In the mathematical subfield of numerical analysis, an I-spline is a monotone spline function.
A family of I-spline functions of degree k with n free parameters is defined in terms of the M-splines M<sub>i</sub>(x|k, t)
where L is the lower limit of the domain of the splines.
Since M-splines are non-negative, I-splines are monotonically non-decreasing.
Let j be the index such that t<sub>j</sub> ⤠x < t<sub>j+1</sub>. Then I<sub>i</sub>(x|k, t) is zero if i > j, and equals one if j − k + 1 > i. Otherwise,
I-splines can be used as basis splines for regression analysis and data transformation when monotonicity is desired (constraining the regression coefficients to be non-negative for a non-decreasing fit, and non-positive for a non-increasing fit).