Finite Sample Performance Research Articles

G-formula for observational studies under stratified interference, with application to bed net use on malaria.

Assessing population-level effects of vaccines and other infectious disease prevention measures is important to the field of public health. In infectious disease studies, one person's treatment may affect another individual's outcome, that is, there may be interference between units. For example, the use of bed nets to prevent malaria by one individual may have an indirect effect on other individuals living in close proximity. In some settings, individuals may form groups or clusters where interference only occurs within groups, that is, there is partial interference. Inverse probability weighted estimators have previously been developed for observational studies with partial interference. Unfortunately, these estimators are not well suited for studies with large clusters. Therefore, in this paper, the parametric g-formula is extended to allow for partial interference. G-formula estimators are proposed for overall effects, effects when treated, and effects when untreated. The proposed estimators can accommodate large clusters and do not suffer from the g-null paradox that may occur in the absence of interference. The large sample properties of the proposed estimators are derived assuming no unmeasured confounders and that the partial interference takes a particular form (referred to as 'weak stratified interference'). Simulation studies are presented demonstrating the finite-sample performance of the proposed estimators. The Demographic and Health Survey from the Democratic Republic of the Congo is then analyzed using the proposed g-formula estimators to assess the effects of bed net use on malaria.

Consistent two-stage estimation in heterogeneous network autoregressive model

Obtaining consistent estimates of network effects in the heterogeneous network autoregressive model presents significant challenges. These challenges arise from the large number of target parameters, potential endogeneity, and non-identifiability issues. To overcome these challenges, we reformulate the model into a higher-order version. Our proposed two-stage estimation procedure first reduces parameter complexity by screening out nodes with negligible network effects. Then, we employ the ordinary least squares method and the instrumental variables technique for effective post-screening estimation. We further investigate the consistency and asymptotic normality of the estimators under appropriate assumptions and explore the cases of heteroscedasticity. The finite sample performance of the two-stage method is evaluated by simulation studies and an empirical analysis.

Goodness of fit test for a skewed generalized normal distribution

ABSTRACT The skewed generalized normal (SGN) distribution with four parameters is a versatile distribution that can effectively model data with skewness and heavy or light tails. In this paper, we conduct two classes of goodness of fit tests for the SGN distribution based on the empirical distribution function (edf) and the sample correlation coefficient. The first class involves transforming the sample into approximately mixed gamma observations, and then applying five classical parametric bootstrap edf-based goodness of fit tests. The second class is based on the inverse probability transformation and utilizes the sample correlation coefficient as the test statistic. We compare the finite sample performances of the proposed tests for different sample sizes and alternative distributions by extensive numerical studies. The simulation results demonstrate that the proposed tests provide a valid alternative to the standard tests using the original data, and the analysis of real data illustrates its application.

On classes of consistent tests for the Type I Pareto distribution based on a characterization involving order statistics

We propose new classes of goodness-of-fit tests for the Pareto Type I distribution. These tests are based on a characterization of the Pareto distribution involving order statistics. We derive the limiting null distribution of the tests and also show that the tests are consistent against fixed alternatives. The finite-sample performance of the newly proposed tests are evaluated and compared to some of the existing tests, where it is found that the new tests are competitive in terms of powers. The paper concludes with an application to a real world data set, namely the earnings of the 22 highest paid participants in the inaugural season of LIV golf.

FDR control for linear log-contrast models with high-dimensional compositional covariates

Linear log-contrast models have been widely used to describe the relationship between the response of interest and the compositional covariates, in which one central task is to identify the significant compositional covariates while controlling the false discovery rate (FDR) at a nominal level. To achieve this goal, a new FDR control method is proposed for linear log-contrast models with high-dimensional compositional covariates. An appealing feature of the proposed method is that it completely bypasses the traditional p-values and utilizes only the symmetry property of the test statistic for the unimportant compositional covariates to give an upper bound of the FDR. Under some regularity conditions, the FDR can be asymptotically controlled at the nominal level for the proposed method in theory, and the theoretical power is also proven to approach one as the sample size tends to infinity. The finite-sample performance of the proposed method is evaluated through extensive simulation studies, and applications to microbiome compositional datasets are also provided.

Dynamic hierarchical state space forecasting.

