1
|
Hu X, Lei J. A Two-Sample Conditional Distribution Test Using Conformal Prediction and Weighted Rank Sum. J Am Stat Assoc 2023. [DOI: 10.1080/01621459.2023.2177165] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/09/2023]
Affiliation(s)
- Xiaoyu Hu
- School of Mathematical Sciences, Center for Statistical Science, Peking University, China
| | - Jing Lei
- Department of Statistics and Data Science, Carnegie Mellon University, USA
| |
Collapse
|
2
|
Khismatullina M, Vogt M. Nonparametric comparison of epidemic time trends: The case of COVID-19. JOURNAL OF ECONOMETRICS 2023; 232:87-108. [PMID: 34054197 PMCID: PMC8141781 DOI: 10.1016/j.jeconom.2021.04.010] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 08/04/2020] [Revised: 02/13/2021] [Accepted: 04/08/2021] [Indexed: 06/12/2023]
Abstract
The COVID-19 pandemic is one of the most pressing issues at present. A question which is particularly important for governments and policy makers is the following: Does the virus spread in the same way in different countries? Or are there significant differences in the development of the epidemic? In this paper, we devise new inference methods that allow to detect differences in the development of the COVID-19 epidemic across countries in a statistically rigorous way. In our empirical study, we use the methods to compare the outbreak patterns of the epidemic in a number of European countries.
Collapse
Affiliation(s)
| | - Michael Vogt
- Institute of Statistics, Department of Mathematics and Economics, Ulm University, 89081 Ulm, Germany
| |
Collapse
|
3
|
Roca-Pardiñas J, Ordóñez C, Machado LM. A method for determining groups in nonparametric regression curves: Application to prefrontal cortex neural activity analysis. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2022; 19:6435-6454. [PMID: 35730265 DOI: 10.3934/mbe.2022302] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/15/2023]
Abstract
Generalized additive models provide a flexible and easily-interpretable method for uncovering a nonlinear relationship between response and covariates. In many situations, the effect of a continuous covariate on the response varies across groups defined by the levels of a categorical variable. When confronted with a considerable number of groups defined by the levels of the categorical variable and a factor-by-curve interaction is detected in the model, it then becomes important to compare these regression curves. When the null hypothesis of equality of curves is rejected, leading to the clear conclusion that at least one curve is different, we may assume that individuals can be grouped into a number of classes whose members all share the same regression function. We propose a method that allows determining such groups with an automatic selection of their number by means of bootstrapping. The validity and behavior of the proposed method were evaluated through simulation studies. The applicability of the proposed method is illustrated using real data from an experimental study in neurology.
Collapse
Affiliation(s)
- Javier Roca-Pardiñas
- Department of Statistics and Operational Research, Vigo University, Vigo 36310, Spain
| | - Celestino Ordóñez
- Department of Mining Exploitation and Prospecting, Geomatics and Computer Graphics Lab, Oviedo University, Mieres 33600, Spain
| | | |
Collapse
|
4
|
Prakash A, Tuo R, Ding Y. Gaussian Process-Aided Function Comparison Using Noisy Scattered Data. Technometrics 2021. [DOI: 10.1080/00401706.2021.1905073] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
Affiliation(s)
- Abhinav Prakash
- Department of Industrial and Systems Engineering, Texas A&M University, College Station, TX
| | - Rui Tuo
- Department of Industrial and Systems Engineering, Texas A&M University, College Station, TX
| | - Yu Ding
- Department of Industrial and Systems Engineering, Texas A&M University, College Station, TX
| |
Collapse
|
5
|
Abstract
Estimation of nonlinear curves and surfaces has long been the focus of semiparametric and nonparametric regression analysis. What has been less studied is the comparison of nonlinear functions. In lower-dimensional situations, inference typically involves comparisons of curves and surfaces. The existing comparative procedures are subject to various limitations, and few computational tools have been made available for off-the-shelf use. To address these limitations, two modified testing procedures for nonlinear curve and surface comparisons are proposed. The proposed computational tools are implemented in an R package, with a syntax similar to that of the commonly used model fitting packages. An R Shiny application is provided with an interactive interface for analysts who do not use R. The new tests are consistent against fixed alternative hypotheses. Theoretical details are presented in an appendix. Operating characteristics of the proposed tests are assessed against the existing methods. Applications of the methods are illustrated through real data examples.
