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I-spline

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I-spline
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In the mathematical subfield of numerical analysis, an I-spline[1][2] is a monotone spline function.

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An I-spline family of order three with four interior knots.

Definition

A family of I-spline functions of degree k with n free parameters is defined in terms of the M-splines Mi(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.

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Computation

Let j be the index such that tj  x < tj+1. Then Ii(x|k, t) is zero if i > j, and equals one if j  k + 1 > i. Otherwise,

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Applications

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).

References

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