Asymptotic Expansions for Sample Quantiles

Asymptotic properties of sample quantiles of discrete distributions

The asymptotic distribution of sample quantiles in the classical definition is well-known to be normal for absolutely continuous distributions. However, this is no longer true for discrete distributions or sampleswith ties.We show that the definition of sample quantiles based on mid-distribution functions resolves this issue and provides a unified framework for asymptotic properties of sample q...

Confidence Intervals for Lower Quantiles Based on Two-Sample Scheme

In this paper, a new two-sampling scheme is proposed to construct appropriate confidence intervals for the lower population quantiles. The confidence intervals are determined in the parametric and nonparametric set up and the optimality problem is discussed in each case. Finally, the proposed procedure is illustrated via a real data set. 

Asymptotic Expansions for Integrals

Asymptotic distribution of two-sample empirical U-quantiles with applications to robust tests for structural change

Asymptotic distribution Asymptotic distribution Asymptotic distribution Asymptotic distribution of two of two of two of two-sample empirical sample empirical sample empirical sample empirical U U U U-quantiles with application quantiles with application quantiles with application quantiles with applications s s s to robust tests for structural to robust tests for structural to robust tests for ...

Asymptotic Expansions

Asymptotic expansions of functions are useful in statistics in three main ways. Firstly, conventional asymptotic expansions of special functions are useful for approximate computation of integrals arising in statistical calculations. An example given below is the use of Stirling's approximation to the gamma function. Second, asymptotic expansions of density or distribution functions of estimato...