Lineage

Lineage

dtfit's estimator is projected weighted nonlinear least squares on the image, one function with two bases. It grew out of the differential-transformation criteria in four stages, each fixing a limit of the one before. Every stage is runnable in the dtfit-legacy package so the evolution can be measured on one problem set.

Stage	What it does	Its limit	Where
Spectrum balance	equates the model's Maclaurin spectrum to the data's, discrete by discrete, from an intermediate polynomial	a symbolic model, an exactly determined balance, no noise averaging	dtfit_legacy.book.dsb_balance, dtfit_legacy.dsb.fit_dsb
Integral least squares, monomial basis	minimizes the integral of the squared residual with both sides in the monomial spectrum	the Hilbert-like weight matrix, condition above 1e16 by order 11	dtfit_legacy.book.lsi_integral_monomial
Integral least squares, Legendre basis	the same criterion on the orthogonal basis; condition linear in the order	the integral quadrature carries grid-dependent bias	dtfit_legacy.integral.fit_lsi
Equal areas	one area equation per window, the model's areas from its truncated spectrum	bias outside the spectrum's convergence radius	dtfit_legacy.book.eac_areas, direct form dtfit_legacy.integral.fit_eac
The image	the discrete sufficient statistic S = Phi^T (w y), G = Phi^T diag(w) Phi; fit by whitened NLLS	needs a start for a model nonlinear in its parameters	dtfit.fit, dtfit.ImageFilter

The recursive filters of the integral criteria are dtfit_legacy.streaming; their map-reduce form is dtfit_legacy.scale. The current filter and stream are dtfit.ImageFilter and dtfit.ImageStream.