This function makes use of subroutine smth.

The syntax of $smth$ is $[smo] = smth(x,y,w,span,cross)$. $x$, $y$ and $w$ are 3 vectors of length $n$ containing respectively the $x$ coordinates, the $y$ coordinates and the weights. Input parameter $span$ is a scalar in the interval (0 1] which defines the length of the elements in the local regressions.

More precisely, if $span$ is in (0 1), the length of elements in the local regressions is $m*2+1$, where $m$ is defined as the $\max([(n \times span)/2],1)$ to ensure that minimum length of the local regression is 3. Symbol $[ \cdot ]$ denotes the integer part.

Parameter $cross$ is a Boolean scalar. If it is set to true, it specifies that, to compute the local regression centered on unit $i$, unit $i$ must be deleted. Therefore, for example,

---

[1] if $m$ is 3 and $cross$ is true, the smoothed value for observation $i$ uses a local regression with $x$ coordinates $(x(i-1), x(i+1))$, $y$ coordinates $(y(i-1), y(i+1))$ and $w$ coordinates $(w(i-1), w(i+1))$, $i=2, \ldots, n-1$. The smoothed values for observation 1 is $y(2)$ and the smoothed value for observation $n$ is $y(n-1)$.

---

[2] If $m$ is 3 and $cross$ is false, the smoothed value for observations $i$ is based on a local regression with $x$ coordinates $(x(i-1), x(i), x(i+1))$, $y$ coordinates $(y(i-1), y(i), y(i+1))$ and $w$ coordinates $(w(i-1), w(1), w(i+1))$, $i=2, \ldots, n-1$. The smoothed values for observation 1 uses a local regression based on $(x(1), x(2))$, $(y(1), y(2))$, and $(w(1), w(2))$ while the smoothed value for observation $n$ uses a local regression based on $(x(n-1), x(n))$, $(y(n-1), y(n))$, and $(w(n-1), w(n))$.

---

[3] If $m=5$ and $cross$ is true, the smoothed value for observations $i$ uses a local regression based on observations $(i-2), (i-1), (i+1), (i+2)$, for $i=3, \ldots, n-2$. The smoothed values for observation 1 uses observations 2 and 3, the smoothed value for observations 2 uses observations 1, 3 and 4 ...

---

[4] If $m$ is 5 and $cross$ is false, the smoothed value for observations $i$ uses a local regression based on observations $(i-2), (i-1), i, (i+1), (i+2)$, for $i=3, \ldots, n-2$.

The smoothed values for observation 1 uses observations 1, 2 and 3, the smoothed value for observations 2 uses observations 1, 2, 3 and 4 ...

---