Canadian Journal of Statistics-Revue Canadienne De Statistique最新文献

In this article, we study the problem of parameter estimation for measurement error models by combining the Bayes method with the instrumental variable approach, deriving the posterior distribution of parameters under different priors with known and unknown variance parameters, respectively, and calculating the Bayes estimator (BE) of the parameters under quadratic loss. However, it is difficult to obtain an explicit expression for BE because of the complex multiple integrals involved. Therefore, we adopt the linear Bayes method, which does not specify the form of the prior and avoids these complicated integral calculations, to obtain an expression for the linear Bayes estimator (LBE) for different priors. We prove that this LBE is superior to the two-stage least squares estimator under the mean squared error matrix criterion. Numerical simulations show that our LBE is very close to the real parameter whether the variance parameters are known or unknown, and it gradually approaches BE as the sample size increases. Our results indicate that this instrumental variable approach is valid for measurement error models.

High-breakdown-point estimators of multivariate location and shape matrices, such as the $��\text{MM}�$-estimator with smoothed hard rejection and the Rocke $��S�$-estimator, are generally designed to have high efficiency for Gaussian data. However, many phenomena are non-Gaussian, and these estimators can therefore have poor efficiency. This article proposes a new tunable $��S�$-estimator, termed the $��{�S�}_{�q�}�$-estimator, for the general class of symmetric elliptical distributions, a class containing many common families such as the multivariate Gaussian, $��t�$-, Cauchy, Laplace, hyperbolic, and normal inverse Gaussian distributions. Across this class, the $��{�S�}_{�q�}�$-estimator is shown to generally provide higher maximum efficiency than other leading high-breakdown estimators while maintaining the maximum breakdown point. Furthermore, the $��{�S�}_{�q�}�$-estimator is demonstrated to be distributionally robust, and its robustness to outliers is demonstrated to be on par with these leading estimators while also being more stable with respect to initial conditions. From a practical viewpoint, these properties make the $��{�S�}_{�q�}�$-estimator broadly applicable for practitioners. These advantages are demonstrated with an example application—the minimum-variance optimal allocation of financial portfolio investments.

Zero inflation, zero deflation, overdispersion, and underdispersion are commonly encountered in count time series. To better describe these characteristics of counts, this article introduces a zero-modified geometric first-order integer-valued autoregressive (INAR(1)) model based on the generalized negative binomial thinning operator, which contains dependent zero-inflated geometric counting series. The new model contains the NGINAR(1) model, ZMGINAR(1) model, and GNBINAR(1) model with geometric marginals as special cases. Some statistical properties are studied, and estimates of the model parameters are derived by the Yule–Walker, conditional least squares, and maximum likelihood methods. Asymptotic properties and numerical results of the estimators are also studied. In addition, some test and forecasting problems are addressed. Three real-data examples are given to show the flexibility and practicability of the new model.

Observational databases provide unprecedented opportunities for secondary use in biomedical research. However, these data can be error-prone and must be validated before use. It is usually unrealistic to validate the whole database because of resource constraints. A cost-effective alternative is a two-phase design that validates a subset of records enriched for information about a particular research question. We consider odds ratio estimation under differential outcome and exposure misclassification and propose optimal designs that minimize the variance of the maximum likelihood estimator. Our adaptive grid search algorithm can locate the optimal design in a computationally feasible manner. Because the optimal design relies on unknown parameters, we introduce a multiwave strategy to approximate the optimal design. We demonstrate the proposed design's efficiency gains through simulations and two large observational studies.

Focusing on polygenic signal detection in high-dimensional genetic association studies of complex traits, we develop a stable and adaptive test for generalized linear models to accommodate different alternatives. To facilitate valid post-selection inference for high-dimensional data, our study here adheres to the original sample-splitting principle but does so repeatedly to increase stability of the inference. We show the asymptotic null distribution of the proposed test for both fixed and diverging numbers of variants. We also show the asymptotic properties of the proposed test under local alternatives, providing insights on why power gain attributed to variable selection and weighting can compensate for efficiency loss due to sample splitting. We support our analytical findings through extensive simulation studies and two applications. The proposed procedure is computationally efficient and has been implemented as the R package DoubleCauchy.

Strong orthogonal arrays are suitable designs for computer experiments because of stratification in low-dimensional projections. However, strong orthogonal arrays may be very expensive for a moderate number of factors. In this article, we develop a method for constructing space-filling designs with more economical run sizes. These designs are not only column-orthogonal but also enjoy a large proportion of low-dimensional stratification properties that strong orthogonal arrays ought to have. Moreover, a class of proposed designs can be 3-orthogonal. In addition, some theoretical results on regular fractional factorial designs are obtained as a by-product.

The choice of a prior distribution is a key aspect of the Bayesian method. However, in many cases, such as the family of power links, this is not trivial. In this article, we introduce a penalized complexity prior (PC prior) of the skewness parameter for this family, which is useful for dealing with imbalanced data. We derive a general expression for this density and show its usefulness for some particular cases such as the power logit and the power probit links. A simulation study and a real data application are used to assess the efficiency of the introduced densities in comparison with the Gaussian and uniform priors. Results show improvement in point and credible interval estimation for the considered models when using the PC prior in comparison to other well-known standard priors.

We develop a group of robust, nonparametric hypothesis tests that detect differences between the covariance operators of several populations of functional data. These tests, called functional Kruskal–Wallis tests for covariance, or FKWC tests, are based on functional data depth ranks. FKWC tests work well even when the data are heavy-tailed, which is shown both in simulation and theory. FKWC tests offer several other benefits: they have a simple asymptotic distribution under the null hypothesis, they are computationally cheap, and they possess transformation-invariance properties. We show that under general alternative hypotheses, these tests are consistent under mild, nonparametric assumptions. As a result, we introduce a new functional depth function called $�{�L�}^{�2�}$-root depth that works well for the purposes of detecting differences in magnitude between covariance kernels. We present an analysis of the FKWC test based on $�{�L�}^{�2�}$-root depth under local alternatives. Through simulations, when the true covariance kernels have an infinite number of positive eigenvalues, we show that these tests have higher power than their competitors while maintaining their nominal size. We also provide a method for computing sample size and performing multiple comparisons.

Mahalanobis distance of covariate means between treatment and control groups is often adopted as a balance criterion when implementing a rerandomization strategy. However, this criterion may not work well for high-dimensional cases because it balances all orthogonalized covariates equally. We propose using principal component analysis (PCA) to identify proper subspaces in which Mahalanobis distance should be calculated. Not only can PCA effectively reduce the dimensionality for high-dimensional covariates, but it also provides computational simplicity by focusing on the top orthogonal components. The PCA rerandomization scheme has desirable theoretical properties for balancing covariates and thereby improving the estimation of average treatment effects. This conclusion is supported by numerical studies using both simulated and real examples.