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Vasiliy Vel'dyaksov1, Alexey Shvedov1Hypothesis Testing in Regression Models with Fuzzy Data
2014.
Vol. 18.
No. 3.
P. 508–523
[issue contents]
Regression analysis is in wide use in scientific investigation. Fuzzy linear regression is an actively developing area of research since in many real-life situations dependent or independent variables are not given as real numbers. The regression problem with fuzzy data is treated in the literature with different kinds of input-output data. We consider the model yi = A + bxi + εi, i = 1,…,n, where A, x1,…,xn – fuzzy numbers; b – real number; ε1,…,εn, y1,…,yn – fuzzy random variables. In [Veldyaksov, Shvedov, 2014] A,b estimates were proposed, using ordinary least squares approach. The estimates rely on calculus of variations, and on previous research conducted for the case when A is a crisp (real) number. Estimate for b is also proposed in [Veldyaksov, Shvedov, 2014]. In first part of this paper, we prove that this estimate is unbiased. We use new fuzzy random variables definition from [Shvedov, 2013]. In second part of this paper we refer to a number of numerical tests to compare confidence intervals for b coefficient, calculated both using traditional approach, and bootstrap approach. We show that the intervals become closer, as number of observations grows. We also propose a procedure for hypothesis testing for b coefficient in regression models with fuzzy data.
Citation:
Vel'dyaksov V., Shvedov A. (2014) Proverka gipotez pri regressii s nechetkimi dannymi [Hypothesis Testing in Regression Models with Fuzzy Data]. HSE Economic Journal, vol. 18, no 3, pp. 508-523 (in Russian)
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