Collapse
Affiliation(s)
- Shi Zhao
- Department of Biostatistics, Indiana University Fairbanks School of Public Health and Indiana University School of Medicine, Indianapolis, Indiana 46202, U.S.A
| | - Giorgos Bakoyannis
- Department of Biostatistics, Indiana University Fairbanks School of Public Health and Indiana University School of Medicine, Indianapolis, Indiana 46202, U.S.A
| | | | - Wanzhu Tu
- Department of Biostatistics, Indiana University Fairbanks School of Public Health and Indiana University School of Medicine, Indianapolis, Indiana 46202, U.S.A
| |
Collapse
|
6
|
Comparing two nonparametric regression curves in the presence of long memory in covariates and errors. METRIKA 2019. [DOI: 10.1007/s00184-019-00735-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
|
7
|
Zhao Y, Zou C, Wang Z. A scalable nonparametric specification testing for massive data. J Stat Plan Inference 2019. [DOI: 10.1016/j.jspi.2018.09.012] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
|
8
|
Sestelo M, Roca‐Pardiñas J. Testing critical points of non‐parametric regression curves: application to the management of stalked barnacles. J R Stat Soc Ser C Appl Stat 2019. [DOI: 10.1111/rssc.12336] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
|
9
|
Affiliation(s)
- Peihua Qiu
- Department of Biostatistics, University of Florida, Gainesville, FL
| | - Xuemin Zi
- School of Science, Tianjin University of Technology and Education, Tianjin, China
| | - Changliang Zou
- Institute of Statistic and LPMC, Nankai University, Nankai Qu, China
| |
Collapse
|
10
|
Affiliation(s)
- Holger Dette
- Fakultät für Mathematik, Ruhr-Universität Bochum, Bochum, Germany
| | | | - Stanislav Volgushev
- Department of Statistical Sciences, University of Toronto, Toronto, Ontario, Canada
- Department of Mathematical & Computational Sciences, University of Toronto Mississauga, Mississauga, Ontario, Canada
| | - Frank Bretz
- Novartis Pharma AG, Basel, Switzerland
- School of Statistics and Management, Shanghai University of Finance and Economics, Shanghai, China
| |
Collapse
|
11
|
Zhang J, Feng Z, Wang X. A constructive hypothesis test for the single-index models with two groups. ANN I STAT MATH 2017. [DOI: 10.1007/s10463-017-0616-y] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
|
12
|
Pardo-Fernández JC, Jiménez-Gamero MD, El Ghouch A. Tests for the equality of conditional variance functions in nonparametric regression. Electron J Stat 2015. [DOI: 10.1214/15-ejs1058] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|
13
|
|
14
|
Park C, Hannig J, Kang KH. Nonparametric Comparison of Multiple Regression Curves in Scale-Space. J Comput Graph Stat 2014. [DOI: 10.1080/10618600.2013.822816] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
|
15
|
Pardo-Fernández JC, Jiménez-Gamero MD, Ghouch AE. A Non-parametricANOVA-type Test for Regression Curves Based on Characteristic Functions. Scand Stat Theory Appl 2014. [DOI: 10.1111/sjos.12102] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
|
16
|
Staicu AM, Li Y, Crainiceanu CM, Ruppert D. Likelihood Ratio Tests for Dependent Data with Applications to Longitudinal and Functional Data Analysis. Scand Stat Theory Appl 2014. [DOI: 10.1111/sjos.12075] [Citation(s) in RCA: 27] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
| | - Yingxing Li
- The Wang Yanan Institute for Studies in Economics; Xiamen University
| | | | - David Ruppert
- Department of Statistical Science and School of Operations Research and Information Engineering; Cornell University
| |
Collapse
|
17
|
Durot C, Groeneboom P, Lopuhaä HP. Testing equality of functions under monotonicity constraints. J Nonparametr Stat 2013. [DOI: 10.1080/10485252.2013.826356] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
|
18
|
|
19
|
Dette H, Wagener J, Volgushev S. Nonparametric comparison of quantile curves: a stochastic process approach. J Nonparametr Stat 2013. [DOI: 10.1080/10485252.2012.732223] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
|
20
|
Abstract
In this article, we address the important problem of comparison of two or more population regression functions. Recently, Pardo-Fernández, Van Keilegom and González-Manteiga (2007) developed test statistics for simple nonparametric regression models: Y(ij) = θ(j)(Z(ij)) + σ(j)(Z(ij))∊(ij), based on empirical distributions of the errors in each population j = 1, … , J. In this paper, we propose a test for equality of the θ(j)(·) based on the concept of generalized likelihood ratio type statistics. We also generalize our test for other nonparametric regression setups, e.g, nonparametric logistic regression, where the loglikelihood for population j is any general smooth function [Formula: see text]. We describe a resampling procedure to obtain the critical values of the test. In addition, we present a simulation study to evaluate the performance of the proposed test and compare our results to those in Pardo-Fernández et al. (2007).
