Finite Sample Research Articles

Generalized bivariate Kummer-beta distribution with marginals defined on the unit interval.

In this paper, a generalized bivariate Kummer-beta distribution is proposed. The name derives from the fact that its particular cases include univariate Kummer-beta distributions. This distribution generalizes a number of existing bivariate beta distributions, including Nadarajah's bivariate distributions, Libby and Novick's bivariate beta distribution and a central bivariate Kummer-beta distribution. Various properties associated with this newly introduced distribution are derived. The derived properties include product moments, marginal densities, marginal moments, conditional densities, conditional moments, Rényi entropy and Shannon entropy. Motivated by possible applications in economics, genetics, hydrology, meteorology, nuclear physics, and reliability, we also derive distributions of the product and the ratio of the components following the proposed distribution. Parameter estimation by maximum likelihood method is discussed by deriving expressions for score functions. Inference based on maximum likelihood estimation supposes that the maximum likelihood estimators have zero bias and zero mean squared errors. A simulation study is performed to check this for finite samples.

An R Package for Nonparametric Inference on Dynamic Populations with Infinitely Many Types.

Fleming-Viot diffusions are widely used stochastic models for population dynamics that extend the celebrated Wright-Fisher diffusions. They describe the temporal evolution of the relative frequencies of the allelic types in an ideally infinite panmictic population, whose individuals undergo random genetic drift and at birth can mutate to a new allelic type drawn from a possibly infinite potential pool, independently of their parent. Recently, Bayesian nonparametric inference has been considered for this model when a finite sample of individuals is drawn from the population at several discrete time points. Previous works have fully described the relevant estimators for this problem, but current software is available only for the Wright-Fisher finite-dimensional case. Here, we provide software for the general case, overcoming some nontrivial computational challenges posed by this setting. The R package FVDDPpkg efficiently approximates the filtering and smoothing distribution for Fleming-Viot diffusions, given finite samples of individuals collected at different times. A suitable Monte Carlo approximation is also introduced in order to reduce the computational cost.

Optimal Subsampling for Functional Quasi-Mode Regression with Big Data

We propose investigating optimal subsampling for functional regression with massive datasets based on the mode value, which is referred to as functional quasi-mode regression, to reduce data volume and alleviate computational burden. Using data-adaptive weights derived from regression residuals, the suggested regression offers enhanced robustness against nonnormal errors compared to traditional least squares or maximum likelihood estimation methods. To estimate the model, we employ B-spline basis functions to approximate the functional coefficient and include a penalty term in the objective function for enforcing smoothness in the resulting estimator. We adopt a computationally efficient mode-expectation-maximization algorithm, augmented by a Gaussian kernel, for numerical estimation. Under mild regularity conditions, we derive the asymptotic distributions of both full data and subsample quasi-mode estimators. The optimal subsampling probabilities by minimizing the asymptotic variance-covariance matrix under A- and L-optimality criteria are identified. These optimal probabilities rely on the full data estimate, prompting the development of a two-step algorithm to approximate the optimal subsampling procedure. The resultant algorithm is processing-efficient and can significantly reduce computational time compared to the full data approach. We also establish the asymptotic normality of the quasi-mode estimator obtained through this two-step algorithm. To assess finite sample performance, we conduct Monte Carlo simulations and analyze air quality data, showcasing the effectiveness of the developed estimator. Supplemental materials for this article are available online.

Hidden-Markov models for ordinal time series

AbstractA common approach for modeling categorical time series is Hidden-Markov models (HMMs), where the actual observations are assumed to depend on hidden states in their behavior and transitions. Such categorical HMMs are even applicable to nominal data but suffer from a large number of model parameters. In the ordinal case, however, the natural order among the categorical outcomes offers the potential to reduce the number of parameters while improving their interpretability at the same time. The class of ordinal HMMs proposed in this article link a latent-variable approach with categorical HMMs. They are characterized by parametric parsimony and allow the easy calculation of relevant stochastic properties, such as marginal and bivariate probabilities. These points are illustrated by numerical examples and simulation experiments, where the performance of maximum likelihood estimation is analyzed in finite samples. The developed methodology is applied to real-world data from a health application.

