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Linear and nonlinear regression with stable errors

稳定分布误差下的线性与非线性回归

In this paper we describe methods and evaluate programs for linear regression by maximum likelihood when the errors have a heavy tailed stable distribution. The asymptotic Fisher information matrix for both the regression coefficients and the error distribution parameters are derived, giving large sample confidence intervals for all parameters. Simulated examples are shown where the errors are stably distributed and also where the errors are heavy tailed but are not stable,…

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TIME SERIES REGRESSION ON INTEGRATED CONTINUOUS-TIME PROCESSES WITH HEAVY AND LIGHT TAILS

重尾与轻尾连续时间积分过程的时间序列回归

The paper presents a cointegration model in continuous time, where the linear combinations of the integrated processes are modeled by a multivariate Ornstein–Uhlenbeck process. The integrated processes are defined as vector-valued Lévy processes with an additional noise term. Hence, if we observe the process at discrete time points, we obtain a multiple regression model. As an estimator for the regression parameter we use the least squares estimator. We show that it is a…

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A NONPARAMETRIC GOODNESS-OF-FIT-BASED TEST FOR CONDITIONAL HETEROSKEDASTICITY

基于非参数拟合优度的条件异方差检验

In this paper we propose a new nonparametric test for conditional heteroskedasticity based on a measure of nonparametric goodness-of-fit (R 2 ) that is obtained from the local polynomial regression of the residuals from a parametric regression on some covariates. We show that after being appropriately standardized, the nonparametric R 2 is asymptotically normally distributed under the null hypothesis and a sequence of Pitman local alternatives. We also prove the consistency…

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ANOTHER LOOK AT THE IDENTIFICATION AT INFINITY OF SAMPLE SELECTION MODELS

重新审视样本选择模型的无穷远识别

It is often believed that without instruments, endogenous sample selection models are identified only if a covariate with a large support is available (see, e.g., Chamberlain, 1986, Journal of Econometrics 32, 189–218; Lewbel, 2007, Journal of Econometrics 141, 777–806) . We propose a new identification strategy mainly based on the condition that the selection variable becomes independent of the covariates for large values of the outcome. No large support on the covariates…

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ORACLE EFFICIENT VARIABLE SELECTION IN RANDOM AND FIXED EFFECTS PANEL DATA MODELS

随机效应与固定效应面板模型中的神谕有效变量选择

This paper generalizes the results for the Bridge estimator of Huang, Horowitz, and Ma (2008) to linear random and fixed effects panel data models which are allowed to grow in both dimensions. In particular, we show that the Bridge estimator isoracle efficient. It can correctly distinguish between relevant and irrelevant variables and the asymptotic distribution of the estimators of the coefficients of the relevant variables is the same as if only these had been included in…

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NONPARAMETRIC TESTS OF MOMENT CONDITION STABILITY

矩条件稳定性的非参数检验

This paper considers testing for moment condition instability for a wide variety of models that arise in econometric applications. We propose a nonparametric test based on smoothing the moment conditions over time. The resulting test takes the form of a U-statistic and has a limiting normal distribution. The proposed test statistic is not affected by changes in the distribution of the data, so long as certain simple regularity conditions hold. We examine the performance of…

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Robust Estimation for Homoscedastic Regression in the Secondary Analysis of Case–Control Data

病例对照数据二次分析中同方差回归的稳健估计

Summary Primary analysis of case–control studies focuses on the relationship between disease D and a set of covariates of interest (Y, X). A secondary application of the case–control study, which is often invoked in modern genetic epidemiologic association studies, is to investigate the interrelationship between the covariates themselves. The task is complicated owing to the case–control sampling, where the regression of Y on X is different from what it is in the population.…

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Group Sequential Tests for Delayed Responses (with discussion)

延迟响应的组序贯检验(附讨论)

Summary Group sequential methods are used routinely to monitor clinical trials and to provide early stopping when there is evidence of a treatment effect, a lack of an effect or concerns about patient safety. In many studies, the response of clinical interest is measured some time after the start of treatment and there are subjects at each interim analysis who have been treated but are yet to respond. We formulate a new form of group sequential test which gives a proper…

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Dimension Reduction and Alleviation of Confounding for Spatial Generalized Linear Mixed Models

空间广义线性混合模型的降维与空间混杂缓解

Summary Non-Gaussian spatial data are very common in many disciplines. For instance, count data are common in disease mapping, and binary data are common in ecology. When fitting spatial regressions for such data, one needs to account for dependence to ensure reliable inference for the regression coefficients. The spatial generalized linear mixed model offers a very popular and flexible approach to modelling such data, but this model suffers from two major shortcomings:…

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Fixed b Subsampling and the Block Bootstrap: Improved Confidence Sets based on p -Value Calibration

固定 b 子抽样与区块自助法:基于 p 值校准的改进置信集

Summary Subsampling and block-based bootstrap methods have been used in a wide range of inference problems for time series. To accommodate the dependence, these resampling methods involve a bandwidth parameter, such as the subsampling window width and block size in the block-based bootstrap. In empirical work, using different bandwidth parameters could lead to different inference results, but traditional first-order asymptotic theory does not capture the choice of the…

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Mann–Whitney Test with Adjustments to Pretreatment Variables for Missing Values and Observational Study

针对缺失值与观察性研究进行处理前变量调整的Mann–Whitney检验

Summary The conventional Wilcoxon or Mann–Whitney test can be invalid for comparing treatment effects in the presence of missing values or in observational studies. This is because the missingness of the outcomes or the participation in the treatments may depend on certain pretreatment variables. We propose an approach to adjust the Mann–Whitney test by correcting the potential bias via consistently estimating the conditional distributions of the outcomes given the…

