Small Sample Properties Research Articles

Nonparametric Instrumental Variable Estimation of Binary Response Models with Continuous Endogenous Regressors

An instrumental variable approach to the nonparametric estimation of binary response models with endogenous variables is presented. Identification is achieved via a reduced form model constructed from the decomposition of the unobserved dependent variable into the space of instruments. It is further assumed that disturbances in this model are independent of instruments, and their distribution is taken to be known. For estimation purposes, the fully nonparametric model is approximated by a sequence of locally weighted parametric models. Consistency and asymptotic normality of this estimator is proven, and a simulation study is performed to corroborate its small sample properties. Relevant policy parameters are constructed via a simulated nonparametric estimator of choice probabilities.

Estimation and inference in spatial models with dominant units

In spatial econometrics literature estimation and inference are carried out assuming that the matrix of spatial or network connections has uniformly bounded absolute column sums in the number of units, n, in the network. This paper relaxes this restriction and allows for one or more units to have pervasive effects in the network. The linear–quadratic central limit theorem of Kelejian and Prucha (2001) is generalized to allow for such dominant units, and the asymptotic properties of the GMM estimators are established in this more general setting. A new bias-corrected method of moments (BMM) estimator is also proposed that avoids the problem of weak instruments by self-instrumenting the spatially lagged dependent variable. Both cases of homoskedastic and heteroskedastic errors are considered and the associated estimators are shown to be consistent and asymptotically normal, depending on the rate at which the maximum column sum of the weights matrix rises with n. The small sample properties of GMM and BMM estimators are investigated by Monte Carlo experiments and shown to be satisfactory. An empirical application to sectoral price changes in the US over the pre- and post-2008 financial crisis is also provided. It is shown that the share of capital can be estimated reasonably well from the degree of sectoral interdependence using the input–output tables, despite the evidence of dominant sectors being present in the US economy.

An Attention-Based Deep Learning Method for Schizophrenia Patients Classification Using DNA Methylation Data.

In this paper, the classification problem of schizophrenia patients from healthy controls is considered, whose goal is to explore the relationship between DNA characteristics and schizophrenia. However, the DNA methylation data has the properties of small samples in high dimension and non-Gaussian distribution which makes it hard to do classification with DNA methylation data. Hence a classification method based on deep learning is designed. We propose a feature selection method based on attention mechanism which embeds a weight gated layer in the network structure to get a task-related sparse representation of the DNA methylation data. The performance of proposed method outperforms existing feature selection methods. On a real-world data set, the classification with proposed method achieves a high accuracy.

Estimation and inference for semi-competing risks based on data from a nested case-control study

In semi-competing risks, the occurrence of some non-terminal event is subject to a terminal event, usually death. While existing methods for semi-competing risks data analysis assume complete information on all relevant covariates, data on at least one covariate are often not readily available in practice. In this setting, for standard univariate time-to-event analyses, researchers may choose from several strategies for sub-sampling patients on whom to collect complete data, including the nested case-control study design. Here, we consider a semi-competing risks analysis through the reuse of data from an existing nested case-control study for which risk sets were formed based on either the non-terminal or the terminal event. Additionally, we introduce the supplemented nested case-control design in which detailed data are collected on additional events of the other type. We propose estimation with respect to a frailty illness-death model through maximum weighted likelihood, specifying the baseline hazard functions either parametrically or semi-parametrically via B-splines. Two standard error estimators are proposed: (i) a computationally simple sandwich estimator and (ii) an estimator based on a perturbation resampling procedure. We derive the asymptotic properties of the proposed methods and evaluate their small-sample properties via simulation. The designs/methods are illustrated with an investigation of risk factors for acute graft-versus-host disease among N = 8838 patients undergoing hematopoietic stem cell transplantation, for which death is a significant competing risk.