Revisiting Panel Data Binary Choice Models with Lagged Dependent Variables*

This paper revisits the identification and estimation of a class of semiparametric (distribution-free) panel data binary choice models with lagged dependent variables, exogenous covariates, and entity fixed effects. We provide a novel identification strategy, using an “identification at infinity” argument. In contrast with the celebrated Honoré and Kyriazidou (2000), our method permits time trends of any form and does not suffer from the “curse of dimensionality”. We propose an easily implementable conditional maximum score estimator. The asymptotic properties of the proposed estimator are fully characterized. A small-scale Monte Carlo study demonstrates that our approach performs satisfactorily in finite samples. We illustrate the usefulness of our method by presenting an empirical application to enrollment in private hospital insurance using the Household, Income and Labor Dynamics in Australia (HILDA) Survey data.

Are information criteria good enough to choose the right the number of regimes in hidden Markov models?

Selecting the number of regimes in Hidden Markov models is an important problem. Many criteria are used to do so, such as Akaike information criterion (AIC), Bayesian information criterion (BIC), integrated completed likelihood (ICL), deviance information criterion (DIC), and Watanabe-Akaike information criterion (WAIC), to name a few. In this article, we introduced goodness-of-fit tests for general Hidden Markov models with covariates, where the distribution of the observations is arbitrary, i.e. continuous, discrete, or a mixture of both. A selection procedure is proposed based on this goodness-of-fit test. The main aim of this article is to compare the classical information criterion with the new criterion when the outcome is either continuous, discrete or zero-inflated. Numerical experiments assess the finite sample performance of the goodness-of-fit tests, and comparisons between the different criteria are made.

Reliability analysis based on doubly-truncated and interval-censored data

Field data provide important information on product reliability. Interval sampling is widely used for collection of field data, which typically report incident cases during a certain time period. Such sampling scheme induces doubly truncated (DT) data if the exact failure time is known. In many situations, the exact failure date is known only to fall within an interval, leading to doubly truncated and interval censored (DTIC) data. This article considers analysis of DTIC data under parametric failure time models. We consider a conditional likelihood approach and propose interval estimation for parameters and the cumulative distribution functions. Simulation studies show that the proposed method performs well for finite sample size.

Statistical inference for Hicks–Moorsteen productivity indices

AbstractThe statistical framework for the Malmquist productivity index (MPI) is now well-developed and emphasizes the importance of developing such a framework for its alternatives. In this paper, we try to fill this gap in the literature for another popular measure, known as the Hicks–Moorsteen productivity index (HMPI). Unlike MPI, the HMPI has a total factor productivity interpretation in the sense of measuring productivity as the ratio of aggregated outputs to aggregated inputs and has other useful advantages over MPI. In this work, we develop a novel framework for statistical inference for HMPI in various contexts: when its components are known or when they are replaced with non-parametric envelopment estimators. This will be done for a particular firm’s HMPI as well as for the simple mean (unweighted) HMPI and the aggregate (weighted) HMPI. Our results further enrich the recent theoretical developments of nonparametric envelopment estimators for the various efficiency and productivity measures. We also examine the performance of these theoretical results for both the unweighted and weighted mean of HMPI for a finite sample, using Monte-Carlo simulations and also provide an empirical illustration along with the computation code.

Deep Neural Network-Based Accelerated Failure Time Models Using Rank Loss.

An accelerated failure time (AFT) model assumes a log-linear relationship between failure times and a set of covariates. In contrast to other popular survival models that work on hazard functions, the effects of covariates are directly on failure times, the interpretation of which is intuitive. The semiparametric AFT model that does not specify the error distribution is sufficiently flexible and robust to depart from the distributional assumption. Owing to its desirable features, this class of model has been considered a promising alternative to the popular Cox model in the analysis of censored failure time data. However, in these AFT models, a linear predictor for the mean is typically assumed. Little research has addressed the non-linearity of predictors when modeling the mean. Deep neural networks (DNNs) have received much attention over the past few decades and have achieved remarkable success in a variety of fields. DNNs have a number of notable advantages and have been shown to be particularly useful in addressing non-linearity. Here, we propose applying a DNN to fit AFT models using Gehan-type loss combined with a sub-sampling technique. Finite sample properties of the proposed DNN and rank-based AFT model (DeepR-AFT) were investigated via an extensive simulation study. The DeepR-AFT model showed superior performance over its parametric and semiparametric counterparts when the predictor was nonlinear. For linear predictors, DeepR-AFT performed better when the dimensions of the covariates were large. The superior performance of the proposed DeepR-AFT was demonstrated using three real datasets.