In this paper, we aim to both borrow information from existing units and incorporate the target unit's history data in time series forecasting. We consider a situation when we have time series data from multiple units that share similar patterns when aligned in terms of an internal time. The internal time is defined as an index according to evolving features of interest. When mapped back to the calendar time, these time series can span different time intervals that can include the future calendar time of the targeted unit, over which we can borrow the information from other units in forecasting the targeted unit. We first build a hierarchical state space model for the multiple time series data in terms of the internal time, where the shared components capture the similarities among different units while allowing for unit-specific deviations. A conditional state space model is then constructed to incorporate the information of existing units as the prior information in forecasting the targeted unit. By running the Kalman filtering based on the conditional state space model on the targeted unit, we incorporate both the information from the other units and the history of the targeted unit. The forecasts are then transformed from internal time back into calendar time for ease of interpretation. A simulation study is conducted to evaluate the finite sample performance. Forecasting state-level new COVID-19 cases in United States is used for illustration.

Reprint of: Robust inference on correlation under general heterogeneity

Considerable evidence in past research shows size distortion in standard tests for zero autocorrelation or zero cross-correlation when time series are not independent identically distributed random variables, pointing to the need for more robust procedures. Recent tests for serial correlation and cross-correlation in Dalla, Giraitis, and Phillips (2022) provide a more robust approach, allowing for heteroskedasticity and dependence in uncorrelated data under restrictions that require a smooth, slowly-evolving deterministic heteroskedasticity process. The present work removes those restrictions and validates the robust testing methodology for a wider class of innovations and regression residuals allowing for heteroscedastic uncorrelated and non-stationary data settings. The updated analysis given here enables more extensive use of the methodology in practical applications. Monte Carlo experiments confirm excellent finite sample performance of the robust test procedures even for extremely complex white noise processes. The empirical examples show that use of robust testing methods can materially reduce spurious evidence of correlations found by standard testing procedures.

A supervised weeding method to cluster high dimensional predictors with application to job market analysis

The clustering of high-dimensional predictors draws increasing attention in various scientific areas, such as text mining and biological data analysis. In standard clustering procedures, when predictors are clustered, they only showcase the inherent patterns within the predictor set, lacking the capacity to predict the response variable. To this end, a new supervised weeding algorithm is advocated to address the dual requirement of detecting sparse clusters and capturing the prediction effects. The proposed algorithm is based on an iterative feature screening and coherence evaluation procedure. It iteratively weeds off the unimportant predictors in a backward fashion, forming sequences of nested sets to determine data-driven optimal cut-offs. This study uses Monte Carlo simulation to assess the finite-sample performance of the proposed method. The findings demonstrate that both the clustering and prediction performance of the proposed method are comparable to existing methods that concentrate solely on one aspect of the dual targets. An analysis of a job description dataset is conducted to explore significant groups of keywords that affect employees' salaries.

Pairwise stochastic approximation for confirmatory factor analysis of categorical data.

Pairwise likelihood is a limited-information method widely used to estimate latent variable models, including factor analysis of categorical data. It can often avoid evaluating high-dimensional integrals and, thus, is computationally more efficient than relying on the full likelihood. Despite its computational advantage, the pairwise likelihood approach can still be demanding for large-scale problems that involve many observed variables. We tackle this challenge by employing an approximation of the pairwise likelihood estimator, which is derived from an optimization procedure relying on stochastic gradients. The stochastic gradients are constructed by subsampling the pairwise log-likelihood contributions, for which the subsampling scheme controls the per-iteration computational complexity. The stochastic estimator is shown to be asymptotically equivalent to the pairwise likelihood one. However, finite-sample performance can be improved by compounding the sampling variability of the data with the uncertainty introduced by the subsampling scheme. We demonstrate the performance of the proposed method using simulation studies and two real data applications.

A Mallows-type model averaging estimator for de-noise linear models

. This article is concerned with model averaging for de-noise linear models, in which some covariates are not observed, but their ancillary variables are available. The least-squares-based estimation procedure is used to estimate the unknown regression parameter in each candidate model after the calibrated error-prone covariates are obtained. Then a Mallows-type weight choice criterion is constructed. When all candidate models are misspecified, the model averaging estimator is asymptotically optimal in the sense that achieving the lowest possible squared error. On the other hand, when the true model is included in the set of candidate models, the model averaging estimator of the regression parameter is root n consistent. The finite sample performance of our model averaging estimator is evaluated by some simulation studies. The proposed procedure is further applied to real-data analysis.

