A class of sequential estimation procedures is considered in the case when relevant data may become available only at random times. The exact distributions of the optimal stopping time and the number of observations at the moment of stopping are derived in some sequential procedures. The results...

A stochastic marked point process model based on doubly stochastic Poisson process is considered in the problem of prediction for the total size of future marks in a given period, given the history of the process. The underlying marked point process <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$(T_{i},Y_{i})_{i\ge 1}$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <msub> <mrow> <mo stretchy="false">(</mo> <msub> <mi>T</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>Y</mi> <mi>i</mi>...</msub></mrow></msub></math></equationsource></equationsource></inlineequation>

Information inequalities in a general sequential model for stochastic processes are presented by applying the approach to estimation through estimating functions. Using this approach, Bayesian versions of the information inequalities are also obtained. In particular, exponential-family processes...

Information inequalities in a general sequential model for stochastic processes are presented by applying the approach to estimation through estimating functions. Using this approach, Bayesian versions of the information inequalities are also obtained. In particular, exponential-family processes...