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Rank Tests for Nonlinear Cointegration

非线性协整的秩检验

A test procedure based on ranks is suggested to test for nonlinear cointegration. For two (or more) time series it is assumed that monotonic transformations exist such that the normalized series can asymptotically be represented as Wiener processes. Rank-test procedures based on the difference between the sequences of ranks are suggested. If there is no cointegration between the time series, the sequences of ranks tend to diverge, whereas under cointegration the sequences of…

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A Formalization of Seasonal Encompassing With an Application to a German Macromodel

季节涵盖的形式化及其在德国宏观模型中的应用

In this article, I apply the encompassing principle to test whether a model that has been estimated with seasonally adjusted (SA) data can encompass a model that is based on nonseasonally adjusted (NSA) data. Building on and extending the work of Ericsson, Hendry and Tran, who analyzed this question in a single-equation framework, I shall suggest how to test whether an SA model that is estimated as a system of simultaneous equations can "seasonally encompass" an NSA model.…

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To Aggregate, Pool, or Neither

预测数据应聚合、合并,还是两者都不采用?

It is well known that, even if all forecasters are rational, unbiasedness tests using consensus forecasts are inconsistent because forecasters have private information. However, if all forecasters face a common realization, pooled estimators are also inconsistent. In contrast, we show that when predictions and realizations are integrated and cointegrated, microhomogeneity ensures that consensus and pooled estimators are consistent. Therefore, contrary to claims in the…

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On the Properties of Regression-Based Tests for Seasonal Unit Roots in the Presence of Higher-Order Serial Correlation

高阶序列相关下基于回归的季节单位根检验性质

We analyze the behavior of widely used regression-based tests for seasonal unit roots when the shocks are serially correlated. We show, in the quarterly case, that the common assumption that serial correlation may be accommodated by augmenting the test regression with appropriate lagged seasonal differences is only partially correct. The limiting null distributions of t statistics for unit roots at the zero and Nyquist frequencies are corrected by the lag augmentation, but…

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Testing Target-Zone Models Using Efficient Method of Moments

使用有效矩方法检验汇率目标区模型

The objectives of this article are threefold: (1) to test target zone models using more efficient and direct econometric methodology than previous research, (2) to identify an implicit band, if it exists, from observed data and to test target-zone models based on the estimated implicit band rather than the stated official band, and (3) to examine whether the exchange rate can be modeled as a managed float system with a central parity that lacks a band. We find strong…

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Structural Breaks, Incomplete Information, and Stock Prices

结构突变、不完全信息与股票价格

This article presents empirical evidence on the existence of structural breaks in the fundamentals process underlying U.S. stock prices. I develop an asset-pricing model that represents breaks in the context of a Markov switching process with an expanding set of nonrecurring states. Different hypotheses on how investors form expectations about future dividends after a break are proposed and analyzed. A model in which investors do not have full information about the…

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A flexible parametric GARCH model with an application to exchange rates

灵活参数化的 GARCH 模型及其汇率应用

Abstract Many asset prices, including exchange rates, exhibit periods of stability punctuated by infrequent, substantial, often one‐sided adjustments. Statistically, this generates empirical distributions of exchange rate changes that exhibit high peaks, long tails, and skewness. This paper introduces a GARCH model, with a flexible parametric error distribution based on the exponential generalized beta (EGB) family of distributions. Applied to daily US dollar exchange rate…

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Trend‐stationary GNP: evidence from a new exact pointwise most powerful invariant unit root test

趋势平稳的 GNP:新精确逐点最强不变单位根检验的证据

Abstract There has been a substantial debate whether GNP has a unit root. However, statistical tests have had little success in distinguishing between unit‐root and trend‐reverting specifications because of poor statistical properties. This paper develops a new exact small‐sample, pointwise most powerful unit root test that is invariant to the unknown mean and scale of the time series tested, that generates exact small‐sample critical values, powers and p ‐values, that has…

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Missing responses in generalised linear mixed models when the missing data mechanism is nonignorable

不可忽略缺失机制下广义线性混合模型的缺失响应

We propose a method for estimating parameters in the generalised linear mixed model with nonignorable missing response data and with nonmonotone patterns of missing data in the response variable. We develop a Monte Carlo EM algorithm for estimating the parameters in the model via the Gibbs sampler. For the normal random effects model, we derive a novel analytical form for the E‐ and M‐steps, which is facilitated by integrating out the random effects. This form leads to a…

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The smoothed median and the bootstrap

平滑中位数与自助法

Even in one dimension the sample median exhibits very poor performance when used in conjunction with the bootstrap. For example, both the percentile‐t bootstrap and the calibrated percentile method fail to give second‐order accuracy when applied to the median. The situation is generally similar for other rank‐based methods, particularly in more than one dimension. Some of these problems can be overcome by smoothing, but that usually requires explicit choice of the smoothing…

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Assessing goodness of fit of spatially inhomogeneous Poisson processes

空间非齐次泊松过程的拟合优度检验

We propose an extension of the classical complete spatial randomness tests to nonstationary Poisson spatial processes. The method consists of first performing the classical tests locally and then grouping the local results into a global test. The global test is a test for nonstationary Poisson process assumption, whereas the local tests can be used in an exploratory way to decide whether the observed process is locally regular or clustered or if we do not reject the…

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Misspecified proportional hazard models and confirmatory analysis of survival data

误设比例风险模型与生存数据的验证性分析

In survival analysis of follow‐up studies with staggered entry, it may be requested to examine a chance finding at an interim analysis in a confirmatory analysis based on ‘independent evidence’. Keiding et al. (1987) suggested incorporating residual lifetimes of initial survivors into the confirmatory analysis and indicated heuristically that this provides valid independent evidence, assuming that the statistical model is true. The present paper provides a full mathematical…

