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We consider positive real valued random data X with the decadic representation X = Σ
D 10 and the first significant digit D = D(X) in {1,2,...,9} of X defined by the condition D = D ≥ 1, D = D = ... = 0. The data X are said to satisfy the Newcomb-Benford law if P{D=d} = log(d+1 / d) for all d in {1,2,...,9}. This law holds for example for the data with logX uniformly distributed on an interval (m,n) where m and n are integers. We show that if logX has a distribution function G(x/σ)...
The paper investigates generalized linear models (GLM's) with binary responses such as the logistic, probit, log-log, complementary log-log, scobit and power logit models. It introduces a median estimator of the underlying structural parameters of these models based on statistically smoothed binary responses. Consistency and asymptotic normality of this estimator are proved. Examples of derivation of the asymptotic covariance matrix under the above mentioned models are presented. Finally some comments...
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