Semiparametric spatial autoregressive models with nonlinear endogeneity

. This article constructs nonparametric two-step least squares (2SLS) and generalized method of moments (GMM) sieve estimators to estimate a functional-coefficient spatial autoregressive model with an endogenous environment variable. We derive the consistency and asymptotic normality results for our proposed sieve estimators. A small Monte Carlo study shows that our proposed estimators exhibit good finite-sample performance. An empirical application is used to illustrate the usefulness of our methods.

Testing for proportions when data are classified into a large number of groups

When dealing with categorical data, a common concern is to check if the observed relative frequencies agree with a certain fixed vector of ideal proportions. Suppose that the population is divided into subpopulations or groups. In such a case, the ideal proportions could vary among groups and one may be interested in simultaneously testing if the observed proportions agree with those ideal proportions in all groups. A novel procedure is proposed for carrying out such a testing problem. The test statistic is shown to be asymptotically normal, avoiding the use of complicated resampling methods to get p-values. The asymptotic behavior of the test under alternatives is also studied. Here, by asymptotic, we mean when the number of groups increases; the sample sizes of the data from each group can either stay bounded or grow with the number of groups. The finite sample performance of the new test is empirically evaluated through an extensive simulation study. The usefulness of the proposal is illustrated with some data sets.

Panel threshold model with covariate-dependent thresholds and unobserved individual-specific threshold effects

This article introduces a panel threshold model with covariate-dependent and time-varying thresholds and unobserved individual-specific threshold effects (PTCDI). We develop methods for estimation and inference for threshold parameters in the proposed PTCDI model by employing the correlated random effects (CRE) device. We also suggest test statistics for linearity, threshold constancy, unobserved individual-specific threshold effects, and for determining the number of thresholds. We derive the asymptotic properties of the proposed estimator in the small-threshold-effect framework and establish the limiting distributions of the suggested test statistics. We also investigate the extension to dynamic panels and show that both the static and dynamic models can be handled uniformly in the CRE framework. Monte Carlo simulation results indicate that the estimation, inference, and testing procedures have the desired performance in finite samples. The model is illustrated with two empirical applications to the relationship between cash flow and investment and the nexus between inflation and economic growth.

Variable selection using data splitting and projection for principal fitted component models in high dimension

Sufficient dimension reduction (SDR) is such an effective way to detect nonlinear relationship between response variable and covariates by reducing the dimensionality of covariates without information loss. The principal fitted component (PFC) model is a way to implement SDR using some class of basis functions, however the PFC model is not efficient when there are many irrelevant or noisy covariates. There have been a few studies on the selection of variables in the PFC model via penalized regression or sequential likelihood ratio test. A novel variable selection technique in the PFC model has been proposed by incorporating a recent development in multiple testing such as mirror statistics and random data splitting. It is highlighted how we construct a mirror statistic in the PFC model using the idea of projection of coefficients to the other space generated from data splitting. The proposed method is superior to some existing methods in terms of false discovery rate (FDR) control and applicability to high-dimensional cases. In particular, the proposed method outperforms other methods as the number of covariates tends to be getting larger, which would be appealing in high dimensional data analysis. Simulation studies and analyses of real data sets have been conducted to show the finite sample performance and the gain that it yields compared to existing methods.

A Frailty Model for Semi-competing Risk Data with Applications to Colon Cancer

In semi-competing risks (which generalizes the competing risks scenario), a subject may experience both terminal and non-terminal events, usually dependent, where the event time to the intermediate non-terminal event (say, tumor recurrence in cancer studies) is subject to censoring by the terminal event (say, death), but not vice-versa. As an alternative to the latent failure time formulation of semi-competing risks with joint survival functions, here, we consider an illness-death (multistate) shared frailty framework, where the dependency between the terminal and non-terminal failure times is incorporated via the power variance frailty between the conditional transition rates that are assumed Markov. Inference is conducted via maximum likelihood. A simulation study is conducted to evaluate the finite sample performance of the model parameters. Finally, we compare and contrast our power variance frailty proposal to known alternatives via application to a colon cancer dataset. Relevant R code for implementation of our model is available in GitHub.

