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 paper considers the problem of parameter estimation in a general class of semiparametric models when observations are subject to missingness at random. The semiparametric models allow for estimating functions that are non-smooth with respect to the parameter. We propose a nonparametric...