\( \newcommand{\kernelregression}{\texttt{KERNEL\_REGRESSION}} \newcommand{\objfunc}{S} \newcommand{\minage}{\alpha} \newcommand{\maxage}{\omega} \newcommand{\dprob}{q} \newcommand{\sdprob}{\tilde{\dprob}} \newcommand{\degree}{p} \newcommand{\xinfovar}[1]{\textit{#1}} \newcommand{\xinfoval}[1]{\texttt{#1}} \newcommand{\ceil}[1]{\left\lceil #1\right\rceil} \newcommand{\esm}{\hat{m}} \newcommand{\kernel}{K} \)

Kernel Regression

This build method smooths a mortality curve using local polynomial regression. Given death probabilities \(\dprob_x\) for \(x=0,1,2,\ldots,\omega\), the smoothed death probability \(\sdprob_x\) is given by \begin{equation} \sdprob_x=\left\{\begin{array}{ll} \exp\left(\esm(x)\right) & x\in [\minage,\omega]\\ \dprob_x & \mathrm{otherwise} \end{array}\right. \end{equation} where \(\omega=110\) and \(\esm(x)\) is a local polynomial regression fit to the observations \((X_i,Y_i)\) where \(X_i=i\) and \(Y_i=\log(\dprob_i)\).

Extra Information

The default behaviour can be modified by appending an extrainfo string to the buildmethod, eg KERNEL_REGRESSION:ExtraInfo. Here ExtraInfo is a comma-separated list of quoted strings of the form "Parameter=Value".

Degree
The degree \(\degree\) of the local polynomial regression can be set with the extrainfo string "Degree=\(\degree\)". The default value is \(\degree=1\).

Bandwidth
The bandwidth of the local polynomial regression can be set with the extrainfo string "Bandwidth=value" where value is either a number specifying the value or a string specifying the bandwidth selector. The default value is Bandwidth=ROT, the modified Ruppert-Sheather-Wand rule-of-thumb bandwidth selector.

Kernel
The local polynomial regression kernel function can be set with the extrainfo string "Kernel=type" where type is a kernel function code. The default value is Kernel=GAUSSIAN.

Minimum Age
The minimum age for smoothing can be set by the extrainfo string "MinAge=\(\minage\)". The default value is \(\minage=1\).