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 |
phi |
|
s |
A period of the regression model. |
e |
The residuals vector. |
sigma |
Value
DELTA() |
returns the values of |
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