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Normal approximation of the distribution of the optimum point in the data processing problem by the method of least moduli. (English. Russian original) Zbl 0611.62055

Cybernetics 21, 831-839 (1985); translation from Kibernetika 1985, No. 6, 86-92 (1985).
Consider the model \(x_ j=x_ j(\theta)=g(j,\theta)+\epsilon_ j\), \(j\geq 1\), where for each j, g(j,\(\theta)\) is a function of the vector \(\theta\in \Theta \subset {\mathbb{R}}^ q\). The least moduli estimate \({\check \theta}_ n\) of the parameter \(\theta\) is defined to minimize \(R_ n(\tau)=\sum^{n}_{j=1}| x_ j(\theta)-g(j,\tau)|\). Under certain conditions, the normal approximation of the distribution of \({\check \theta}_ n\) is given.
Reviewer: Bai Zhidong

MSC:

62H12 Estimation in multivariate analysis
62E20 Asymptotic distribution theory in statistics
62H10 Multivariate distribution of statistics
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