統計解析R たぶんpart3くらい

統計解析R たぶんpart3くらい (587ﾚｽ)
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299: デフォルトの名無しさん [] 2019/09/13(金) 20:17:51.16 ID:wTJZs2gr

## Convex on Rails
多分、[村人の定理](https://en.wikipedia.org/wiki/Mathematical_folklore)
同値な関数達
``` {r}
ebdf_0 = function (xi) {
n = length (xi); qi = cumsum (sort (xi));
function (x) { purrr::reduce (.init = 0, .x = 1 : n, .f = function (out, j) {
pmax (out, j * x - qi [j]); }) / n; }; }; ebdf_1 = function (xi) {
n = length (xi); function (x) {
purrr::reduce (.init = 0, .x = xi, .f = function (out, xi) {
out + prelu (x - xi); }) / n; }; }; ebdf_huge = function (xi) {
n = length (xi); function (x) {
purrr::reduce (.init = 0, .x = 1 : n, .f = function (out, j) {
purrr::reduce (.init = out, .x = combn (1 : n, j, simplify = F), function (out, js) { pmax (out, j * x - sum (xi [js])); }); }) / n; }; };
ebdf_2 = function (xi) { n = length (xi); xi = sort (xi); qi = cumsum (xi);
function (x) { purrr::reduce (.init = n * x - qi [n], .x = n : 1, .f = function (out, j) {
out - plure ((out + qi [j]) / j - xi [j]); }) / n; }; };
dog_data = with (big_data, {
equal = testthat::expect_equal; xi = c (- 1, 0, 2, 3); test ('ebdf', {
doit = function (xi) { bdf_0 = ebdf_0 (xi); bdf_1 = ebdf_1 (xi);
bdf_2 = ebdf_2 (xi); bdf_huge = ebdf_huge (xi);
x = seq (min (xi) - 1, max (xi) + 1, len = 1e+3);
equal (bdf_0 (x), bdf_1 (x)); equal (bdf_0 (x), bdf_2 (x));
if (size (xi) < 5) { equal (bdf_0 (x), bdf_huge (x)); } }; doit (xi);
n = 10; doit (c (rnorm (n, - 1, 1), rnorm (n, 1, 2))); });
add (big_data, xi = xi, equal = equal); });
```
続く

http://mevius.5ch.net/test/read.cgi/tech/1340339592/299

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