What price semiparametric Cox regression?

Jullum, Martin; Hjort, Nils Lid

doi:10.1007/s10985-018-9450-7

Cited by 17 publications

(23 citation statements)

References 20 publications

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“…With appropriate efforts this leads to FIC and AFIC formulae for choosing between semiparametric and parametric hazard models, in terms of precision of estimators for either cumulative hazards or survival curves. This is indeed the main theme in Jullum and Hjort (2017b).…”

Section: Proportional Hazard Regressionmentioning

confidence: 79%

Parametric or nonparametric: The FIC approach

Jullum¹,

Hjort²

2018

STAT SINICA

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Should one rely on a parametric or nonparametric model when analysing a given data set? This classic question cannot be answered by traditional model selection criteria like AIC and BIC, since a nonparametric model has no likelihood. The purpose of the present paper is to develop a focused information criterion (FIC) for comparing general non-nested parametric models with a nonparametric alternative. It relies in part on the notion of a focus parameter, a population quantity of particular interest in the statistical analysis. The FIC compares and ranks candidate models based on estimated precision of the different model-based estimators for the focus parameter. It has earlier been developed for several classes of problems, but mainly involving parametric models. The new FIC, including also nonparametrics, is novel also in the mathematical context, being derived without the local neighbourhood asymptotics underlying previous versions of FIC. Certain average-weighted versions, called AFIC, allowing several focus parameters to be considered simultaneously, are also developed. We concentrate on the standard i.i.d. setting and certain direct extensions thereof, but also sketch further generalisations to other types of data. Theoretical and simulation-based results demonstrate desirable properties and satisfactory performance.

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Section: Proportional Hazard Regressionmentioning

confidence: 79%

Parametric or nonparametric: The FIC approach

Jullum¹,

Hjort²

2018

STAT SINICA

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“…This paper concerns extending the FIC theory to these different estimation procedures. This partly follows the line of arguments used in Jullum and Hjort (, ) but, by necessity, involves certain extra efforts, as we work with more complex estimation strategies than the pure nonparametric and the ML.…”

Section: Introduction and Copula Modelsmentioning

confidence: 84%

“…However, in many cases, the model itself is not the goal, but rather a means to estimate a specific quantity, such as the mean or the probability of a certain event. The main idea behind the FIC, first introduced by Claeskens and Hjort () and later modified by Jullum and Hjort (, ), is that one wants to select a model that is good for a specific task. In our setting, we quantify this specific task as that of estimating a focus parameter, say, T ( G ), a functional of the data‐generating distribution.…”

Section: Fic For Copula Modelsmentioning

confidence: 99%

“…We are looking for candidate models such that

{\overset{T}{true}}_{cnd}

is close to T true . As with Jullum and Hjort (, ), we use a quadratic loss function, leading by definition to the MSE as the criterion of closeness. We hence define the FIC as the estimated MSE

FIC = \overset{MSE}{true} false({\overset{T}{true}}_{cnd} false) = {\overset{Var}{true}}_{G} false({\overset{T}{true}}_{cnd} false) + \overset{{bias}^{2}}{true} ((), {\overset{T}{true}}_{cnd}, T_{true}) .

We return to estimates for the variance of

{\overset{T}{true}}_{cnd}

below, with different recipes for different estimators.…”

Section: Fic For Copula Modelsmentioning

confidence: 99%

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Focused information criteria for copulas

