This article considers the estimation for bivariate distribution function (d.f.) <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$F_0(t, z)$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <msub> <mi>F</mi> <mn>0</mn> </msub> <mrow> <mo stretchy="false">(</mo> <mi>t</mi> <mo>,</mo> <mi>z</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math> </EquationSource> </InlineEquation> of survival time <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$$T$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi>T</mi> </math> </EquationSource> </InlineEquation> and covariate variable <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$$Z$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi>Z</mi> </math> </EquationSource> </InlineEquation> based on bivariate data where <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$$T$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi>T</mi> </math> </EquationSource> </InlineEquation> is subject to right censoring. We derive the empirical...</equationsource></equationsource></inlineequation></equationsource></equationsource></inlineequation></equationsource></equationsource></inlineequation></equationsource></equationsource></inlineequation>

We estimate the drift parameter in a simple linear model driven by sub-fractional Brownian motion. We construct a maximum likelihood estimator (MLE) for the drift parameter by using a random walk approximation of the sub-fractional Brownian motion and study the asymptotic behaviors of the...