Based on a random sample of size <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$$n$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi>n</mi> </math> </EquationSource> </InlineEquation> from an unknown <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$$d$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi>d</mi> </math> </EquationSource> </InlineEquation>-dimensional density <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$$f$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi>f</mi> </math> </EquationSource> </InlineEquation>, the nonparametric estimations of a single integrated density partial derivative functional as well as a vector of such functionals are considered. These single and vector functionals...</equationsource></equationsource></inlineequation></equationsource></equationsource></inlineequation></equationsource></equationsource></inlineequation>

This paper presents a truncated estimation method of ratio type functionals by dependent sample of finite size. This method makes it possible to obtain estimators with guaranteed accuracy in the sense of the <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$L_m$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <msub> <mrow> <mi>L</mi> </mrow> <mrow> <mi>m</mi> </mrow> </msub> </mrow> </math> </EquationSource> </InlineEquation>-norm, <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$$m\ge 2$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <mi>m</mi> <mo>≥</mo> <mn>2</mn> </mrow> </math> </EquationSource> </InlineEquation>. As an illustration, the...</equationsource></equationsource></inlineequation></equationsource></equationsource></inlineequation>

In this study, we define a chi-square random field on a multi-dimensional lattice points index set with a direct product covariance structure and consider the distribution of the maximum of this random field. We provide two approximate formulas for the upper tail probability of the distribution...

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 develop a bootstrap procedure for Lévy-driven continuous-time autoregressive (CAR) processes observed at discrete regularly-spaced times. It is well known that a regularly sampled stationary Ornstein–Uhlenbeck process [i.e. a CAR(1) process] has a discrete-time autoregressive...

Copulas have become very popular as modelling tools in probability applications. Given a finite number of expectation constraints for functions defined on the unit square, the minimum information copula is that copula which has minimum information (Kullback–Leibler divergence) from the uniform...

In this paper, we study a special capture–recapture model, the <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$M_t$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <msub> <mi>M</mi> <mi>t</mi> </msub> </math> </EquationSource> </InlineEquation> model, using objective Bayesian methods. The challenge is to find a justified objective prior for an unknown population size <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$$N$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi>N</mi> </math> </EquationSource> </InlineEquation>. We develop an asymptotic objective prior for the discrete parameter <InlineEquation ID="IEq3"> <EquationSource...</equationsource></inlineequation></equationsource></equationsource></inlineequation></equationsource></equationsource></inlineequation>

Just as ARMA processes play a central role in the representation of stationary time series with discrete time parameter, <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$(Y_n)_{n\in \mathbb {Z}}$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <msub> <mrow> <mo stretchy="false">(</mo> <msub> <mi>Y</mi> <mi>n</mi> </msub> <mo stretchy="false">)</mo> </mrow> <mrow> <mi>n</mi> <mo>∈</mo> <mi mathvariant="double-struck">Z</mi> </mrow> </msub> </math> </EquationSource> </InlineEquation>, CARMA processes play an analogous role in the representation of stationary time series with continuous time...</equationsource></equationsource></inlineequation>

We develop particle Gibbs samplers for static-parameter estimation in discretely observed piecewise deterministic process (PDPs). PDPs are stochastic processes that jump randomly at a countable number of stopping times but otherwise evolve deterministically in continuous time. A sequential Monte...