Guided structure learning of DAGs for count data

In this paper, we tackle structure learning of directed acyclic graphs (DAGs), with the idea of exploiting available prior knowledge of the domain at hand to guide the search of the best structure. In particular, we assume to know the topological ordering of variables in addition to the given data. We study a new algorithm for learning the structure of DAGs, proving its theoretical consistency in the limit of infinite observations. Furthermore, we experimentally compare the proposed algorithm to several popular competitors, to study its behaviour in finite samples. Biological validation of the algorithm is presented through the analysis of non-small cell lung cancer data.

Score test for marks in Hawkes processes

AbstractA score statistic for detecting the impact of marks in a linear Hawkes self-exciting point process is proposed, with its asymptotic properties, finite sample performance, power properties using simulation and application to real data presented. A major advantage of the proposed inference procedure is that the Hawkes process can be fitted under the null hypothesis that marks do not impact the intensity process. Hence, for a given record of a point process, the intensity process is estimated once only and then assessed against any number of potential marks without refitting the joint likelihood each time. Marks can be multivariate and serially dependent. The score function for any given set of marks is easily constructed as the covariance of functions of future intensities fits the unmarked process with functions of the marks under assessment. The asymptotic distribution of the score statistic is a Chi-squared distribution, with degrees of freedom equal to the number of parameters required to specify the boost function. Model-based or nonparametric estimation of required features of the mark’s marginal moments and serial dependence can be used. Using sample moments of the marks in the test statistic construction does not impact the size and power properties.

Asymptotic properties for generalized edge frequency polygon of nonparametric density estimation

This article pays attention to the generalized edge frequency polygon. By taking weighted averages of the heights in the neighbouring 2 k ( k ≥ 1 ) bins, we can reduce the asymptotic mean integrated squared error than that of the frequency polygon estimator. As a density estimator based on histogram technique, the generalized edge frequency polygon has the advantage of computational simplicity and has been widely used in many fields. The purpose of this article is to investigate the weak consistency, the uniformly weak consistency and the rate of the uniformly weak consistency for generalized edge frequency polygon of density function under α-mixing samples, which improve and extend those of frequency polygon in the literature. In particular, the simulation study and real data analysis based on finite samples are performed to verify the validity of the theoretical results.

Frequency domain local bootstrap in short and long memory time series

Bootstrap methods in the frequency domain are effective instruments to approximate the distribution of many statistics of weakly dependent (short memory) series but their validity with long memory remains mostly unsolved. This article proposes a frequency domain local bootstrap (FDLB) based on resampling a locally studentized version of the periodogram in a neighborhood of the frequency of interest. A bound of the Mallows distance between the distributions of the periodogram and its FDLB bootstrap counterpart is offered for anti-persistent, weakly dependent, stationary, and non stationary long memory series. This result is in turn used to justify the use of the FDLB for some statistics that are weighted averages of periodogram ordinates. Finally, the validity of the FDLB to estimate the distribution of the local Whittle estimator is proved and its finite sample behavior analyzed in a Monte Carlo and in an empirical application, comparing its performance with rival alternatives.

Unified inference for an integer-valued AR(1) model

. Conditional least squares estimation is often employed to infer an integer-valued AR(1) model and its convergence rate and asymptotic variance differ for the stable and nearly unstable cases. This article adopts a random weighted bootstrap method to provide a unified interval estimation and hypothesis test regardless of the underlying process being either stable or nearly unstable. A simulation study confirms the good finite sample performance of the proposed inference. We also apply it to test for a unit root test in a COVID-19 dataset.

Leveraging External Aggregated Information for the Marginal Accelerated Failure Time Model.

It is becoming increasingly common for researchers to consider leveraging information from external sources to enhance the analysis of small-scale studies. While much attention has focused on univariate survival data, correlated survival data are prevalent in epidemiological investigations. In this article, we propose a unified framework to improve the estimation of the marginal accelerated failure time model with correlated survival data by integrating additional information given in the form of covariate effects evaluated in a reduced accelerated failure time model. Such auxiliary information can be summarized by using valid estimating equations and hence can then be combined with the internal linear rank-estimating equations via the generalized method of moments. We investigate the asymptotic properties of the proposed estimator and show that it is more efficient than the conventional estimator using internal data only. When population heterogeneity exists, we revise the proposed estimation procedure and present a shrinkage estimator to protect against bias and loss of efficiency. Moreover, the proposed estimation procedure can be further refined to accommodate the non-negligible uncertainty in the auxiliary information, leading to more trustable inference conclusions. Simulation results demonstrate the finite sample performance of the proposed methods, and empirical application on the Prostate, Lung, Colorectal, and Ovarian Cancer Screening Trial substantiates its practical relevance.

