Table 4 Eight selection criteria formulas.

AIC

\(\left( \frac{SSE}{n} \right)\left( e \right)^{{2\left( {k + 1} \right)/n}}\)

⁷¹

FPE

\(\left( \frac{SSE}{n} \right)\frac{{n + \left( {k + 1} \right)}}{{n - \left( {k + 1} \right)}}\)

⁷²

GCV

\(\left( \frac{SSE}{n} \right)\left[ {1 - \left( {\frac{k + 1}{n}} \right)} \right]^{ - 2} .\)

⁷³

HQ

\(\left( \frac{SSE}{n} \right)\left( {\ln n} \right)^{{2\left( {k + 1} \right)/n}}\)

⁷⁴

RICE

\(\left( \frac{SSE}{n} \right)\left[ {1 - \left( {\frac{{2\left( {k + 1} \right)}}{n}} \right)} \right]^{ - 1}\)

⁷⁵

SCHWARZ

\(\left( \frac{SSE}{n} \right)n^{{\left( {k + 1} \right)/n}}\)

⁷⁶

SGMASQ

\(\left( \frac{SSE}{n} \right)\left[ {1 - \left( {\frac{k + 1}{n}} \right)} \right]^{ - 1}\)

⁷⁷

SHIBATA

\(\left( \frac{SSE}{n} \right)\frac{{n + 2\left( {k + 1} \right)}}{n}\)

⁷⁸