In a spatial-temporal model, structural change and/or spatial heterogeneity can easily affect estimation of parameters. Following the spatial-temporal model in [1], we develop a nonparametric procedure for test-ing the presence of structural change and spatial heterogeneity using bootstrap techniques and the forward search algorithm. The time series bootstrap can filter the effect of temporary structural change in the con-struction of a confidence interval for the temporal parameter. The forward search will also facilitate the construction of a robust confidence interval for the spatial parameter. These confidence intervals are then used in deciding on the null hypothesis that there is no structural change/spatial heterogeneity. Simulation studies illustrate the ability of the proposed test procedure in detecting presence of structural change and spatial heterogeneity under certain conditions.
Cochran's $Q$ statistic is routinely used for testing heterogeneity in meta-analysis. Its expected value is also used for estimation of between-study variance $τ^2$. Cochran's $Q$, or $Q_{IV}$, uses estimated inverse-variance weights which makes approximating its distribution rather complicated. As an alternative, we are investigating a new $Q$ statistic, $Q_F$, whose constant weights use only the studies' effective sample sizes. For standardized mean difference as the measure of effect, we study, by simulation, approximations to distributions of $Q_{IV}$ and $Q_F$, as the basis for tests of h…
Consider a large social network with possibly severe degree heterogeneity and mixed-memberships. We are interested in testing whether the network has only one community or there are more than one communities. The problem is known to be non-trivial, partially due to the presence of severe degree heterogeneity. We construct a class of test statistics using the numbers of short paths and short cycles, and the key to our approach is a general framework for canceling the effects of degree heterogeneity. The tests compare favorably with existing methods. We support our methods with careful analysis …
Identifying informative predictors in a high dimensional regression model is a critical step for association analysis and predictive modeling. Signal detection in the high dimensional setting often fails due to the limited sample size. One approach to improve power is through meta-analyzing multiple studies on the same scientific question. However, integrative analysis of high dimensional data from multiple studies is challenging in the presence of between study heterogeneity. The challenge is even more pronounced with additional data sharing constraints under which only summary data but not i…
How can researchers test for heterogeneity in the local structure of a network? In this paper, we present a framework that utilizes random sampling to give subgraphs which are then used in a goodness of fit test to test for heterogeneity. We illustrate how to use the goodness of fit test for an analytically derived distribution as well as an empirical distribution. To demonstrate our framework, we consider the simple case of testing for edge probability heterogeneity. We examine the significance level, power and computation time for this case with appropriate examples. Finally we outline how t…
In this paper, we study the problem of testing the mean vectors of high dimensional data in both one-sample and two-sample cases. The proposed testing procedures employ maximum-type statistics and the parametric bootstrap techniques to compute the critical values. Different from the existing tests that heavily rely on the structural conditions on the unknown covariance matrices, the proposed tests allow general covariance structures of the data and therefore enjoy wide scope of applicability in practice. To enhance powers of the tests against sparse alternatives, we further propose two-step pr…
We discuss a simplified version of the testing problem considered by Pelican and Graham (2019): testing for interdependencies in preferences over links among N (possibly heterogeneous) agents in a network. We describe an exact test which conditions on a sufficient statistic for the nuisance parameter characterizing any agent-level heterogeneity. Employing an algorithm due to Blitzstein and Diaconis (2011), we show how to simulate the null distribution of the test statistic in order to estimate critical values and/or p-values. We illustrate our methods using the Nyakatoke risk-sharing network. …
We consider the problem of testing for treatment effect heterogeneity in observational studies, and propose a nonparametric test based on multisample U-statistics. To account for potential confounders, we use reweighted data where the weights are determined by estimated propensity scores. The proposed method does not require any parametric assumptions on the outcomes and bypasses the need for modeling the treatment effect for each study subgroup. We establish the asymptotic normality for the test statistic, and demonstrate its superior numerical performance over several competing approaches vi…
Researchers are usually interested in examining the impact of covariates when separating heterogeneous samples into latent classes that are more homogeneous. The majority of theoretical and empirical studies with such aims have focused on identifying covariates as predictors of class membership in the structural equation modeling framework. In other words, the covariates only indirectly affect the sample heterogeneity. However, the covariates' influence on between-individual differences can also be direct. This article presents a mixture model that investigates covariates to explain within-clu…
Based on structured data derived from large complex systems, we computationally further develop and refine a major factor selection protocol by accommodating structural dependency and heterogeneity among many features to unravel data's information content. Two operational concepts: ``de-associating'' and its counterpart ``shadowing'' that play key roles in our protocol, are reasoned, explained, and carried out via contingency table platforms. This protocol via ``de-associating'' capability would manifest data's information content by identifying which covariate feature-sets do or don't provide…
We developed a novel approach to identification and model testing in linear structural equation models (SEMs) based on auxiliary variables (AVs), which generalizes a widely-used family of methods known as instrumental variables. The identification problem is concerned with the conditions under which causal parameters can be uniquely estimated from an observational, non-causal covariance matrix. In this paper, we provide an algorithm for the identification of causal parameters in linear structural models that subsumes previous state-of-the-art methods. In other words, our algorithm identifies s…
Individuals may differ in their parameter values. This article discusses a three-step method of studying such differences by calculating and then modeling "individual parameter contributions", making the study of heterogeneity in arbitrary structural equation model parameters as technically challenging as performing linear regression. The proposed approach allows for a contribution to the study of differential error variances in survey methodology that would have been difficult to make otherwise.
