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>

Density-distribution sunflower plots are used to display high-density bivariate data. They are useful for data where a conventional scatterplot is difficult to read due to overstriking of the plot symbol. The x – y plane is subdivided into a lattice of small, regular, hexagonal bins. These...

A bandwidth selector for local polynomial fitting is proposed following the bootstrap idea, which is just a double smoothing bandwidth selector with a bootstrap variance estimator, defined as the mean squared residuals of a pilot estimate. No simulated resampling is required in this context,...

In this paper a modified double smoothing bandwidth selector, MDS, based on a new criterion, which combines the plug-in and the double smoothing ideas, is proposed. A self-complete iterative double smoothing rule (_IDS ) is introduced as a pilot method. The asymptotic properties of both_IDS...

A bandwidth selector for local polynomial fitting is proposed following the bootstrap idea, which is just a double smoothing bandwidth selector with a bootstrap variance estimator, defined as the mean squared residuals of a pilot estimate. No simulated resampling is required in this context,...

A bandwidth selector for local polynomial fitting is proposed following the bootstrap idea, which is just a double smoothing bandwidth selector with a bootstrap variance estimator, defined as the mean squared residuals of a pilot estimate. No simulated resampling is required in this context,...

Quadratic loss is predominantly used in the literature as the performance measure for nonparametric density estimation, while nonparametric mixture models have been studied and estimated almost exclusively via the maximum likelihood approach. In this paper, we relate both for estimating a...

The non-parametric estimation of average causal effects in observational studies often relies on controlling for confounding covariates through smoothing regression methods such as kernel, splines or local polynomial regression. Such regression methods are tuned via smoothing parameters which...