Hjort

Haff

2019

Scandinavian J Statistics

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In this paper, we extend the focused information criterion (FIC) to copula models. Copulas are often used for applications where the joint tail behavior of the variables is of particular interest, and selecting a copula that captures this well is then essential. Traditional model selection methods such as the Akaike information criterion (AIC) and the Bayesian information criterion (BIC) aim at finding the overall best‐fitting model, which is not necessarily the one best suited for the application at hand. The FIC, on the other hand, evaluates and ranks candidate models based on the precision of their point estimates of a context‐given focus parameter. This could be any quantity of particular interest, for example, the mean, a correlation, conditional probabilities, or measures of tail dependence. We derive FIC formulae for the maximum likelihood estimator, the two‐stage maximum likelihood estimator, and the so‐called pseudo‐maximum‐likelihood (PML) estimator combined with parametric margins. Furthermore, we confirm the validity of the AIC formula for the PML estimator combined with parametric margins. To study the numerical behavior of FIC, we have carried out a simulation study, and we have also analyzed a multivariate data set pertaining to abalones. The results from the study show that the FIC successfully ranks candidate models in terms of their performance, defined as how well they estimate the focus parameter. In terms of estimation precision, FIC clearly outperforms AIC, especially when the focus parameter relates to only a specific part of the model, such as the conditional upper‐tail probability.

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“…Also, FIC type II allows non-parametric alternatives to be compared with parametric ones. The framework has been adapted to survival analysis (Jullum & Hjort, 2018) and certain types of time-series modelling (Hermansen, Hjort & Jullum, 2015), but is difficult to use in a regression setting when one wishes to select between models with different sets of covariates (Jullum, 2015).…”

Section: Three Fic Frameworkmentioning

confidence: 99%

Confidence distributions for change-points and regime shifts

Cunen

Hermansen

Hjort

2018

Journal of Statistical Planning and Inference

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Four years ago, almost to the day, I started my PhD period at the University of Oslo. I was excited, but also slightly worried. With my background in applied statistics and biology from the Norwegian University of Life Science (NMBU), I felt a certain awe upon entering the Department of Mathematics. Looking back I can attest that my worries were not misguided, the PhD process has partly been difficult. I had much more to learn than I anticipated, and during the first two years I considered giving up multiple times. Luckily, I stayed, and I have been rewarded with a much deeper and broader understanding of the field of statistics than I started out with. The original plans for this thesis were somewhat different from the final result. They were primarily concerned with ideas related to the last paper in this thesis, Paper IV. Eventually, other ideas emerged and caught our interest, sometimes originating from applied problems, for example leading to Papers II and III. However, in all these papers, similar methods came into use, and I therefore maintain that I did not stray too far from the intended path. My main supervisor, Nils Lid Hjort, has played an important role in this thesis. He has been a great support throughout the process; helpful and always enthusiastic. Importantly, he has encouraged me to pursue various activities outside of 'regular' PhD work, for example the writing of blog posts, which has led to a number of popular science talks. Also, Nils is the leader of the FocuStat group, and I am very grateful for having been part of such an active and close-knit research group. My deep thanks to all FocuStat members for a large number of interesting discussions and pleasant company. I am also very grateful to my other co-authors, Gudmund Horn Hermansen, Lars Walløe and Håvard Mokleiv Nygård. Lars, in particular, gave me the opportunity to present and defend my work at the Scientific Committee of the International Whaling Commission. Thanks to my co-supervisor Bo Lindqvist for pleasant conversations and meetings, most memorably at the ISI World Statistics Congress in Marrakech. I first learnt to love statistics at NMBU, for this I owe particular thanks to Trygve Almøy and Solve Saebø. Further, I am very grateful to professor Sylvia Richardson at the MRC Biostatistical Unit in Cambridge, where I was a visitor for the autumn semester in 2017, and to all the PhD students at the BSU for making my stay so pleasant and memorable. Special thanks to all colleagues at UiO, particularly the PhD students. Finally, I am grateful to friends and family for filling my life with joy and distractions. Particularly Jonas, for numerous discussions on statistical topics and great support, especially in the final weeks before submission; Sigrun, my oldest and best friend; my parents Josiane and Per Axel, for their help and encouragement; and my dear siblings, Christophe and Mélanie.

show abstract

What price semiparametric Cox regression?

Cited by 17 publications

References 20 publications

Parametric or nonparametric: The FIC approach

Parametric or nonparametric: The FIC approach

Focused information criteria for copulas

Confidence distributions for change-points and regime shifts

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