اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدInference for high-dimensional linear mixed-effects models: A quasi-likelihood approach
205
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
Linear mixed-effects models are widely used in analyzing clustered or repeated measures data. We propose a quasi-likelihood approach for estimation and inference of the unknown parameters in linear mixed-effects models with high-dimensional fixed effects. The proposed method is applicable to general settings where the dimension of the random effects and the cluster sizes are possibly large. Regarding the fixed effects, we provide rate optimal estimators and valid inference procedures that do not rely on the structural information of the variance components. We also study the estimation of variance components with high-dimensional fixed effects in general settings. The algorithms are easy to implement and computationally fast. The proposed methods are assessed in various simulation settings and are applied to a real study regarding the associations between body mass index and genetic polymorphic markers in a heterogeneous stock mice population.
قيم البحث
اقرأ أيضاً
The focus of modern biomedical studies has gradually shifted to explanation and estimation of joint effects of high dimensional predictors on disease risks. Quantifying uncertainty in these estimates may provide valuable insight into prevention strat
egies or treatment decisions for both patients and physicians. High dimensional inference, including confidence intervals and hypothesis testing, has sparked much interest. While much work has been done in the linear regression setting, there is lack of literature on inference for high dimensional generalized linear models. We propose a novel and computationally feasible method, which accommodates a variety of outcome types, including normal, binomial, and Poisson data. We use a splitting and smoothing approach, which splits samples into two parts, performs variable selection using one part and conducts partial regression with the other part. Averaging the estimates over multiple random splits, we obtain the smoothed estimates, which are numerically stable. We show that the estimates are consistent, asymptotically normal, and construct confidence intervals with proper coverage probabilities for all predictors. We examine the finite sample performance of our method by comparing it with the existing methods and applying it to analyze a lung cancer cohort study.
Heterogeneity is an important feature of modern data sets and a central task is to extract information from large-scale and heterogeneous data. In this paper, we consider multiple high-dimensional linear models and adopt the definition of maximin eff
ect (Meinshausen, B{u}hlmann, AoS, 43(4), 1801--1830) to summarize the information contained in this heterogeneous model. We define the maximin effect for a targeted population whose covariate distribution is possibly different from that of the observed data. We further introduce a ridge-type maximin effect to simultaneously account for reward optimality and statistical stability. To identify the high-dimensional maximin effect, we estimate the regression covariance matrix by a debiased estimator and use it to construct the aggregation weights for the maximin effect. A main challenge for statistical inference is that the estimated weights might have a mixture distribution and the resulted maximin effect estimator is not necessarily asymptotic normal. To address this, we devise a novel sampling approach to construct the confidence interval for any linear contrast of high-dimensional maximin effects. The coverage and precision properties of the proposed confidence interval are studied. The proposed method is demonstrated over simulations and a genetic data set on yeast colony growth under different environments.
High-dimensional statistical inference with general estimating equations are challenging and remain less explored. In this paper, we study two problems in the area: confidence set estimation for multiple components of the model parameters, and model
specifications test. For the first one, we propose to construct a new set of estimating equations such that the impact from estimating the high-dimensional nuisance parameters becomes asymptotically negligible. The new construction enables us to estimate a valid confidence region by empirical likelihood ratio. For the second one, we propose a test statistic as the maximum of the marginal empirical likelihood ratios to quantify data evidence against the model specification. Our theory establishes the validity of the proposed empirical likelihood approaches, accommodating over-identification and exponentially growing data dimensionality. The numerical studies demonstrate promising performance and potential practical benefits of the new methods.
We address the issue of performing testing inference in generalized linear models when the sample size is small. This class of models provides a straightforward way of modeling normal and non-normal data and has been widely used in several practical
situations. The likelihood ratio, Wald and score statistics, and the recently proposed gradient statistic provide the basis for testing inference on the parameters in these models. We focus on the small-sample case, where the reference chi-squared distribution gives a poor approximation to the true null distribution of these test statistics. We derive a general Bartlett-type correction factor in matrix notation for the gradient test which reduces the size distortion of the test, and numerically compare the proposed test with the usual likelihood ratio, Wald, score and gradient tests, and with the Bartlett-corrected likelihood ratio and score tests. Our simulation results suggest that the corrected test we propose can be an interesting alternative to the other tests since it leads to very accurate inference even for very small samples. We also present an empirical application for illustrative purposes.
For a high-dimensional linear model with a finite number of covariates measured with error, we study statistical inference on the parameters associated with the error-prone covariates, and propose a new corrected decorrelated score test and the corre
sponding one-step estimator. We further establish asymptotic properties of the newly proposed test statistic and the one-step estimator. Under local alternatives, we show that the limiting distribution of our corrected decorrelated score test statistic is non-central normal. The finite-sample performance of the proposed inference procedure is examined through simulation studies. We further illustrate the proposed procedure via an empirical analysis of a real data example.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
