[논문]Local linear regression analysis for interval-valued data

Jang, Jungteak; Kang, Kee-Hoon

doi:10.29220/csam.2020.27.3.365

[국내논문] Local linear regression analysis for interval-valued data 원문보기

Communications for statistical applications and methods = 한국통계학회논문집, v.27 no.3, 2020년, pp.365 - 376

Jang, Jungteak (Department of Statistics, Hankuk University of Foreign Studies) , Kang, Kee-Hoon (Department of Statistics, Hankuk University of Foreign Studies)

Abstract ▼ AI-Helper

Interval-valued data, a type of symbolic data, is given as an interval in which the observation object is not a single value. It can also occur frequently in the process of aggregating large databases into a form that is easy to manage. Various regression methods for interval-valued data have been proposed relatively recently. In this paper, we introduce a nonparametric regression model using the kernel function and a nonlinear regression model for the interval-valued data. We also propose applying the local linear regression model, one of the nonparametric methods, to the interval-valued data. Simulations based on several distributions of the center point and the range are conducted using each of the methods presented in this paper. Various conditions confirm that the performance of the proposed local linear estimator is better than the others.

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제안 방법

In this paper, we review a nonparametric regression and a nonlinear regression model that focuses on interval-valued data. In addition, we propose a different version of nonparametric regression that uses local linear estimation.
In this paper, the simulation is limited but considers types of data generation that can be inferred later. The simulation consists of two experiments and assumes a nonlinear form for both the center point and the range.
In this paper, the simulation is limited but considers types of data generation that can be inferred later. The simulation consists of two experiments and assumes a nonlinear form for both the center point and the range. Data sets for Experiment 1 in the simulation were generated as follows.
Additionally, we proposed a local linear regression estimator as one of the nonparametric approaches. This paper uses simulation without comparing the theoretical characteristics of the various methods. However, we admit that the general conclusion is limited because not all situations can be considered in the simulation.

이론/모형

To optimize this nonlinear objective function, we can use the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm, stochastic gradient, conjugate gradient, and simulated annealing method. In this paper, we employ the BFGS algorithm and conjugate gradient algorithm. See Edwin and Stanislaw (2013) for more detailed descriptions of these algorithms.
Table 1 and Figure 2 indicated the results of Experiment 1. NLM BFGS and NLM CG correspond to the nonlinear regression model estimated by using the BFGS algorithm and the conjugate gradient algorithm. IKR NWand IKR LL correspond to the kernel estimates by the Nadaraya-Watson method and the local linear method.

참고문헌 (15)

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상세보기
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상세보기
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상세보기
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