Nonparametric Estimation of Conditional Copula Using Smoothed Checkerboard Bernstein Sieves

Conditional copulas are useful tools for modeling the dependence between multiple response variables that may vary with a given set of predictor variables. Conditional dependence measures such as conditional Kendall’s tau and Spearman’s rho that can be expressed as functionals of the conditional copula are often used to evaluate the strength of dependence conditioning on the covariates. In general, semiparametric estimation methods of conditional copulas rely on an assumed parametric copula family where the copula parameter is assumed to be a function of the covariates. The functional relationship can be estimated nonparametrically using different techniques, but it is required to choose an appropriate copula model from various candidate families. In this paper, by employing the empirical checkerboard Bernstein copula (ECBC) estimator, we propose a fully nonparametric approach for estimating conditional copulas, which does not require any selection of parametric copula models. Closed-form estimates of the conditional dependence measures are derived directly from the proposed ECBC-based conditional copula estimator. We provide the large-sample consistency of the proposed estimator as well as the estimates of conditional dependence measures. The finite-sample performance of the proposed estimator and comparison with semiparametric methods are investigated through simulation studies. An application to real case studies is also provided.

A hybrid nonparametric multivariate density estimator with applications to risk management

. Multivariate density estimation is plagued by the curse of dimensionality in theory and practice. We propose a hybrid density estimator of a multivariate density f that combines the strengths of the kernel estimator and the exponential series estimator. This estimator refines a preliminary kernel estimate f ̂ 0 with a multiplicative correction that estimates the ratio r = f / f ̂ 0 with an exponential series estimator. Thanks to the consistency of the pilot estimate, the coefficients of the series expansion tend to approach zero asymptotically. Accordingly, we design a thresholding method for basis function selection. A major obstacle of multivariate exponential series estimator is the calculation of its normalization factor. We resolve this difficulty with Monte Carlo integration, using the pilot kernel estimate as the trial density for importance sampling. This approach greatly enhances the practicality of the hybrid estimator. Numerical simulations demonstrate the good finite sample performance of the hybrid estimator. We present one empirical application in financial risk management.

Estimating conditional average treatment effects with heteroscedasticity by model averaging and matching

We propose a model averaging approach, combined with a partition and matching method to estimate the conditional average treatment effects under heteroskedastic error settings. The proposed approach has asymptotic optimality and consistency of weights and estimator. Numerical studies show that our method has good finite-sample performances.

Variable selection and inference strategies for multiple compositional regression

An important problem in compositional data analysis is variable selection in linear regression models with compositional covariates. In the context of microbiome data analysis, there is a demand for considering grouping information such as structures among taxa and multiple sampling sites, resulting in multiple compositional covariates. We develop and compare two different methods of variable selection and inference strategies, based on the debiased lasso and a resampling-based approach. Confidence intervals for individual regression coefficients, obtained from each of the two methods, are shown to be asymptotically valid even in a high-dimension, low-sample-size regime. However, microbiome data often have extremely small sample sizes, rendering asymptotic results unreliable. Through extensive numerical comparisons of the finite-sample performances of the two methods, we find that resampling-based approaches outperform the debiased compositional lasso in cases of extremely small sample sizes, showing higher positive predictive values. Conversely, for larger sample sizes, debiasing yields better results. We apply the proposed multiple compositional regression to steer microbiome data, identifying key bacterial taxa associated with important cattle quality measures.

Bootstrap prediction inference of nonlinear autoregressive models

The nonlinear autoregressive (NLAR) model plays an important role in modeling and predicting time series. One‐step ahead prediction is straightforward using the NLAR model, but the multi‐step ahead prediction is cumbersome. For instance, iterating the one‐step ahead predictor is a convenient strategy for linear autoregressive (LAR) models, but it is suboptimal under NLAR. In this article, we first propose a simulation and/or bootstrap algorithm to construct optimal point predictors under an or loss criterion. In addition, we construct bootstrap prediction intervals in the multi‐step ahead prediction problem; in particular, we develop an asymptotically valid quantile prediction interval as well as a pertinent prediction interval for future values. To correct the undercoverage of prediction intervals with finite samples, we further employ predictive – as opposed to fitted – residuals in the bootstrap process. Simulation and empirical studies are also given to substantiate the finite sample performance of our methods.