Browse
Submit Data
Databases
API
Help

Dataset Information

26 Views

0 Connections

0 Citations

0 Reanalyses

0 Downloads

Omics score: 0

Drawing inferences for high-dimensional linear models: A selection-assisted partial regression and smoothing approach.

ABSTRACT: Drawing inferences for high-dimensional models is challenging as regular asymptotic theories are not applicable. This article proposes a new framework of simultaneous estimation and inferences for high-dimensional linear models. By smoothing over partial regression estimates based on a given variable selection scheme, we reduce the problem to low-dimensional least squares estimations. The procedure, termed as Selection-assisted Partial Regression and Smoothing (SPARES), utilizes data splitting along with variable selection and partial regression. We show that the SPARES estimator is asymptotically unbiased and normal, and derive its variance via a nonparametric delta method. The utility of the procedure is evaluated under various simulation scenarios and via comparisons with the de-biased LASSO estimators, a major competitor. We apply the method to analyze two genomic datasets and obtain biologically meaningful results.

SUBMITTER: Fei Z

PROVIDER: S-EPMC6570588 | biostudies-literature | 2019 Jun

REPOSITORIES: biostudies-literature

ACCESS DATA

Json Xml

Publications

Drawing inferences for high-dimensional linear models: A selection-assisted partial regression and smoothing approach.

Fei Zhe Z Zhu Ji J Banerjee Moulinath M Li Yi Y

Biometrics 20190329 2

Drawing inferences for high-dimensional models is challenging as regular asymptotic theories are not applicable. This article proposes a new framework of simultaneous estimation and inferences for high-dimensional linear models. By smoothing over partial regression estimates based on a given variable selection scheme, we reduce the problem to low-dimensional least squares estimations. The procedure, termed as Selection-assisted Partial Regression and Smoothing (SPARES), utilizes data splitting a ...[more]

PMID: 30549000

Similar Datasets

Variable selection for partially linear models via partial correlation.

Project description:The partially linear model (PLM) is a useful semiparametric extension of the linear model that has been well studied in the statistical literature. This paper proposes a variable selection procedure for the PLM with ultrahigh dimensional predictors. The proposed method is different from the existing penalized least squares procedure in that it relies on partial correlation between the partial residuals of the response and the predictors. We systematically study the theoretical properties of the proposed procedure and prove its model consistency property. We further establish the root-n convergence of the estimator of the regression coefficients and the asymptotic normality of the estimate of the baseline function. We conduct Monte Carlo simulations to examine the finite-sample performance of the proposed procedure and illustrate the proposed method with a real data example.

| S-EPMC6555488 | biostudies-literature

Estimation and Inference for High Dimensional Generalized Linear Models: A Splitting and Smoothing Approach.

Project description: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 strategies 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.

| S-EPMC8442657 | biostudies-literature

Testing a single regression coefficient in high dimensional linear models.

Project description:In linear regression models with high dimensional data, the classical z-test (or t-test) for testing the significance of each single regression coefficient is no longer applicable. This is mainly because the number of covariates exceeds the sample size. In this paper, we propose a simple and novel alternative by introducing the Correlated Predictors Screening (CPS) method to control for predictors that are highly correlated with the target covariate. Accordingly, the classical ordinary least squares approach can be employed to estimate the regression coefficient associated with the target covariate. In addition, we demonstrate that the resulting estimator is consistent and asymptotically normal even if the random errors are heteroscedastic. This enables us to apply the z-test to assess the significance of each covariate. Based on the p-value obtained from testing the significance of each covariate, we further conduct multiple hypothesis testing by controlling the false discovery rate at the nominal level. Then, we show that the multiple hypothesis testing achieves consistent model selection. Simulation studies and empirical examples are presented to illustrate the finite sample performance and the usefulness of the proposed method, respectively.

| S-EPMC5484175 | biostudies-literature

Tests for regression coefficients in high dimensional partially linear models.

Project description:We propose a U-statistics test for regression coefficients in high dimensional partially linear models. In addition, the proposed method is extended to test part of the coefficients. Asymptotic distributions of the test statistics are established. Simulation studies demonstrate satisfactory finite-sample performance.

| S-EPMC7236654 | biostudies-literature

L2RM: Low-rank Linear Regression Models for High-dimensional Matrix Responses.

Project description:The aim of this paper is to develop a low-rank linear regression model (L2RM) to correlate a high-dimensional response matrix with a high dimensional vector of covariates when coefficient matrices have low-rank structures. We propose a fast and efficient screening procedure based on the spectral norm of each coefficient matrix in order to deal with the case when the number of covariates is extremely large. We develop an efficient estimation procedure based on the trace norm regularization, which explicitly imposes the low rank structure of coefficient matrices. When both the dimension of response matrix and that of covariate vector diverge at the exponential order of the sample size, we investigate the sure independence screening property under some mild conditions. We also systematically investigate some theoretical properties of our estimation procedure including estimation consistency, rank consistency and non-asymptotic error bound under some mild conditions. We further establish a theoretical guarantee for the overall solution of our two-step screening and estimation procedure. We examine the finite-sample performance of our screening and estimation methods using simulations and a large-scale imaging genetic dataset collected by the Philadelphia Neurodevelopmental Cohort (PNC) study.

| S-EPMC7781207 | biostudies-literature

Efficient test-based variable selection for high-dimensional linear models.