A Conway–Maxwell-multinomial distribution for flexible modeling of clustered categorical data

Categorical data are often observed as counts resulting from a fixed number of trials in which each trial consists of making one selection from a prespecified set of categories. The multinomial distribution serves as a standard model for such data but assumes that trials are independent and identically distributed. Extensions such as the Dirichlet-multinomial and random-clumped multinomial distribution can express positive association, where trials are more likely to result in a common category due to membership in a common cluster. This work considers a Conway–Maxwell-multinomial (CMM) distribution for modeling clustered categorical data exhibiting positively or negatively associated trials. The CMM distribution features a dispersion parameter which allows it to adapt to a range of association levels and includes several recognizable distributions as special cases. We explore properties of CMM, illustrate its flexible characteristics, identify a method to efficiently compute maximum likelihood (ML) estimates, present simulations of small sample properties under ML estimation, and demonstrate the model via data analysis examples.

Iterated multisource exchangeability models for individualized inference with an application to mobile sensor data.

Researchers are increasingly interested in using sensor technology to collect accurate activity information and make individualized inference about treatments, exposures, and policies. How to optimally combine population data with data from an individual remains an open question. Multisource exchangeability models (MEMs) are a Bayesian approach for increasing precision by combining potentially heterogeneous supplemental data sources into analysis of a primary source. MEMs are a potentially powerful tool for individualized inference but can integrate only a few sources; their model space grows exponentially, making them intractable for high-dimensional applications. We propose iterated MEMs (iMEMs), which identify a subset of the most exchangeable sources prior to fitting a MEM model. iMEM complexity scales linearly with the number of sources, and iMEMs greatly increase precision while maintaining desirable asymptotic and small sample properties. We apply iMEMs to individual-level behavior and emotion data from a smartphone app and show that they achieve individualized inference with up to 99% efficiency gain relative to standard analyses that do not borrowinformation.

General Diagnostic Tests for Cross Section Dependence in Panels

This paper proposes simple tests of error cross-sectional dependence which are applicable to a variety of panel data models, including stationary and unit root dynamic heterogeneous panels with short T and large N. The proposed tests are based on the average of pair-wise correlation coefficients of the OLS residuals from the individual regressions in the panel and can be used to test for cross-sectional dependence of any fixed order p, as well as the case where no a priori ordering of the cross-sectional units is assumed, referred to as $$\hbox {CD}(p)$$ and $$\hbox {CD}$$ tests, respectively. Asymptotic distribution of these tests is derived and their power function analyzed under different alternatives. It is shown that these tests are correctly centred for fixed N and T and are robust to single or multiple breaks in the slope coefficients and/or error variances. The small sample properties of the tests are investigated and compared to the Lagrange multiplier test of Breusch and Pagan using Monte Carlo experiments. It is shown that the tests have the correct size in very small samples and satisfactory power, and, as predicted by the theory, they are quite robust to the presence of unit roots and structural breaks. The use of the $$\hbox {CD}$$ test is illustrated by applying it to study the degree of dependence in per capita output innovations across countries within a given region and across countries in different regions. The results show significant evidence of cross-dependence in output innovations across many countries and regions in the World.

Inference in partially identified heteroskedastic simultaneous equations models

Identification through heteroskedasticity in heteroskedastic simultaneous equations models (HSEMs) is considered. The possibility that heteroskedasticity identifies structural parameters only partially is explicitly allowed for. The asymptotic properties of the identified parameters are derived. Moreover, tests for identification through heteroskedasticity are developed and their asymptotic distributions are provided. Monte Carlo simulations are used to explore the small sample properties of the asymptotically valid methods. Finally, the approach is applied to investigate the relation between the degree of economic openness and inflation.

Testing identification via heteroskedasticity in structural vector autoregressive models

Summary Tests for identification through heteroskedasticity in structural vector autoregressive analysis are developed for models with two volatility states where the time point of volatility change is known. The tests are Wald-type tests for which only the unrestricted model, including the covariance matrices of the two volatility states, has to be estimated. The residuals of the model are assumed to be from the class of elliptical distributions, which includes Gaussian models. The asymptotic null distributions of the test statistics are derived, and simulations are used to explore their small-sample properties. Two empirical examples illustrate the usefulness of the tests in applied work.

