The data that are analysed are from a monitoring survey which was carried out in 1994 in the forests of Baden-Württemberg, a federal state in the south-western region of Germany. The survey is part of a large monitoring scheme that has been carried out since the 1980s at different spatial and...

The distributional assumption for a generalized linear model is often checked by plotting the ordered deviance residuals against the quantiles of a standard normal distribution. Such plots can be difficult to interpret, because even when the model is correct, the plot often deviates...

A scoring rule <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$S(x; q)$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <mi>S</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo>;</mo> <mi>q</mi> <mo stretchy="false">)</mo> </mrow> </math> </EquationSource> </InlineEquation> provides a way of judging the quality of a quoted probability density <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$$q$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi>q</mi> </math> </EquationSource> </InlineEquation> for a random variable <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$$X$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi>X</mi> </math> </EquationSource> </InlineEquation> in the light of its outcome <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$$x$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi>x</mi> </math> </EquationSource> </InlineEquation>. It is called proper if honesty is your best policy, i.e., when you believe <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$$X$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi>X</mi>...</math></equationsource></equationsource></inlineequation></equationsource></equationsource></inlineequation></equationsource></equationsource></inlineequation></equationsource></equationsource></inlineequation></equationsource></equationsource></inlineequation>

We display pseudo-likelihood as a special case of a general estimation technique based on proper scoring rules. Such a rule supplies an unbiased estimating equation for any statistical model, and this can be extended to allow for missing data. When the scoring rule has a simple local structure,...

The skew-normal model is a class of distributions that extends the Gaussian family by including a skewness parameter. This model presents some inferential problems linked to the estimation of the skewness parameter. In particular its maximum likelihood estimator can be infinite especially for...

The problem of testing smooth components of an extended generalized additive model for equality to zero is considered. Confidence intervals for such components exhibit good across-the-function coverage probabilities if based on the approximate result <inline-formula><inline-graphic xlink:href="ASS048IM1" xmlns:xlink="http://www.w3.org/1999/xlink"/></inline-formula>, where f is the vector of evaluated values...