Project description:Variable selection plays a fundamental role in high-dimensional data analysis. Various methods have been developed for variable selection in recent years. Well-known examples are forward stepwise regression (FSR) and least angle regression (LARS), among others. These methods typically add variables into the model one by one. For such selection procedures, it is crucial to find a stopping criterion that controls model complexity. One of the most commonly used techniques to this end is cross-validation (CV) which, in spite of its popularity, has two major drawbacks: expensive computational cost and lack of statistical interpretation. To overcome these drawbacks, we introduce a flexible and efficient test-based variable selection approach that can be incorporated into any sequential selection procedure. The test, which is on the overall signal in the remaining inactive variables, is based on the maximal absolute partial correlation between the inactive variables and the response given active variables. We develop the asymptotic null distribution of the proposed test statistic as the dimension tends to infinity uniformly in the sample size. We also show that the test is consistent. With this test, at each step of the selection, a new variable is included if and only if the p-value is below some pre-defined level. Numerical studies show that the proposed method delivers very competitive performance in terms of variable selection accuracy and computational complexity compared to CV.

| S-EPMC6317739 | biostudies-other

Weight Smoothing for Generalized Linear Models Using a Laplace Prior.

Project description:When analyzing data sampled with unequal inclusion probabilities, correlations between the probability of selection and the sampled data can induce bias if the inclusion probabilities are ignored in the analysis. Weights equal to the inverse of the probability of inclusion are commonly used to correct possible bias. When weights are uncorrelated with the descriptive or model estimators of interest, highly disproportional sample designs resulting in large weights can introduce unnecessary variability, leading to an overall larger mean square error compared to unweighted methods. We describe an approach we term 'weight smoothing' that models the interactions between the weights and the estimators as random effects, reducing the root mean square error (RMSE) by shrinking interactions toward zero when such shrinkage is allowed by the data. This article adapts a flexible Laplace prior distribution for the hierarchical Bayesian model to gain a more robust bias-variance tradeoff than previous approaches using normal priors. Simulation and application suggest that under a linear model setting, weight-smoothing models with Laplace priors yield robust results when weighting is necessary, and provide considerable reduction in RMSE otherwise. In logistic regression models, estimates using weight-smoothing models with Laplace priors are robust, but with less gain in efficiency than in linear regression settings.

| S-EPMC5719898 | biostudies-literature

Variable Selection for Nonparametric Quantile Regression via Smoothing Spline AN OVA.

Project description:Quantile regression provides a more thorough view of the effect of covariates on a response. Nonparametric quantile regression has become a viable alternative to avoid restrictive parametric assumption. The problem of variable selection for quantile regression is challenging, since important variables can influence various quantiles in different ways. We tackle the problem via regularization in the context of smoothing spline ANOVA models. The proposed sparse nonparametric quantile regression (SNQR) can identify important variables and provide flexible estimates for quantiles. Our numerical study suggests the promising performance of the new procedure in variable selection and function estimation. Supplementary materials for this article are available online.

| S-EPMC3926212 | biostudies-literature

SPReM: Sparse Projection Regression Model For High-dimensional Linear Regression.

Project description:The aim of this paper is to develop a sparse projection regression modeling (SPReM) framework to perform multivariate regression modeling with a large number of responses and a multivariate covariate of interest. We propose two novel heritability ratios to simultaneously perform dimension reduction, response selection, estimation, and testing, while explicitly accounting for correlations among multivariate responses. Our SPReM is devised to specifically address the low statistical power issue of many standard statistical approaches, such as the Hotelling's T2 test statistic or a mass univariate analysis, for high-dimensional data. We formulate the estimation problem of SPREM as a novel sparse unit rank projection (SURP) problem and propose a fast optimization algorithm for SURP. Furthermore, we extend SURP to the sparse multi-rank projection (SMURP) by adopting a sequential SURP approximation. Theoretically, we have systematically investigated the convergence properties of SURP and the convergence rate of SURP estimates. Our simulation results and real data analysis have shown that SPReM out-performs other state-of-the-art methods.

| S-EPMC4627720 | biostudies-literature

An asymptotic and empirical smoothing parameters selection method for smoothing spline ANOVA models in large samples.

Project description:Large samples are generated routinely from various sources. Classic statistical models, such as smoothing spline ANOVA models, are not well equipped to analyse such large samples because of high computational costs. In particular, the daunting computational cost of selecting smoothing parameters renders smoothing spline ANOVA models impractical. In this article, we develop an asympirical, i.e., asymptotic and empirical, smoothing parameters selection method for smoothing spline ANOVA models in large samples. The idea of our approach is to use asymptotic analysis to show that the optimal smoothing parameter is a polynomial function of the sample size and an unknown constant. The unknown constant is then estimated through empirical subsample extrapolation. The proposed method significantly reduces the computational burden of selecting smoothing parameters in high-dimensional and large samples. We show that smoothing parameters chosen by the proposed method tend to the optimal smoothing parameters that minimize a specific risk function. In addition, the estimator based on the proposed smoothing parameters achieves the optimal convergence rate. Extensive simulation studies demonstrate the numerical advantage of the proposed method over competing methods in terms of relative efficacy and running time. In an application to molecular dynamics data containing nearly one million observations, the proposed method has the best prediction performance.

| S-EPMC8294473 | biostudies-literature

OmicsDI is part of the ELIXIR infrastructure

OmicsDI is an Elixir interoperability service. Learn more ›

Tweets

OmicsDI Databases

PRIDE
PeptideAtlas
MassIVE
JPOST Repository
Physiome Model Repository

EGA
EVA
ENA
LINCS
PAXDB
Cell Collective

MetaboLights
Metabolomics Workbench
MetabolomeExpress
GNPS
BioModels
FAIRDOMHub

ArrayExpress
dbGaP
ExpressionAtlas
GEO
NODE

Information

Databases
Help
API
Contact us
Code on GitHub
Terms of use
Submit Data