nonlinear modal regression can help policymakers to implement fast actions to curb the spread of the infection, avoid overburdening the health system and understand the development of COVID‐19 from some points.

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“…For Theorem 1, the first term

{false(n h^{3} false)}^{- 1 false/ 2}

in the convergence rates characterizes the magnitude of the estimation variance, while the second term

h^{2}

characterizes the magnitude of the estimation bias. It is necessary to emphasize that these results are consistent with those in Yao and Li (2014) and Ullah et al (2021) for the i.i.d. data.…”

Section: Nonlinear Modal Regressionsupporting

confidence: 89%

“…DGP 1 We generate the dependent data from the following model