RANDOMIZATION TESTS OF COPULA SYMMETRY

New nonparametric tests of copula exchangeability and radial symmetry are proposed. The novel aspect of the tests is a resampling procedure that exploits group invariance conditions associated with the relevant symmetry hypothesis. They may be viewed as feasible versions of randomization tests of symmetry, the latter being inapplicable due to the unobservability of marginals. Our tests are simple to compute, control size asymptotically, consistently detect arbitrary forms of asymmetry, and do not require the specification of a tuning parameter. Simulations indicate excellent small sample properties compared with existing procedures involving the multiplier bootstrap.

Econometric analysis of production networks with dominant units

This paper introduces the notions of strongly and weakly dominant units for networks, and shows that pervasiveness of shocks to a network is measured by the degree of dominance of its most pervasive unit; shown to be equivalent to the inverse of the shape parameter of the power law fitted to the network outdegrees. New cross-section and panel extremum estimators of the degree of dominance in networks are proposed, and their asymptotic properties investigated. The small sample properties of the proposed estimators are examined by Monte Carlo experiments, and their use is illustrated by an empirical application to US input–output tables.

Development of Magnetic Material Testing Equipment

Abstract This paper deals with the development of equipment that can accurately determine the magnetic properties of small volume thin plate samples. The alloys to be tested are sheets of amorphous structure, such as Finemet alloy, which has excellent high frequency magnetic properties, making it a good candidate for the construction of high efficiency electric motors. This article discusses the components and operation of the equipment under development, whilst giving a brief overview of the efficiency classification of electric motors and the importance of the emerging efficiency class.

Hypothesis testing based on a vector of statistics

This paper presents a new approach to hypothesis testing based on a vector of statistics. It involves simulating the statistics under the null hypothesis and then estimating the joint density of the statistics. This allows the p-value of the smallest acceptance region test to be estimated. We prove this p-value is a consistent estimate under some regularity conditions. The small-sample properties of the proposed procedure are investigated in the context of testing for autocorrelation, testing for normality, and testing for model misspecification through the information matrix. We find that our testing procedure has appropriate sizes and good powers.

Demand forecasting under fill rate constraints—The case of re-order points

We consider computation of demand forecasts fulfilling an assumption about the level of the P2 service measure in continuous review inventory systems with fixed order quantities and re-order points as decision variables. First, we introduce a family of loss functions whose expectations are uniquely minimized at the functional of demand of interest here. Then, concentrating on the linear-quadratic loss and assuming some regularity conditions, we provide consistency and asymptotic normality conditions for the direct M-estimator of the appropriate decision levels in the case of iid data. The large sample properties of this direct estimator are examined, under different distributional assumptions, in comparison with the two-step estimator based on the maximum likelihood principle. Furthermore, we also study the small sample properties of these two estimators (and also another one utilizing a nonparametric kernel density estimation) and study the small sample coverage of confidence intervals for the decision levels constructed according to the derived asymptotic formulas. Finally, we also discuss possible extensions of this estimation framework to the case of dependent data and introduce certain classes of dynamic models for forecasting under the P2 constraint.

A simple wavelet-based test for serial correlation in panel data models

Hong and Kao (2004) proposed a class of general applicable wavelet-based tests for serial correlation of unknown form in the residuals from a panel regression model. The tests can be applied to both static and dynamic panel models. Their test, however, is computationally difficult to implement, and simulation studies show that the test has poor small-sample properties. In this paper, we extend Gençay’s (2010) time-series test for serial correlation to panel data case. Our new test is also wavelet based and maintains the advantages of the Hong and Kao (2004) test, but it is much simpler and easier to implement. Furthermore, simulation results show that our test has quicker convergence rate and hence better small-sample properties, compared to Hong and Kao (2004) test. We also compare our test with several other existing tests for series correlation, and our test has in general better statistical properties in terms of both size and power.

Forecasting using heterogeneous panels with cross-sectional dependence

In this paper, we focus on forecasting methods that use heterogeneous panels in the presence of cross-sectional dependence in terms of both spatial error dependence and common factors. We propose two main approaches to estimating the factor structure: a residuals-based approach, and an approach that uses a panel of auxiliary variables to extract the factors. Small sample properties of the proposed methods are investigated through Monte Carlo simulations and applied to predict house price inflation in OECD countries.

