| 1. |
- Arnroth, Lukas
(författare)
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Posterior rates of convergence for composite quantile regression
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Ingår i: Biometrika. - 0006-3444 .- 1464-3510.
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Tidskriftsartikel (refereegranskat)abstract
- Composite quantile regression is based on the convex combination of single quantile quantile loss functionsand enjoys many advantages over single quantile regression. The Bayesian extension is based onthe finite mixture of asymmetric Laplace densities. This paper mainly aims to contribute to the theoreticaljustification of Bayesian composite quantile regression from the perspective of Bayesian densityestimation. As such, we further show that the asymmetric Laplace distribution can be used for Bayesiandensity estimation in general. We obtain upper bounds on rates of convergence for mixtures of asymmetricLaplace densities. For finite mixtures we obtain the parametric rate up to a logarithmic factor,and a slower rate for infinite mixture.
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| 2. |
- Ciocanea-Teodorescu, I, et al.
(författare)
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Sensitivity analysis for unmeasured confounding in the estimation of marginal causal effects
- 2022
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Ingår i: BIOMETRIKA. - : Oxford University Press (OUP). - 0006-3444 .- 1464-3510. ; 109:4, s. 1101-1116
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Tidskriftsartikel (övrigt vetenskapligt/konstnärligt)abstract
- One of the main threats to the validity of causal effect estimates from observational data is the existence of unmeasured confounders. A plethora of methods has been proposed to quantify deviation from conditional exchangeability, which arises when confounding is not properly accounted for, with each method having its own set of limitations and underlying assumptions. Few methods both scale well with the increasing complexity of potential measured confounders and avoid making strong simplifying assumptions about the effect of the unmeasured confounder within strata of the measured confounders. For binary outcomes, we propose a quantification of the deviation from conditional exchangeability, based on standardization within levels of the exposure, which can accommodate any type of measured and unmeasured confounders or desired estimand. In the case of binary exposure, this amounts to varying two parameters across a grid of values, no matter how complex the measured confounding. We propose three methods of estimation for the causal estimand of interest under our proposed sensitivity analysis. This allows for an easily applied, easily interpreted sensitivity analysis that makes minimal assumptions about the type of unmeasured confounding and places no limits on the complexity of the potential measured confounders.
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| 3. |
- Cronie, Ottmar, 1979, et al.
(författare)
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A cross-validation-based statistical theory for point processes
- 2024
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Ingår i: Biometrika. - : Oxford University Press. - 0006-3444 .- 1464-3510. ; 111:2, s. 625-641
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Tidskriftsartikel (refereegranskat)abstract
- Motivated by the general ability of cross-validation to reduce overfitting and mean square error, we develop a cross-validation-based statistical theory for general point processes. It is based on the combination of two novel concepts for general point processes: cross-validation and prediction errors. Our cross-validation approach uses thinning to split a point process/pattern into pairs of training and validation sets, while our prediction errors measure discrepancy between two point processes. The new statistical approach, which may be used to model different distributional characteristics, exploits the prediction errors to measure how well a given model predicts validation sets using associated training sets. Having indicated that our new framework generalizes many existing statistical approaches, we then establish different theoretical properties for it, including large sample properties. We further recognize that nonparametric intensity estimation is an instance of Papangelou conditional intensity estimation, which we exploit to apply our new statistical theory to kernel intensity estimation. Using independent thinning-based cross-validation, we numerically show that the new approach substantially outperforms the state-of-the-art in bandwidth selection. Finally, we carry out intensity estimation for a dataset in forestry and a dataset in neurology.
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| 4. |
- Cronie, Ottmar, et al.
(författare)
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A non-model-based approach to bandwidth selection for kernel estimators of spatial intensity functions
- 2018
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Ingår i: Biometrika. - : Oxford University Press. - 0006-3444 .- 1464-3510. ; 105:2, s. 455-462
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Tidskriftsartikel (refereegranskat)abstract
- We propose a new bandwidth selection method for kernel estimators of spatial point process intensity functions. The method is based on an optimality criterion motivated by the Campbell formula applied to the reciprocal intensity function. The new method is fully nonparametric, does not require knowledge of higher-order moments, and is not restricted to a specific class of point process. Our approach is computationally straightforward and does not require numerical approximation of integrals.
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| 5. |
- de Luna, Xavier, et al.
(författare)
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Covariate selection for the non-parametric estimation of an average treatment effect
- 2011
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Ingår i: Biometrika. - : Oxford University Press. - 0006-3444 .- 1464-3510. ; 98:4, s. 861-875
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Tidskriftsartikel (refereegranskat)abstract
- Observational studies in which the effect of a nonrandomized treatment on an outcome of interest is estimated are common in domains such as labour economics and epidemiology. Such studies often rely on an assumption of unconfounded treatment when controlling for a given set of observed pre-treatment covariates. The choice of covariates to control in order to guarantee unconfoundedness should primarily be based on subject matter theories, although the latter typically give only partial guidance. It is tempting to include many covariates in the controlling set to try to make the assumption of an unconfounded treatment realistic. Including unnecessary covariates is suboptimal when the effect of a binary treatment is estimated nonparametrically. For instance, when using a n1/2-consistent estimator, a loss of efficiency may result from using covariates that are irrelevant for the unconfoundedness assumption. Moreover, bias may dominate the variance when many covariates are used. Embracing the Neyman–Rubin model typically used in conjunction with nonparametric estimators of treatment effects, we characterize subsets from the original reservoir of covariates that are minimal in the sense that the treatment ceases to be unconfounded given any proper subset of these minimal sets. These subsets of covariates are shown to be identified under mild assumptions. These results lead us to propose data-driven algorithms for the selection of minimal sets of covariates.