Collapse
Affiliation(s)
- Arnab Maity
- Department of Statistics, North Carolina State University, Raleigh, NC 27695, U.S.A.
| |
Collapse
|
21
|
Roca-Pardiñas J, Cadarso-Suárez C, Pardo-Vazquez JL, Leboran V, Molenberghs G, Faes C, Acuña C. Assessing neural activity related to decision-making through flexible odds ratio curves and their derivatives. Stat Med 2011; 30:1695-711. [PMID: 21433050 DOI: 10.1002/sim.4220] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/08/2009] [Accepted: 01/04/2011] [Indexed: 11/06/2022]
Abstract
It is well established that neural activity is stochastically modulated over time. Therefore, direct comparisons across experimental conditions and determination of change points or maximum firing rates are not straightforward. This study sought to compare temporal firing probability curves that may vary across groups defined by different experimental conditions. Odds-ratio (OR) curves were used as a measure of comparison, and the main goal was to provide a global test to detect significant differences of such curves through the study of their derivatives. An algorithm is proposed that enables ORs based on generalized additive models, including factor-by-curve-type interactions to be flexibly estimated. Bootstrap methods were used to draw inferences from the derivatives curves, and binning techniques were applied to speed up computation in the estimation and testing processes. A simulation study was conducted to assess the validity of these bootstrap-based tests. This methodology was applied to study premotor ventral cortex neural activity associated with decision-making. The proposed statistical procedures proved very useful in revealing the neural activity correlates of decision-making in a visual discrimination task.
Collapse
Affiliation(s)
- Javier Roca-Pardiñas
- Department of Statistics and Operations Research, University of Vigo, Vigo, Pontevedra, Spain.
| | | | | | | | | | | | | |
Collapse
|
22
|
|
23
|
|
24
|
Wilcox RR. Robust ANCOVA using a smoother with bootstrap bagging. THE BRITISH JOURNAL OF MATHEMATICAL AND STATISTICAL PSYCHOLOGY 2009; 62:427-437. [PMID: 18652737 DOI: 10.1348/000711008x325300] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/26/2023]
Abstract
Many robust analogs of the classic analysis of covariance (ANCOVA) method have been proposed, some of which are based on some type of regression smoother. A method that first appeared in this journal, which is relatively simple and performs well in simulations, is based on a running interval smoother combined with comparing medians or 20% trimmed means. It makes no parametric assumption about the regression lines and does not assume that the regression lines are parallel. A possible way of improving the efficiency of the running interval smoother is to use bootstrap bagging and a minor goal here is to report some results supporting this approach. The major goal is to consider how ANCOVA might be performed when bootstrap bagging is used. Simple extensions of extant approaches that use some type of bootstrap method were found to be unsatisfactory. However, a basic percentile bootstrap method was found to perform well in simulations. And a reanalysis of data dealing with teachers' expectations about the cognitive ability of students illustrates that bootstrap bagging can make a practical difference.
Collapse
Affiliation(s)
- Rand R Wilcox
- Department of Psychology, University of Southern California, Los Angeles, California, USA.
| |
Collapse
|
25
|
Davies P, Kovac A. Quantifying the cost of simultaneous non-parametric approximation of several samples. Electron J Stat 2009. [DOI: 10.1214/08-ejs298] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|
26
|
Vilar-Fernández JM, Vilar-Fernández JA, González-Manteiga W. Bootstrap tests for nonparametric comparison of regression curves with dependent errors. TEST-SPAIN 2007. [DOI: 10.1007/s11749-006-0005-y] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
|
27
|
Li F. Testing for the Equality of Two Nonparametric Regression Curves with Long Memory Errors. COMMUN STAT-SIMUL C 2007. [DOI: 10.1080/03610910600716324] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
Affiliation(s)
- Fang Li
- a Department of Mathematical Sciences , Indiana University Purdue University at Indianapolis , Indianapolis , Indiana , USA
| |
Collapse
|
28
|
Koul HL, Li F. Testing for Superiority among Two Time Series. STATISTICAL INFERENCE FOR STOCHASTIC PROCESSES 2005. [DOI: 10.1007/s11203-003-8475-y] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
|
29
|
Kulasekera KB, Wang J. Smoothing Parameter Selection for Power Optimality in Testing of Regression Curves. J Am Stat Assoc 1997. [DOI: 10.1080/01621459.1997.10474003] [Citation(s) in RCA: 23] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/28/2022]
|