Cumulative risk regression in case-cohort studies using pseudo-observations.

Case-cohort studies are useful when information on certain risk factors is difficult or costly to ascertain. Particularly, a case-cohort study may be well suited in situations where several case series are of interest, e.g. in studies with competing risks, because the same sub-cohort may serve as a comparison group for all case series. Previous analyses of this kind of sampled cohort data most often involved estimation of rate ratios based on a Cox regression model. However, with competing risks this method will not provide parameters that directly describe the association between covariates and cumulative risks. In this paper, we study regression analysis of cause-specific cumulative risks in case-cohort studies using pseudo-observations. We focus mainly on the situation with competing risks. However, as a by-product, we also develop a method by which absolute mortality risks may be analyzed directly from case-cohort survival data. We adjust for the case-cohort sampling by inverse sampling probabilities applied to a generalized estimation equation. The large-sample properties of the proposed estimator are developed and small-sample properties are evaluated in a simulation study. We apply the methodology to study the effect of a specific diet component and a specific gene on the absolute risk of atrial fibrillation.

Roughness in Spot Variance? A GMM Approach for Estimation of Fractional Log-Normal Stochastic Volatility Models Using Realized Measures

In this paper, we develop a generalized method of moments approach for joint estimation of the parameters of a fractional log-normal stochastic volatility model. We show that with an arbitrary Hurst exponent an estimator based on integrated variance is consistent. Moreover, under stronger conditions we also derive a central limit theorem. These results stand even when integrated variance is replaced with a realized measure of volatility calculated from discrete high-frequency data. However, in practice a realized estimator contains sampling error, the effect of which is to skew the fractal coeffcient toward roughness. We construct an analytical approach to control this error. In a simulation study, we demonstrate convincing small sample properties of our approach based both on integrated and realized variance over the entire memory spectrum. We show that the bias correction attenuates any systematic deviance in the estimated parameters. Our procedure is applied to empirical high-frequency data from numerous leading equity indexes. With our robust approach the Hurst index is estimated around 0.05, confirming roughness in integrated variance.

Measurement of Factor Strenght: Theory and Practice

This paper proposes an estimator of factor strength and establishes its consistency and asymptotic distribution. The estimator is based on the number of statistically significant factor loadings, taking multiple testing into account. Both cases of observed, and unobserved factors are considered. The small sample properties of the proposed estimator are investigated using Monte Carlo experiments. It is shown that the proposed estimation and inference procedures perform well, and have excellent power properties, especially when the factor strength is sufficiently high. Empirical applications to factor models for asset returns show that out of 146 factors recently considered in the literature, only the market factor is truly strong, while all other factors are at best semi-strong, with their strength varying considerably over time. Similarly, we only find evidence of semi-strong factors using a large number of U.S. macroeconomic indicators.

Estimation and Inference in Spatial Models with Dominant Units

In spatial econometrics literature estimation and inference are carried out assuming that the matrix of spatial or network connections has uniformly bounded absolute column sums in the number of units, n, in the network. This paper relaxes this restriction and allows for one or more units to have pervasive effects in the network. The linear-quadratic central limit theorem of Kelejian and Prucha (2001) is generalized to allow for such dominant units, and the asymptotic properties of the GMM estimators are established in this more general setting. A new bias-corrected method of moments (BMM) estimator is also proposed that avoids the problem of weak instruments by self-instrumenting the spatially lagged dependent variable. Both cases of homoscedastic and heteroskedastic errors are considered and the associated estimators are shown to be consistent and asymptotically normal, depending on the rate at which the maximum column sum of the weights matrix rises with n. The small sample properties of GMM and BMM estimators are investigated by Monte Carlo experiments and shown to be satisfactory. An empirical application to sectoral price changes in the US over the pre- and post-2008 financial crisis is also provided. It is shown that the share of capital can be estimated reasonably well from the degree of sectoral interdependence using the input-output tables, despite the evidence of dominant sectors being present in the US economy.