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| 6. |
- Hall, P, et al.
(författare)
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On prediction intervals based on predictive likelihood or bootstrap methods
- 1999
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Ingår i: Biometrika. - 0006-3444 .- 1464-3510. ; 86:4, s. 871-880
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Tidskriftsartikel (refereegranskat)abstract
- We argue that prediction intervals based on predictive likelihood do not correct for curvature with respect to the parameter value when they implicitly approximate an unknown probability density. Partly as a result of this difficulty, the order of coverage error associated with predictive intervals and predictive limits is equal to only the inverse of sample size. In this respect those methods do not improve on the simpler,'naive' or 'estimative' approach. Moreover, in cases of practical importance the latter can be preferable, in terms of both the size and sign of coverage error. We show that bootstrap calibration of both naive and predictive-likelihood approaches increases coverage accuracy of prediction intervals by an order of magnitude, and, in the case of naive intervals, preserves that method's numerical and analytical simplicity. Therefore, we argue, the bootstrap-calibrated naive approach is a particularly competitive alternative to more conventional, but more complex, techniques based on predictive likelihood.
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| 7. |
- Hall, P, et al.
(författare)
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Permutation tests for equality of distributions in high-dimensional settings
- 2002
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Ingår i: Biometrika. - : Oxford University Press (OUP). - 0006-3444 .- 1464-3510. ; 89:2, s. 359-374
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Tidskriftsartikel (refereegranskat)abstract
- Motivated by applications in high-dimensional settings, we suggest a test of the hypothesis H-0 that two sampled distributions are identical. It is assumed that two independent datasets are drawn from the respective populations, which may be very general. In particular, the distributions may be multivariate or infinite-dimensional, in the latter case representing, for example, the distributions of random functions from one Euclidean space to another. Our test uses a measure of distance between data. This measure should be symmetric but need not satisfy the triangle inequality, so it is not essential that it be a metric. The test is based on ranking the pooled dataset, with respect to the distance and relative to any fixed data value, and repeating this operation for each fixed datum. A permutation argument enables a critical point to be chosen such that the test has concisely known significance level, conditional on the set of all pairwise distances.
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| 8. |
- Holst, Lars
(författare)
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Asymptotic normality and efficiency for certain goodness-of-fit tests
- 1972
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Ingår i: Biometrika. - 0006-3444 .- 1464-3510. ; 59:1, s. 137-145
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Tidskriftsartikel (refereegranskat)abstract
- Assume that a random sample of size n has been taken from a multinomial distribution with N cells. Let ξk be the number of observations in the kth cell and setZn=(ξ1, 1/N)+Fn(ξn,N/N).It is proved that, under general conditions, Zn is asymptotically normal when n and N tend to infinity so that n/N ↑ α > 0. This result is used to study asymptotic efficiency for certain goodness-of-fit tests. The chi-squared statistic turns out to be optimal in some situations.
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| 9. |
- Jack, Cuzick, et al.
(författare)
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Frequency estimation from crossings of an unknown level
- 1980
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Ingår i: Biometrika. - : Oxford University Press (OUP). - 0006-3444 .- 1464-3510. ; 67:1, s. 65-72
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Tidskriftsartikel (refereegranskat)abstract
- By counting the number of upcrossings of the mean level by a stationary Gaussian process one can estimate the mean frequency of the process. Here we present a frequency estimator based on the number of upcrossings of one unknown level hoped to be near the mean, and the percentage of the total observation time spent above the level. This is equivalent to observing upcrossings of a known level in a process with unknown mean and variance. Formulae are given for the bias and variance of the estimator, and conditions for its asymptotic normality. Numerical examples show that the estimator behaves reasonably for levels within one standard deviation from the process mean.
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| 10. |
- Jin, Shaobo, 1987-, et al.
(författare)
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A note on the accuracy of adaptive Gauss-Hermite quadrature
- 2020
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Ingår i: Biometrika. - : Oxford Academic. - 0006-3444 .- 1464-3510. ; 107:3, s. 737-744
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Tidskriftsartikel (refereegranskat)abstract
- Numerical quadrature methods are needed for many models in order to approximate integrals in the likelihood function. In this note, we correct the error rate given by Liu & Pierce (1994) for integrals approximated with adaptive Gauss–Hermite quadrature and show that the approximation is less accurate than previously thought. We discuss the relationship between the error rates of adaptive Gauss–Hermite quadrature and Laplace approximation, and provide a theoretical explanation of simulation results obtained in previous studies regarding the accuracy of adaptive Gauss–Hermite quadrature.
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