Beyond unimodal regression: modelling multimodality with piecewise unimodal, mixture or additive regression
نویسندگان
چکیده
Research in the field of nonparametric shape constrained regression has been extensive and there is need for such methods in various application areas, since shape constraints can reflect prior knowledge about the underlying relationship. It is, for example, often natural that some intensity first increases and then decreases over time, which can be described by a unimodal shape constraint. But the prior knowledge in different applications is also of increasing complexity and data shapes may vary from few to plenty of modes and from piecewise unimodal to superpositions of unimodal function courses. Thus, we go beyond unimodal regression in this report and capture multimodality by employing piecewise unimodal regression, mixture regression or additive regression models. We give an overview of the statistical methods, namely the unimodal spline regression approach by [1] and its aforementioned extensions for use with multimodal data. The usefulness of the methods is demonstrated by applying them to data sets from three different application areas: breath gas analysis, marine biology and astroparticle physics. Though the three application areas are quite different, the proposed extensions of unimodal regression yield very helpful results in each of it. This encourages using the methodologies proposed here in many other areas of application as well.
منابع مشابه
A robust thresholding algorithm for unimodal image histograms
This article introduces a method to determine the threshold of unimodal image histograms in a robust manner. It is based on a piecewise linear regression that finds the two segments that fit the descending slope of the histogram. The algorithm gives a good estimation of the threshold, and is practically insensitive to the noise distribution, to the quantity of objects to segment, and to random ...
متن کاملModel-based approaches to nonparametric Bayesian quantile regression
In several regression applications, a different structural relationship might be anticipated for the higher or lower responses than the average responses. In such cases, quantile regression analysis can uncover important features that would likely be overlooked by mean regression. We develop two distinct Bayesian approaches to fully nonparametric model-based quantile regression. The first appro...
متن کاملAdaptive Risk Bounds in Unimodal Regression
We study the statistical properties of the least squares estimator in unimodal sequence estimation. Although closely related to isotonic regression, unimodal regression has not been as extensively studied. We show that the unimodal least squares estimator is adaptive in the sense that the risk scales as a function of the number of values in the true underlying sequence. Such adaptivity properti...
متن کاملLinear Time Isotonic and Unimodal Regression in the L1 and L∞ Norms
We consider L1-isotonic regression and L∞ isotonic and unimodal regression. For L1isotonic regression, we present a linear time algorithm when the number of outputs are bounded. We extend the algorithm to construct an approximate isotonic regression in linear time when the output range is bounded. We present linear time algorithms for L∞ isotonic and unimodal regression.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2014