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By Augustin T., Wolff J.

Retrospectively gathered length information are usually stated incorrectly. a huge form of such an errors is heaping - respondents are inclined to round-off or round-up the knowledge in response to a few rule of thumb. for 2 designated situations of the Weibull version we research the behaviour of the 'naive estimators', which easily forget about the dimension errors because of heaping, and derive closed expressions for the asymptotic bias. those effects provide a proper justification of empirical proof and simulation-based findings said within the literature. also, events the place a awesome bias needs to be anticipated may be pointed out, and an actual bias correction could be played.

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An } and B = {b1 , b2 . . bn } are sets of lower and upper bounds of the integral, and W = {w1 , w2 . . wn } is the set of the weights, with bj > aj and wj = 0 for 1 ≤ j ≤ n. It can be clearly seen that the input space can be regarded as a hyper-rectangle bounded by A and B in n-dimensional space From a geometric point of view, the hyperplane P can be regarded as a dividing plane. It divides the n-dimensional space into three parts: the points on P, the points below P, and the points above P.

A single neuron is considered first, and algorithms with approximately derived analytical expressions that are functions of expected input deviation are given for the computation of its sensitivity. Then another algorithm is given to compute the sensitivity of the entire MLP network. Chapter 4 Sensitivity Analysis with Parameterized Activation Function Among all the traditional methods introduced in Chap. 2, none has involved activation function in the calculation of sensitivity analysis. This chapter attempts to generalize Piché’s method by parameterizing antisymmetric squashing activation functions, through which a universal expression of MLP’s sensitivity will be derived without any restriction on input or output perturbations.

Initialization. Form the matrix H in Eq. 7) with the RBF function responses of all the training examples. STEP 2. First critical vector neuron selection. Calculate the sensitivity of each column of H with Eq. 5). The column that provides the maximum sensitivity is selected as the first column of matrix Q(1) . Calculate the classification error Err(1) with the selected RBF center. Let K= 2. STEP 3. Orthogonalization and critical vector selection. Orthogonalize all remaining columns of H with all the columns of Q(K−1) using Eq.

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A bias analysis of Weibull models under heaped data by Augustin T., Wolff J.


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