Vasiliy Vel'dyaksov1, Alexey Shvedov1
  • 1 National Research University Higher School of Economics, 20 Myasnitskaya Str., Moscow, 101000, Russian Federation

Hypothesis 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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