Distinguishing Time-Varying Factor Models

Time-varying factor models have been widely used to model changing relationships among economic and financial variables. The existing literature usually specifies the time-varying factor loadings as deterministic functions of time or unit root processes. This article proposes two consistent tests to distinguish between these two specifications based on a randomization approach. By setting the null hypothesis as either specification, we show that the proposed test statistics follow an asymptotic Chi-squared distribution under the respective null hypotheses and diverge to infinity in probability under the respective alternatives. Simulation studies reveal that both test statistics perform reasonably well in finite samples. We apply the proposed tests to the U.S. macroeconomic and global macroeconomic and financial datasets. The results suggest that the time-varying factor loadings as deterministic functions of time should be adopted for these two applications.

Estimation of Expectile‐Based Marginal Expected Shortfall Under Asymptotic Independence

ABSTRACTThe expectile‐based marginal expected shortfall (XMES) is an analogue of the quantile‐based marginal expected shortfall (QMES). We study the asymptotic behaviour of XMES when the underlying random variables are asymptotically independent. We consider two different methods for the estimation of XMES: one based on least asymmetrically weighted squares and the other making use of the QMES. We establish the asymptotic theories for both estimators. Additionally, we investigate the finite sample performance of our methods through a simulation study and present a concrete application to financial data.

Empirical Likelihood for Composite Quantile Regression Models with Missing Response Data

Under the assumption of missing response data, empirical likelihood inference is studied via composite quantile regression. Firstly, three empirical likelihood ratios of composite quantile regression are given and proved to be asymptotically χ2. Secondly, without an estimation of the asymptotic covariance, confidence intervals are constructed for the regression coefficients. Thirdly, three estimators are presented for the regression parameters to obtain its asymptotic distribution. The finite sample performance is assessed through simulation studies, and the symmetry confidence intervals of the parametric are constructed. Finally, the effectiveness of the proposed methods is illustrated by analyzing a real-world data set.

Experimental validity of using a ResNet to predict sound absorption coefficients of finite samples

The validity of using a neural network to predict sound absorption coefficients of finite porous materials is tested with experimental data with a flush-mounted glass wool sample on a baffle. The network is pre-trained and validated with numerical simulations of flushed-mounted finite absorbers using a Delany-Bazley-Miki model. The experimental setup consists of a 12 x 12 microphone array placed above the absorber and a sound source placed at angles of 0, 40, and 75 degrees with respect to the normal of the sample. The sound absorption coefficients predicted at normal incidence by the network are compared with the impedance tube method as a reference result.

Spatiotemporal multilevel joint modeling of longitudinal and survival outcomes in end-stage kidney disease.

Individuals with end-stage kidney disease (ESKD) on dialysis experience high mortality and excessive burden of hospitalizations over time relative to comparable Medicare patient cohorts without kidney failure. A key interest in this population is to understand the time-dynamic effects of multilevel risk factors that contribute to the correlated outcomes of longitudinal hospitalization and mortality. For this we utilize multilevel data from the United States Renal Data System (USRDS), a national database that includes nearly all patients with ESKD, where repeated measurements/hospitalizations over time are nested in patients and patients are nested within (health service) regions across the contiguous U.S. We develop a novel spatiotemporal multilevel joint model (STM-JM) that accounts for the aforementioned hierarchical structure of the data while considering the spatiotemporal variations in both outcomes across regions. The proposed STM-JM includes time-varying effects of multilevel (patient- and region-level) risk factors on hospitalization trajectories and mortality and incorporates spatial correlations across the spatial regions via a multivariate conditional autoregressive correlation structure. Efficient estimation and inference are performed via a Bayesian framework, where multilevel varying coefficient functions are targeted via thin-plate splines. The finite sample performance of the proposed method is assessed through simulation studies. An application of the proposed method to the USRDS data highlights significant time-varying effects of patient- and region-level risk factors on hospitalization and mortality and identifies specific time periods on dialysis and spatial locations across the U.S. with elevated hospitalization and mortality risks.