DELTA {PerRegMod}R Documentation

Calculating the component of vector DELTA

Description

DELTA() function gives the value of the component of vector DELTA \boldsymbol{\Delta}. See Regui et al. (2024) for periodic simple regression model. \mathbf{\Delta}= \left[\begin{array}{c} \mathbf{\Delta}_1 \\ \mathbf{\Delta}_2\\ \mathbf{\Delta}_3 \end{array}\right]\ , where \mathbf{\Delta}_1 is a vector of dimension S with component \frac{n^{\frac{-1}{2} } }{\widehat{ \sigma}_s}\sum\limits_{\underset{ }{r=0}}^{m-1}\widehat{\phi}(Z_{s+Sr,t}), \mathbf{\Delta}_2 is a vector of dimension pS with component \frac{ n^{\frac{-1}{2} } }{\widehat{\sigma}_{s}}\sum\limits_{\underset{ }{r=0}}^{m-1} \widehat{\phi}(Z_{s+Sr})K_{s}^{(n)} \mathbf{X}_{s+Sr} , \mathbf{\Delta}_3 is a vector of dimension S with component \frac{n^{\frac{-1}{2} } }{2\widehat{\sigma}_{s}^{2}}\sum\limits_{\underset{ }{r=0}}^{m-1}{Z_{s+Sr} \widehat{\phi}(Z_{s+Sr})-1 }.

Usage

DELTA(x,phi,s,e,sigma)

Arguments

x

A list of independent variables with dimension p.

phi

phi_n.

s

A period of the regression model.

e

The residuals vector.

sigma

sd_estimation_for_each_s.

Value

DELTA()

returns the values of \mathbf{\Delta}. See Regui et al. (2024) for simple periodic coefficients regression model.

References

Regui, S., Akharif, A., & Mellouk, A. (2024). "Locally optimal tests against periodic linear regression in short panels." Communications in Statistics-Simulation and Computation, 1–15. doi:10.1080/03610918.2024.2314662


[Package PerRegMod version 4.4.3 Index]