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Estimation of the Mean of Functional Time Series and a Two-Sample Problem

函数型时间序列的均值估计与两样本检验

Summary The paper is concerned with inference based on the mean function of a functional time series. We develop a normal approximation for the functional sample mean and then focus on the estimation of the asymptotic variance kernel. Using these results, we develop and asymptotically justify testing procedures for the equality of means in two functional samples exhibiting temporal dependence. Evaluated by means of a simulation study and application to a real data set, these…

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Estimation and inference in unstable nonlinear least squares models

不稳定非线性最小二乘模型的估计与推断

There is compelling evidence that many macroeconomic and financial variables are not generated by linear models. This evidence is based on testing linearity against either smooth nonlinearity or piece-wise linearity, but there is no framework that encompasses both. This paper provides an econometric framework that allows for both breaks and smooth nonlinearity in between breaks. We estimate the unknown break-dates simultaneously with other parameters via nonlinear…

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Jackknife estimation of stationary autoregressive models

平稳自回归模型的刀切估计

This paper explores the properties of jackknife methods of estimation in stationary autoregressive models. Some general results concerning the correct weights for bias reduction under various sampling schemes are provided and the asymptotic properties of a jackknife estimator based on non-overlapping sub-samples are derived for the case of a stationary autoregression of order p when the number of sub-samples is either fixed or increases with the sample size at an appropriate…

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On bootstrapping panel factor series

面板因子序列的自助法

This paper studies the asymptotic validity of sieve bootstrap for nonstationary panel factor series. Two main results are shown. Firstly, a bootstrap Invariance Principle is derived pointwise in i, obtaining an upper bound for the order of truncation of the AR polynomial that depends on n and T. Consistent estimation of the long run variances is also studied for (n,T)→∞. Secondly, joint bootstrap asymptotics is also studied, investigating the conditions under which the…

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A zero inefficiency stochastic frontier model

允许零无效率的随机前沿模型

Traditional stochastic frontier models impose inefficient behavior on all firms in the sample of interest. If the data under investigation represent a mixture of both fully efficient and inefficient firms then off-the-shelf frontier models are statistically inadequate. We introduce the zero inefficiency stochastic frontier model which can accommodate the presence of both efficient and inefficient firms in the sample. We derive the corresponding log-likelihood function,…

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Testing functional inequalities

函数不等式检验

This paper develops tests for inequality constraints of nonparametric regression functions. The test statistics involve a one-sided version of Lp-type functionals of kernel estimators (1≤p<∞). Drawing on the approach of Poissonization, this paper establishes that the tests are asymptotically distribution free, admitting asymptotic normal approximation. In particular, the tests using the standard normal critical values have asymptotically correct size and are consistent…

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Bootstrapping realized multivariate volatility measures

多元已实现波动指标的自助法

We propose a bootstrap method for statistics that are a function of multivariate high frequency returns such as realized regression, covariance and correlation coefficients. We show that the finite sample performance of the bootstrap is superior to the existing first-order asymptotic theory. Nevertheless, and contrary to the existing results in the bootstrap literature for regression models subject to error heteroskedasticity, the Edgeworth expansion for the pairs bootstrap…

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Examining the Distributional Effects of Military Service on Earnings: A Test of Initial Dominance

兵役对收入分布的影响:初始区间占优检验

Existing empirical evidence suggests that the effects of Vietnam veteran status on earnings in the decade-and-a-half following service may be concentrated in the lower tail of the earnings distribution. Motivated by this evidence, we develop a formal statistical procedure that is specifically designed to test for lower tail dominance in the distributions of earnings. When applied to the same data as in previous studies, the test reveals that the distribution of earnings for…

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Testing Linear Factor Pricing Models With Large Cross Sections: A Distribution-Free Approach

大横截面线性因子定价模型检验:分布无关方法

In this article, we develop a finite-sample distribution-free procedure to test the beta-pricing representation of linear factor pricing models. In sharp contrast to extant finite-sample tests, our framework allows for unknown forms of nonnormalities, heteroscedasticity, and time-varying covariances. The power of the proposed test procedure increases as the time series lengthens and/or the cross section becomes larger. So the criticism sometimes heard that nonparametric…

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Optimal Bandwidth Selection for Nonparametric Conditional Distribution and Quantile Functions

非参数条件分布与分位数函数的最优带宽选择

We propose a data-driven least-square cross-validation method to optimally select smoothing parameters for the nonparametric estimation of conditional cumulative distribution functions and conditional quantile functions. We allow for general multivariate covariates that can be continuous, categorical, or a mix of either. We provide asymptotic analysis, examine finite-sample properties via Monte Carlo simulation, and consider an application involving testing for first-order…

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Do Oil Prices Help Forecast U.S. Real GDP? The Role of Nonlinearities and Asymmetries

油价能否帮助预测美国实际 GDP?非线性与非对称性的作用

There is a long tradition of using oil prices to forecast U.S. real GDP. It has been suggested that the predictive relationship between the price of oil and one-quarter-ahead U.S. real GDP is nonlinear in that (a) oil price increases matter only to the extent that they exceed the maximum oil price in recent years, and that (b) oil price decreases do not matter at all. We examine, first, whether the evidence of in-sample predictability in support of this view extends to…

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Markov-Switching MIDAS Models

马尔可夫状态切换MIDAS模型

This article introduces a new regression model—Markov-switching mixed data sampling (MS-MIDAS)—that incorporates regime changes in the parameters of the mixed data sampling (MIDAS) models and allows for the use of mixed-frequency data in Markov-switching models. After a discussion of estimation and inference for MS-MIDAS and a small sample simulation-based evaluation, the MS-MIDAS model is applied to the prediction of the U.S. economic activity, in terms of both quantitative…

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