soxumis saxelmwifo universitetis S r o m e b i VII

In the present paper, we consider the problem of estimation ofprobability distribution parameters by using a specific variant of observations.It is assumed that observations are grouped and there might be casesof partial or full non-observation of individual realization variables.We propose to use a somewhat more refined (in a certain sense) versionof the mlm and show that it leads to asymptotically consistent and effectiveestimators.342. Statement of the problem and the method its solution. Let X be a random variable with a distribution functionF x F x, , where is an unknown vector parameter in a finite-qdimensional space R . Assume that is a compactum. We need toconstruct the consistent estimator using observation data on the randomvariable X . The experiment is set up so that we do not know theactual number of realizations, but know only a part of them.Let the fixed points t1 t2 tn be given on thestraight line R (we do not exclude the case where the first or the lastpoint takes an infinite value). These points form intervals which may beof three categories:0) an interval интервал t i, t i 1 belongs to the zero-th category if inthis interval neither individual values of the sample nor the total quantityof sample values of the random value X are known:1) an interval t i, t i 1 belongs to the first category if in this categoryindividual values of the sampling are unknown, but the number ofsample values of the random value X is known. As usual, this number isdenoted by ni.t belongs to the second category if in this in-i, t i 12) an interval terval individual values of the samplingx ,i1, xi2, xinare known.iIn the sequel, summation or integration over the intervals of the zero-th,first or second categories will be denoted by the symbols (0), (1)или (2), respectively.We call a sampling of this type a partially grouped sampling withcensoring. Censored samplings of both types, as well as truncated samplingsare obviously a particular case of the problem stated. The absenceof information in the intervals of the zero-th category creates a difficulty