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- W2265092854 abstract "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 + ei, i = 1,…,n, where A, x1,…,xn - fuzzy numbers; b - real number; e1,…,en, 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." @default.
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- W2265092854 date "2014-01-01" @default.
- W2265092854 modified "2023-09-24" @default.
- W2265092854 title "Hypothesis Testing in Regression Models with Fuzzy Data" @default.
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