Non-Parametric Estimation of a Single Inflection Point in Noisy Observed Signal

Abstract

R s ∈ , and r is an unknown underlying regression function. The regression function r can be locally approximated at the point s by a polynomial of order p AbstractInflection point detection is an important yet challenging problem in science and engineering. This paper addresses the estimation of a single inflection point location in noisy observations using non-parametric polynomial regression. To address the bandwidth problem, a constrained approach is proposed to ensure having a single inflection point, thereby reducing the uncertainty in the inflection point location whereas being flexible on the shape of the underlying signal. The performance of the proposed method is evaluated through simulations. It is shown that the proposed method can effectively estimate the inflection point under high noise conditions.

Change-point estimation using shape-restricted regression splines

“…In Kachouie and Schwartzman (2013), when the authors choose the bandwidth h, they do not use the cross validation score, since this may result in multiple inflection-point estimates.…”

“…Kachouie and Schwartzman (2013) propose an estimator using local polynomial regression to detect a single inflection point in an underlying smooth signal curve. To ensure that only one inflection point is detected, a constrained method is proposed for bandwidth selection.…”

“…In this section, we only considerm S with the monotonicity constraint on f m . First, we comparem S withm K of Kachouie and Schwartzman (2013) andm C in the R package inflection by the SMSE criteria defined in the unimodal Table 12. Coverage rate and C.I.…”

“…We choose two convex-concave curves to compare our estimatorm S with the estimator m K of Kachouie and Schwartzman (2013) and the estimatorm C in the R package inflection through simulations. The first curve is the Gompertz sigmoid curve f m = 10e −e 5(1−2x) , and the second is f m = 5{1 + tanh[10(x − .5)]}, which is a multiple of the cumulative distribution function of a logistic distribution.…”

“…Inflection-Point Case. The method used in Kachouie and Schwartzman (2013) is local polynomial regression. We choose the degree p of the local polynomials to be 3 in the following simulation, which will be applied to construct a confidence interval for …”