Consider the semiparametric transformation model <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$\Lambda _{\theta _o}(Y)=m(X)+\varepsilon $$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <msub> <mi mathvariant="normal">Λ</mi> <msub> <mi mathvariant="italic">θ</mi> <mi>o</mi> </msub> </msub> <mrow> <mo stretchy="false">(</mo> <mi>Y</mi> <mo stretchy="false">)</mo> </mrow> <mo>=</mo> <mi>m</mi> <mrow> <mo stretchy="false">(</mo> <mi>X</mi> <mo stretchy="false">)</mo> </mrow> <mo>+</mo> <mi mathvariant="italic">ε</mi> </mrow> </math> </EquationSource> </InlineEquation>, where <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$$\theta _o$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <msub> <mi mathvariant="italic">θ</mi> <mi>o</mi> </msub> </math> </EquationSource> </InlineEquation> is an unknown finite dimensional parameter, the functions <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$$\Lambda _{\theta _o}$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <msub> <mi mathvariant="normal">Λ</mi> <msub> <mi mathvariant="italic">θ</mi> <mi>o</mi> </msub> </msub> </math> </EquationSource> </InlineEquation> and <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$$m$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi>m</mi> </math> </EquationSource> </InlineEquation> are...</equationsource></equationsource></inlineequation></equationsource></equationsource></inlineequation></equationsource></equationsource></inlineequation></equationsource></equationsource></inlineequation>

This discussion paper led to an article in the <I>Journal of Time Series Analysis</I> (2010). Vol. 31, pages 407-414.<P> State space models with nonstationary processes and fixed regression effects require a state vector with diffuse initial conditions. Different likelihood functions can be adopted for...</p></i>

A semiparametric fixed effects model is introduced to describe the nonlinear trending phenomenon in panel data analysis and it allows for the cross-sectional dependence in both the regressors and the residuals. A pooled semiparametric profile likelihood dummy variable approach based on the...