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Bias correction for score tests arising from misspecified proportional hazards regression models

误设比例风险回归模型所产生得分检验的偏差校正

When censoring depends on both treatment group and covariates, tests for a randomised treatment effect arising from Cox's proportional hazards model are not in general centred at zero under the null and can be seriously distorted. We propose a corrected test that modifies the at‐risk indicator in a way that corrects for this bias. The resulting test is asymptotically valid regardless of whether or not the fitted model is correctly specified. Implementation of the corrected…

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Estimation of variance components with high breakdown point and high efficiency

兼具高崩溃点与高效率的方差分量估计

For the one‐way random effects model three noniterative robust variance component estimators are investigated. For these estimators block breakdown points, measurement breakdown points and efficiency are derived. It is shown that the block breakdown points are approximating 50% and that the measurement breakdown points are not smaller than 25%. By deriving the asymptotic normal distribution of these estimators we show that two of the new estimators have an asymptotic…

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On the Bayesian analysis of population size

总体规模的贝叶斯分析

We consider the problem of estimating the total size of a population from a series of incomplete census data. We observe that inference is typically highly sensitive to the choice of model and we demonstrate how Bayesian model averaging techniques easily overcome this problem. We combine and extend the work of Madigan & York (1997) and Dellaportas & Forster (1999) using reversible jump Markov chain Monte Carlo simulation to calculate posterior model probabilities which can…

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On functional misspecification of covariates in the Cox regression model

Cox 回归模型中协变量函数形式的误设

Model misspecification is discussed for the analysis of censored survival data with the Cox regression model. The maximum partial likelihood estimator for covariate effects has an asymptotic normal distribution under model misspecification (Lin & Wei, 1989). Situations where the assumed functional form for covariates is wrong are considered in a general framework in which we also derive the limit of Breslow's (1972) estimator. Furthermore, we give explicit expressions for…

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On the asymptotic distribution for Peto's combined test for carcinogenicity assays under equal and unequal censoring

相同与不同删失下 Peto 致癌性联合检验的渐近分布

Peto et al. (1980) proposed a combined test statistic for carcinogenicity studies in a pooled analysis of incidental and fatal tumours. For the analysis of the incidental tumours one needs to divide the time span of the study into subintervals. Rather than using the data‐driven method approach to create these intervals as was suggested by Peto et al. (1980), in practical applications one uses a fixed number of prespecified intervals. For this method we derive the asymptotic…

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A simple resampling method by perturbing the minimand

通过扰动优化目标进行简单重抽样

Suppose that under a semiparametric setting an estimator of a vector of parameters of interest is obtained by optimising an objective function which has a U‐process structure. The covariance matrix of the estimator is generally a function of the underlying density function, which may be difficult to estimate well by conventional methods. In this paper, we present a simple resampling method by perturbing the objective function repeatedly. Inferences of the parameters can then…

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Approximations to the profile empirical likelihood function for a scalar parameter in the context of M-estimation

M估计中标量参数剖面经验似然函数的近似

Empirical likelihood possesses many of the important properties of genuine parametric likelihood, but it is computationally burdensome, especially when nuisance parameters are present. This paper presents two approximations to the profile empirical likelihood function for a scalar parameter of interest in the context of M‐estimation; the simpler approximation is based on the third derivative of the profile log empirical likelihood function at its maximising point, while the…

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Manifest characterization and testing for certain latent properties

若干潜在性质的可观测表征与检验

Work due to Junker and more recently due to Junker and Ellis characterized desired latent properties of an educational testing procedure in terms of a collection of other manifest properties. This is important because one can only propose tests for manifest quantities, not latent ones. Here, we complete the conversion of a pair of latent properties to equivalent conditions in terms of four manifest quantities and identify a general method for producing tests for manifest…

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Adaptive estimation in autoregression or -mixing regression via model selection

通过模型选择实现自回归或 β 混合回归中的自适应估计

We study the problem of estimatingsome unknown regression function in a $\beta$-mixing dependent framework. To this end, we consider some collection of models which are finite dimensional spaces. A penalized least-squares estimator (PLSE) is built on a data driven selected model among this collection. We state non asymptotic risk bounds for this PLSE and give several examples where the procedure can be applied (autoregression, regression with arithmetically $\beta$-mixing…

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M-estimation for location and regression parameters in group models: A case study using Stiefel manifolds

群模型中位置与回归参数的 M 估计:Stiefel 流形案例

We discuss here a general approach to the calculation of the asymptotic covariance of $M$-estimates for location parameters in statistical group models when an invariant objective function is used. The calculation reduces to standard tools in group representation theory and the calculation of some constants. Only the constants depend upon the precise forms of the density or of the objective function. If the group is sufficiently large this represents a major simplification…

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Weak convergence of the empirical process of residuals in linear models with many parameters

多参数线性模型中残差经验过程的弱收敛

When fitting, by least squares, a linear model (with an intercept term) with $p$ parameters to $n$ data points, the asymptotic behavior of the residual empirical process is shown to be the same as in the single sample problem provided $p^3 \log^2 (p) /n \to 0$ for any error density having finite variance and a bounded first derivative. No further conditions are imposed on the sequence of design matrices. The result is extended to more general estimates with the property that…

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Asymptotic approximations in the near‐integrated model with a non‐zero initial condition

非零初始条件下近单整模型的渐近近似

This paper considers various asymptotic approximations in the near-integrated first-order autoregressive model with a non-zero initial condition. We first extend the work of Knight and Satchell (1993), who considered the random walk case with a zero initial con-dition, to derive the expansion of the relevant joint moment generating function in this more general framework. We also consider, as alternative approximations, the stochastic expansion of Phillips (1987c) and the…

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