"getHistory"(this, ...)TMLE.NPVI.numeric matrix which encapsulates a summary of
the TMLE procedure. If $k$ successive updates were performed,
then the matrix has either $k+1$ rows (if
cleverCovTheta was set to FALSE in the call to
tmle.npvi) or 2k+1 rows (otherwise). The
matrix has 14 columns:
"eps", values of the unique
fluctuation parameter (if cleverCovTheta was set to
FALSE in the call to tmle.npvi), or
values of the parameter involved in the fluctuation of
the joint distribution of $(X,W)$ during each update
(otherwise).
"lli", increases in likelihood
yielded by each update (if cleverCovTheta was set to
FALSE in the call to tmle.npvi), or
increases in likelihood yielded by the fluctuation of the
joint distribution of $(X,W)$ during each update (otherwise).
"mic1", empirical means of the first
component of the efficient influence curve at each step of the TMLE
procedure.
"epsT", values of the fluctuation
parameter involved in the fluctuation of the conditional distribution of
$Y$ given $(X,W)$ during each update (if cleverCovTheta
was set to TRUE in the call to tmle.npvi), or NA
(otherwise).
"lliT", successive increases in likelihood
yielded by the fluctuation of the conditional distribution of
$Y$ given $(X,W)$ during each update (if
cleverCovTheta was set to TRUE in the call to
tmle.npvi), or NA (otherwise).
"mic2", empirical means of the second
component of the efficient influence curve at each step of the TMLE
procedure.
"psi", increasingly targeted
estimators $\Psi(P_n^k)$ of the parameter of interest. The last one is the TMLE. Their computation
involves simulation of B iid copies of
$(X,W)$ under $P_n^k$.
"psi.sd", estimated standard deviations of
the increasingly targeted estimators of the parameter of
interest. The last one corresponds to the TMLE. The computation involves the same B iid copies of
$(X,W)$ as above.
"psiPn", same as "psi" except that the *observed*
$(X_i,W_i)$ are used instead of simulated copies drawn from
$P_n^k$. Of course, "psi" must be favored.
"psiPn.sd", same as "psi.sd" except that the
*observed* $(X_i,W_i)$ are used instead of simulated copies drawn
from $P_n^k$. Of course, "psi.sd" must be favored.
"mic", empirical means of the efficient
influence curve at each step of the TMLE procedure. This column is the sum of the "mic1" and "mic2" columns.
"div", total variation distances between
each pair of successive distributions constructed in the course of the
TMLE procedure.
"sic", estimated standard deviations of the efficient
influence curve at each step of the TMLE procedure.
"phi", non-parametric substitution estimator of
$\phi=\Phi(P)$ where $$\Phi(P) =
\frac{E_P[f(X)Y]}{E_P[f(X)^2]},$$
with $P$ the distribution of the random vector $(W,X,Y)$. The alternative parameter $\phi$ should be interpreted as the counterpart of $\psi$ which neglects $W$.
"sicAlt", estimated standard deviations of the efficient
influence curve of $\Psi - \Phi$ at each step of the TMLE procedure.