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  • SAGE Publications  (7)
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  • SAGE Publications  (7)
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  • 1
    Online Resource
    Online Resource
    Quantile regression with monotonicity restrictions using P-splines and the L1-norm
    SAGE Publications ; 2006
    In:  Statistical Modelling Vol. 6, No. 3 ( 2006-10), p. 189-207
    Details
    In: Statistical Modelling, SAGE Publications, Vol. 6, No. 3 ( 2006-10), p. 189-207
    Abstract: Quantile regression is an alternative to OLS regression. In quantile regression, the sum of absolute deviations or the L1-norm is minimized, whereas the sum of squared deviations or the L2-norm is minimized in OLS regression. Quantile regression has the advantage over OLS-regression of being more robust to outlying observations. Furthermore, quantile regression provides information complementing the information provided by OLS-regression. In this study, a non-parametric approach to quantile regression is presented, which constrains the estimated-quantile function to be monotone increasing. In particular, P-splines with an additional asymmetric penalty enforcing monotonicity are used within an L1-framework. This can be translated into a linear programming problem, which will be solved using an interior point algorithm. As an illustration, the presented approach will be applied to estimate quantile growth curves and quantile antibody levels as a function of age.
    Type of Medium: Online Resource
    ISSN: 1471-082X , 1477-0342
    URL: Article
    DOI: 10.1191/1471082X06st118oa
    Language: English
    Publisher: SAGE Publications
    Publication Date: 2006
    detail.hit.zdb_id: 2053876-5
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    Online Resource
  • 2
    Online Resource
    Online Resource
    Sums of smooth exponentials to decompose complex series of counts
    SAGE Publications ; 2016
    In:  Statistical Modelling Vol. 16, No. 4 ( 2016-08), p. 279-296
    Details
    In: Statistical Modelling, SAGE Publications, Vol. 16, No. 4 ( 2016-08), p. 279-296
    Abstract: Representing the conditional mean in Poisson regression directly as a sum of smooth components can provide a realistic model of the data generating process. Here, we present an approach that allows such an additive decomposition of the expected values of counts. The model can be formulated as a penalized composite link model and can, therefore, be estimated by a modified iteratively weighted least-squares algorithm. Further shape constraints on the smooth additive components can be enforced by additional penalties, and the model is extended to two dimensions. We present two applications that motivate the model and demonstrate the versatility of the approach.
    Type of Medium: Online Resource
    ISSN: 1471-082X , 1477-0342
    URL: Article
    DOI: 10.1177/1471082X16641796
    Language: English
    Publisher: SAGE Publications
    Publication Date: 2016
    detail.hit.zdb_id: 2053876-5
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  • 3
    Online Resource
    Online Resource
    Discussion: The beauty of expectiles
    SAGE Publications ; 2013
    In:  Statistical Modelling Vol. 13, No. 4 ( 2013-08), p. 317-322
    Details
    In: Statistical Modelling, SAGE Publications, Vol. 13, No. 4 ( 2013-08), p. 317-322
    Type of Medium: Online Resource
    ISSN: 1471-082X , 1477-0342
    URL: Article
    DOI: 10.1177/1471082X13494313
    Language: English
    Publisher: SAGE Publications
    Publication Date: 2013
    detail.hit.zdb_id: 2053876-5
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  • 4
    Online Resource
    Online Resource
    Smoothing and forecasting mortality rates
    SAGE Publications ; 2004
    In:  Statistical Modelling Vol. 4, No. 4 ( 2004-12), p. 279-298
    Details
    In: Statistical Modelling, SAGE Publications, Vol. 4, No. 4 ( 2004-12), p. 279-298
    Abstract: The prediction of future mortality rates is a problem of fundamental importance for the insurance and pensions industry. We show how the method of P-splines can be extended to the smoothing and forecasting of two-dimensional mortality tables. We use a penalized generalized linear model with Poisson errors and show how to construct regression and penalty matrices appropriate for two-dimensional modelling. An important feature of our method is that forecasting is a natural consequence of the smoothing process. We illustrate our methods with two data sets provided by the Continuous Mortality Investigation Bureau, a central body for the collection and processing of UK insurance and pensions data.
    Type of Medium: Online Resource
    ISSN: 1471-082X , 1477-0342
    URL: Article
    DOI: 10.1191/1471082X04st080oa
    Language: English
    Publisher: SAGE Publications
    Publication Date: 2004
    detail.hit.zdb_id: 2053876-5
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  • 5
    Online Resource
    Online Resource
    L- and V-curves for optimal smoothing
    SAGE Publications ; 2015
    In:  Statistical Modelling Vol. 15, No. 1 ( 2015-02), p. 91-111
    Details
    In: Statistical Modelling, SAGE Publications, Vol. 15, No. 1 ( 2015-02), p. 91-111
    Abstract: The L-curve is a tool for the selection of the regularization parameter in ill-posed inverse problems. It is a parametric plot of the size of the residuals vs that of the penalty. The corner of the L indicates the right amount of regularization. In the context of smoothing the L-curve is easy to compute and works surprisingly well, even for data with correlated noise. We present the theoretical background and applications to real data together with an alternative criterion for finding the corner automatically. We introduce as simplification, the V-curve, which replaces finding the corner of the L-curve by locating a minimum.
    Type of Medium: Online Resource
    ISSN: 1471-082X , 1477-0342
    URL: Article
    DOI: 10.1177/1471082X14549288
    Language: English
    Publisher: SAGE Publications
    Publication Date: 2015
    detail.hit.zdb_id: 2053876-5
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  • 6
    Online Resource
    Online Resource
    Ill-posed problems with counts, the composite link model and penalized likelihood
    SAGE Publications ; 2007
    In:  Statistical Modelling Vol. 7, No. 3 ( 2007-10), p. 239-254
    Details
    In: Statistical Modelling, SAGE Publications, Vol. 7, No. 3 ( 2007-10), p. 239-254
    Abstract: Certain data sets with distributions or counts can be interpreted as indirect observations of latent distributions or (time) series of counts. The structure of such data matches elegantly with the composite link model (CLM). The parameters can be estimated with iteratively re-weighted linear regression. Unfortunately, the estimating equations generally are singular or severely ill-conditioned. An effective solution is to impose smoothness on the solution, by penalizing the likelihood with a roughness measure. The optimal smoothing parameter is found efficiently by minimizing Akaike's Information Criterion (AIC). Several applications are presented.
    Type of Medium: Online Resource
    ISSN: 1471-082X , 1477-0342
    URL: Article
    DOI: 10.1177/1471082X0700700302
    Language: English
    Publisher: SAGE Publications
    Publication Date: 2007
    detail.hit.zdb_id: 2053876-5
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  • 7
    Online Resource
    Online Resource
    Editorial
    SAGE Publications ; 2014
    In:  Statistical Methods in Medical Research Vol. 23, No. 4 ( 2014-08), p. 317-317
    Details
    In: Statistical Methods in Medical Research, SAGE Publications, Vol. 23, No. 4 ( 2014-08), p. 317-317
    Type of Medium: Online Resource
    ISSN: 0962-2802 , 1477-0334
    URL: Article
    DOI: 10.1177/0962280214541023
    Language: English
    Publisher: SAGE Publications
    Publication Date: 2014
    detail.hit.zdb_id: 2001539-2
    detail.hit.zdb_id: 1136948-6
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