Two concepts of optimality corresponding to Bayesian robust analysis are considered: conditional Γ-minimaxity and stability. Conditions for coincidence of optimal decisions of both kinds are stated.
The problem of sequential fixed-precision estimation of the minimum point of a quadratic regression function is investigated. Stochastic approximation methods are mentioned. One presents also some sequential fixed-precision procedures for the minimum of a random variable, i.e. for the lower bound of the support of its distribution function. One attempts to apply these procedures to estimation of the minimal value of a regression function. Asymptotically consistent fixed-precision estimation is considered....
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Professor Ryszard Zieliński's results in stochastic approximation, extremal experimental design in the framework of response surface analysis and fixed-precision set estimation are outlined. First, he proposed a randomized version of Fabian's (1967) gradient estimate in the Kiefer-Wolfowitz procedure, which reduced the number of required observations and improved the rate of convergence. Second, when considering response surface analysis and experimental designs for the gradient estimation, he constructed...
A homogeneous Poisson process (N(t),t ≥ 0) with the intensity function m(t)=θ is observed on the interval [0,T]. The problem consists in estimating θ with balancing the LINEX loss due to an error of estimation and the cost of sampling which depends linearly on T. The optimal T is given when the prior distribution of θ is not uniquely specified.
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