scholarly journals Inference for the mean of large $p$ small $n$ data: A finite-sample high-dimensional generalization of Hotelling’s theorem

2013 ◽  
Vol 7 (0) ◽  
pp. 2005-2031 ◽  
Author(s):  
Piercesare Secchi ◽  
Aymeric Stamm ◽  
Simone Vantini
Keyword(s):  
High Dimensional ◽  
Finite Sample ◽  
Large P Small N ◽  
The Mean ◽  
Small N

scholarly journals Mean Empirical Likelihood Inference for Response Mean with Data Missing at Random

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Hanji He ◽  
Guangming Deng
Keyword(s):  
Empirical Likelihood ◽  
Missing At Random ◽  
Confidence Regions ◽  
Likelihood Inference ◽  
High Dimensional ◽  
Finite Sample ◽  
The Mean ◽  
Data Missing ◽  
Consistency And Asymptotic Normality ◽  
The Impact

We extend the mean empirical likelihood inference for response mean with data missing at random. The empirical likelihood ratio confidence regions are poor when the response is missing at random, especially when the covariate is high-dimensional and the sample size is small. Hence, we develop three bias-corrected mean empirical likelihood approaches to obtain efficient inference for response mean. As to three bias-corrected estimating equations, we get a new set by producing a pairwise-mean dataset. The method can increase the size of the sample for estimation and reduce the impact of the dimensional curse. Consistency and asymptotic normality of the maximum mean empirical likelihood estimators are established. The finite sample performance of the proposed estimators is presented through simulation, and an application to the Boston Housing dataset is shown.

scholarly journals Basis Expansions for Functional Snippets

Biometrika ◽  
2020 ◽  
Author(s):  
Zhenhua Lin ◽  
Jane-Ling Wang ◽  
Qixian Zhong
Keyword(s):  
Data Analysis ◽  
Convergence Rate ◽  
Functional Data Analysis ◽  
Functional Data ◽  
Covariance Function ◽  
Covariance Estimation ◽  
Simulation Studies ◽  
Finite Sample ◽  
Covariance Functions ◽  
The Mean

Summary Estimation of mean and covariance functions is fundamental for functional data analysis. While this topic has been studied extensively in the literature, a key assumption is that there are enough data in the domain of interest to estimate both the mean and covariance functions. In this paper, we investigate mean and covariance estimation for functional snippets in which observations from a subject are available only in an interval of length strictly (and often much) shorter than the length of the whole interval of interest. For such a sampling plan, no data is available for direct estimation of the off-diagonal region of the covariance function. We tackle this challenge via a basis representation of the covariance function. The proposed estimator enjoys a convergence rate that is adaptive to the smoothness of the underlying covariance function, and has superior finite-sample performance in simulation studies.

scholarly journals Penalized orthogonal-components regression for large p small n data

2009 ◽  
Vol 3 (0) ◽  
pp. 781-796 ◽  
Author(s):  
Dabao Zhang ◽  
Yanzhu Lin ◽  
Min Zhang
Keyword(s):  
Large P Small N ◽  
Orthogonal Components ◽  
Small N

scholarly journals Variation in Marginal Response to Nitrogen Fertilizer between Locations

2000 ◽  
Vol 32 (2) ◽  
pp. 363-372 ◽  
Author(s):  
Dale K. Graybeal
Keyword(s):  
North Carolina ◽  
Nitrogen Fertilizer ◽  
Logistic Growth ◽  
Growth Equation ◽  
Finite Sample ◽  
Dummy Variable ◽  
Bootstrap Simulation ◽  
Sample Covariance ◽  
The Mean ◽  
Parameter Values

AbstractA logistic growth equation with time and location varying parameters was used to model corn response to applied nitrogen. A nonlinear dummy-variable regression model provided a parsimonious representation of site and time effects on parameter values. The model was used to test for the equality of the mean marginal product of nitrogen fertilizer between locations on the coastal plain of North Carolina. Monte Carlo simulation and bootstrap simulation were used to construct finite sample covariance estimates. Results support rejection of the hypothesis that mean marginal products are equal when nitrogen is applied at 168 kg/ac. A comparison of bootstrapped errors and asymptotic errors suggests that results based on asymptotic theory are fairly reliable in this case.

scholarly journals High-dimensional regression adjustments in randomized experiments

2016 ◽  
Vol 113 (45) ◽  
pp. 12673-12678 ◽  
Author(s):  
Stefan Wager ◽  
Wenfei Du ◽  
Jonathan Taylor ◽  
Robert J. Tibshirani
Keyword(s):  
Treatment Effect ◽  
Average Treatment Effect ◽  
High Dimensional ◽  
Randomized Experiments ◽  
Finite Sample ◽  
Simple Method ◽  
Average Treatment ◽  
Population Average ◽  
High Dimensional Regression ◽  
Effect Estimation

We study the problem of treatment effect estimation in randomized experiments with high-dimensional covariate information and show that essentially any risk-consistent regression adjustment can be used to obtain efficient estimates of the average treatment effect. Our results considerably extend the range of settings where high-dimensional regression adjustments are guaranteed to provide valid inference about the population average treatment effect. We then propose cross-estimation, a simple method for obtaining finite-sample–unbiased treatment effect estimates that leverages high-dimensional regression adjustments. Our method can be used when the regression model is estimated using the lasso, the elastic net, subset selection, etc. Finally, we extend our analysis to allow for adaptive specification search via cross-validation and flexible nonparametric regression adjustments with machine-learning methods such as random forests or neural networks.

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