Testing for stability in linear panel data models has become an important topic in both the statistics and econometrics research communities. The available methodologies address testing for changes in the mean/linear trend, or testing for breaks in the covariance structure by checking for the constancy of common factor loadings. In such cases when an external shock induces a change to the stochastic structure of panel data, it is unclear whether the change would be reflected in the mean, the covariance structure, or both. In this paper, we develop a test for structural stability of linear pane…
In this article, a novel identification test is proposed, which can be applied to parameteric models such as Mixture of Normal (MN) distributions, Markow Switching(MS), or Structural Autoregressive (SVAR) models. In the approach, it is assumed that model parameters are identified under the null whereas under the alternative they are not identified. Thanks to the setting, the Maximum Likelihood (ML) estimator preserves its properties under the null hypothesis. The proposed test is based on a comparison of two consistent estimators based on independent subsamples of the data set. A Wald type sta…
Given a symmetric social network, we are interested in testing whether it has only one community or multiple communities. The desired tests should (a) accommodate severe degree heterogeneity, (b) accommodate mixed-memberships, (c) have a tractable null distribution, and (d) adapt automatically to different levels of sparsity, and achieve the optimal phase diagram. How to find such a test is a challenging problem. We propose the Signed Polygon as a class of new tests. Fixing $m \geq 3$, for each $m$-gon in the network, define a score using the centered adjacency matrix. The sum of such scores i…
Randomized experimentation (also known as A/B testing or bucket testing) is widely used in the internet industry to measure the metric impact obtained by different treatment variants. A/B tests identify the treatment variant showing the best performance, which then becomes the chosen or selected treatment for the entire population. However, the effect of a given treatment can differ across experimental units and a personalized approach for treatment selection can greatly improve upon the usual global selection strategy. In this work, we develop a framework for personalization through (i) estim…
We develop a monitoring procedure to detect changes in a large approximate factor model. Letting $r$ be the number of common factors, we base our statistics on the fact that the $\left( r+1\right) $-th eigenvalue of the sample covariance matrix is bounded under the null of no change, whereas it becomes spiked under changes. Given that sample eigenvalues cannot be estimated consistently under the null, we randomise the test statistic, obtaining a sequence of \textit{i.i.d} statistics, which are used for the monitoring scheme. Numerical evidence shows a very small probability of false detections…
Empirical analysis in economics often faces the difficulty that the data is correlated and heterogeneous in some unknown form. Spatial parametric approaches have been widely used to account for dependence structures, but the problem of directly deal with spatially varying parameters has been largely unexplored. The problem can be serious in all those cases in which we have no prior information justified by the economic theory. In this paper we propose an algorithm-based procedure which is able to endogenously identify structural breaks in space. The proposed algorithm is illustrated by using t…
University of California San Diego（加州大学圣迭戈分校）；KU Leuven（鲁汶大学）
Many scientific and engineering challenges -- ranging from pharmacokinetic drug dosage allocation and personalized medicine to marketing mix (4Ps) recommendations -- require an understanding of the unobserved heterogeneity in order to develop the best decision making-processes. In this paper, we develop a hypothesis test and the corresponding p-value for testing for the significance of the homogeneous structure in linear mixed models. A robust matching moment construction is used for creating a test that adapts to the size of the model sparsity. When unobserved heterogeneity at a cluster level…
