<Para ID="Par1">We congratulate the authors for a stimulating and valuable manuscript, providing a careful review of the state-of-the-art in cross-sectional and time-series benchmarking procedures for small area estimation. They develop a novel two-stage benchmarking method for hierarchical time series models,...</para>

We consider a varying coefficient regression model for sparse functional data, with time varying response variable depending linearly on some time-independent covariates with coefficients as functions of time-dependent covariates. Based on spline smoothing, we propose data-driven simultaneous...

Let <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$\{\chi _{k}(t), t\ge 0\}$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <mo stretchy="false">{</mo> <msub> <mi mathvariant="italic">χ</mi> <mi>k</mi> </msub> <mrow> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> <mo>,</mo> <mi>t</mi> <mo>≥</mo> <mn>0</mn> <mo stretchy="false">}</mo> </mrow> </math> </EquationSource> </InlineEquation> be a stationary <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$$\chi $$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi mathvariant="italic">χ</mi> </math> </EquationSource> </InlineEquation>-process with <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$$k$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi>k</mi> </math> </EquationSource> </InlineEquation> degrees of freedom. In this paper, we consider the maxima <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$$M_{k}(T)= \max \{\chi _{k}(t), \forall t\in [0,T]\}$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <msub> <mi>M</mi> <mi>k</mi> </msub> <mrow> <mo stretchy="false">(</mo> <mi>T</mi> <mo stretchy="false">)</mo> </mrow> <mo>=</mo> <mo movablelimits="true">max</mo> <mrow> <mo stretchy="false">{</mo> <msub> <mi mathvariant="italic">χ</mi> <mi>k</mi> </msub> <mrow> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> <mo>,</mo> <mo>∀</mo> <mi>t</mi>...</mo></mrow></mrow></math></equationsource></equationsource></inlineequation></equationsource></equationsource></inlineequation></equationsource></equationsource></inlineequation></equationsource></equationsource></inlineequation>

Non-inferiority of one treatment to another based on ratio is a common issue in medical research. Nam and Blackwelder derived a Fieller-type statistic from constrained maximum likelihood estimation of nuisance parameters. Although it improved that of Lachenbruch and Lynch, its size still exceeds...

In this paper, we propose a method to choose a test result from several competing ones. The choice is based on the p value under the alternative, i.e., the probability of obtaining an extreme or a more extreme result than the one actually observed, assuming that the alternative hypothesis is...