Panel Data Inference under Spatial Dependence

This paper focuses on inference based on the usual panel data estimators of a one-way error component regression model when the true specification is a spatial error component model. Among the estimators considered, are pooled OLS, random and fixed effects, maximum likelihood under normality, etc. The spatial effects capture the cross-section dependence, and the usual panel data estimators ignore this dependence. Two popular forms of spatial autocorrelation are considered, namely, spatial auto-regressive random effects (SAR-RE) and spatial moving average random effects (SMA-RE). We show that when the spatial coefficients are large, test of hypothesis based on the usual panel data estimators that ignore spatial dependence can lead to misleading inference

State dependence in work-related training participation among British employees: A comparison of different random effects probit estimators.

This paper compares three different estimation approaches for the random effects dynamic panel data model, under the probit assumption on the distribution of the errors. These three approaches are attributed to Heckman (1981), Wooldridge (2005) and Orme (2001). The results are then compared with those obtained from generalised method of moments (GMM) estimators of a dynamic linear probability model, namely the Arellano and Bond (1991) and Blundell and Bond (1998) estimators. A model of work-related training participation for British employees is estimated using individual level data covering the period 1991-1997 from the British Household Panel Survey. This evaluation adds to the existing body of empirical evidence on the performance of these estimators using real data, which supplements the conclusions from simulation studies. The results suggest that for the dynamic random effects probit model the performance of no one estimator is superior to the others. GMM estimation of a dynamic LPM of training participation suggests that the random effects estimators are not sensitive to the distributional assumptions of the unobserved effect.state dependence; training; dynamic panel data models

Consistent estimation of the proportion of false nulls and FDR for adaptive multiple testing Normal means under weak dependence

We consider multiple testing means of many dependent Normal random variables that do not necessarily follow a joint Normal distribution. Under weak dependence, we show the uniform consistency of proportion estimators that are constructed as solutions to Lebesgue-Stieltjes equations for the setting of a point, bounded and one-sided null, respectively, and characterize via the index of weak dependence the sparsest proportion these estimators can consistently estimate. On the other hand, under a principal correlation structure and employing a suitable definition of p-value for composite null hypotheses, we show that three key empirical processes induced by a single-step multiple testing procedure (MTP) satisfy the strong law of large numbers for testing each of the three types of nulls. Further, under this structure and for testing a point null and a one-sided null respectively, we construct an adaptive single-step MTP that employs a proportion estimator mentioned earlier, and show that the false discovery proportion of this procedure satisfies the weak law of large numbers and hence consistently estimates the false discovery rate of the procedure. In addition, we report some findings on the estimators of Jin and of Meinshausen and Rice of the proportion of false nulls in the critically and very sparse regimes under weak dependence and model misspecifications, respectively.Comment: 42 pages; 5 figures; extended methods on adaptive FDR estimation to include composite nulls; added consistency results of proportion estimator for composite nulls; added simulation studies on robustness of proportion estimators; extended simulation to include things related to randomized p-value

Panel Data Inference under Spatial Dependence

This paper focuses on inference based on the usual panel data estimators of a one-way error component regression model when the true specification is a spatial error component model. Among the estimators considered, are pooled OLS, random and fixed effects, maximum likelihood under normality, etc. The spatial effects capture the cross-section dependence, and the usual panel data estimators ignore this dependence. Two popular forms of spatial autocorrelation are considered, namely, spatial auto-regressive random effects (SAR-RE) and spatial moving average random effects (SMA-RE). We show that when the spatial coefficients are large, test of hypothesis based on the usual panel data estimators that ignore spatial dependence can lead to misleading inference

Random Utility, Repeated Choice, and Consumption Dependence

We study consumption dependence in the context of random utility and repeated choice. We show that, in the presence of consumption dependence, the random utility model is a misspecified model of repeated rational choice. This misspecification leads to biased estimators and failures of standard random utility axioms. We characterize exactly when and by how much the random utility model is misspecified when utilities are consumption dependent. As one possible solution to this problem, we consider time disaggregated data. We offer a characterization of consumption dependent random utility when we observe time disaggregated data. Using this characterization, we develop a hypothesis test for consumption dependent random utility that offers computational improvements over the natural extension of Kitamura and Stoye (2018) to our setting

One-point Statistics of the Cosmic Density Field in Real and Redshift Spaces with A Multiresolutional Decomposition

In this paper, we develop a method of performing the one-point statistics of a perturbed density field with a multiresolutional decomposition based on the discrete wavelet transform (DWT). We establish the algorithm of the one-point variable and its moments in considering the effects of Poisson sampling and selection function. We also establish the mapping between the DWT one-point statistics in redshift space and real space, i.e. the algorithm for recovering the DWT one-point statistics from the redshift distortion of bulk velocity, velocity dispersion, and selection function. Numerical tests on N-body simulation samples show that this algorithm works well on scales from a few hundreds to a few Mpc/h for four popular cold dark matter models. Taking the advantage that the DWT one-point variable is dependent on both the scale and the shape (configuration) of decomposition modes, one can design estimators of the redshift distortion parameter (beta) from combinations of DWT modes. When the non-linear redshift distortion is not negligible, the beta estimator from quadrupole-to-monopole ratio is a function of scale. This estimator would not work without adding information about the scale-dependence, such as the power-spectrum index or the real-space correlation function of the random field. The DWT beta estimators, however, do not need such extra information. Numerical tests show that the proposed DWT estimators are able to determine beta robustly with less than 15% uncertainty in the redshift range 0 < z < 3.Comment: 39 pages, 12 figures, ApJ accepte

Rank-based Estimation under Asymptotic Dependence and Independence, with Applications to Spatial Extremes

Multivariate extreme value theory is concerned with modeling the joint tail behavior of several random variables. Existing work mostly focuses on asymptotic dependence, where the probability of observing a large value in one of the variables is of the same order as observing a large value in all variables simultaneously. However, there is growing evidence that asymptotic independence is equally important in real world applications. Available statistical methodology in the latter setting is scarce and not well understood theoretically. We revisit non-parametric estimation and introduce rank-based M-estimators for parametric models that simultaneously work under asymptotic dependence and asymptotic independence, without requiring prior knowledge on which of the two regimes applies. Asymptotic normality of the proposed estimators is established under weak regularity conditions. We further show how bivariate estimators can be leveraged to obtain parametric estimators in spatial tail models, and again provide a thorough theoretical justification for our approach.Comment: 64 pages, 16 figure