Arrival rate approximation by nonnegative cubic splines
Alizadeh, Farid and Noyan, Nilay and Eckstein, Jonathan and Rudolf, Gabor (2007) Arrival rate approximation by nonnegative cubic splines. (Accepted/In Press) AbstractWe describe an optimization method to approximate the arrival rate function of a nonhomogeneous Poisson process based on observed arrival data. We estimate the function by cubic splines, using an optimization model based on the maximum likelihood principle. A critical feature of the model is that the splines are constrained to be everywhere nonnegative. We enforce these constraints by using a characterization of nonnegative polynomials by positive semidefinite matrices. We also describe versions of our model that allow for periodic arrival rate functions and input data of limited time precision. We formulate the estimation problem as a convex nonlinear program, and solve it with standard nonlinear optimization packages. We present numerical results using both an actual record of email arrivals over a period of sixty weeks, and artificially generated data sets. We also present a crossvalidation procedure for determining an appropriate number of spline knots to model a set of arrival observations. Available Versions of this Item Arrival rate approximation by nonnegative cubic splines. (deposited 31 Oct 2007 08:45) [Currently Displayed]
Repository Staff Only: item control page
