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马尔可夫状态切换自回归模型中极大似然估计的渐近性质AI 解读

An autoregressive process with Markov regime is an autoregressive process for which the regression function at each time point is given by a nonobservable Markov chain. In this paper we consider the asymptotic properties of the maximum likelihood estimator in a possibly nonstationary process of this kind for which the hidden state space is compact but not necessarily finite. Consistency and asymptotic normality are shown to follow from uniform exponential forgetting of the…

随机间隔离散观测下扩散过程估计量的一般理论AI 解读

We provide a general method to analyze the asymptotic properties of a variety of estimators of continuous time diffusion processes when the data are not only discretely sampled in time but the time separating successive observations may possibly be random. We introduce a new operator, the generalized infinitesimal generator, to obtain Taylor expansions of the asymptotic moments of the estimators. As a special case, our results apply to the situation where the data are…

This paper establishes the global asymptotic equivalence between a Poisson process with variable intensity and white noise with drift under sharp smoothness conditions on the unknown function. This equivalence is also extended to density estimation models by Poissonization. The asymptotic equivalences are established by constructing explicit equivalence mappings. The impact of such asymptotic equivalence results is that an investigation in one of these nonparametric models…

空间子抽样方差估计的最优子样本规模AI 解读

We consider the problem of determining the optimal block (or subsample) size for a spatial subsampling method for spatial processes observed on regular grids. We derive expansions for the mean square error of the subsampling variance estimator, which yields an expression for the theoretically optimal block size. The optimal block size is shown to depend in an intricate way on the geometry of the spatial sampling region as well as characteristics of the underlying random…

霍夫变换估计量AI 解读

This article pursues a statistical study of the Hough transform, the celebrated computer vision algorithm used to detect the presence of lines in a noisy image. We first study asymptotic properties of the Hough transform estimator, whose objective is to find the line that “best” fits a set of planar points. In particular, we establish strong consistency and rates of convergence, and characterize the limiting distribution of the Hough transform estimator. While the…

非参数函数的筛经验似然比检验AI 解读

Generalized likelihood ratio statistics have been proposed in Fan, Zhang and Zhang [Ann. Statist. 29 (2001) 153–193] as a generally applicable method for testing nonparametric hypotheses about nonparametric functions. The likelihood ratio statistics are constructed based on the assumption that the distributions of stochastic errors are in a certain parametric family. We extend their work to the case where the error distribution is completely unspecified via newly proposed…

中位数的稳健非参数推断AI 解读

We consider the problem of constructing robust nonparametric confidence intervals and tests of hypothesis for the median when the data distribution is unknown and the data may contain a small fraction of contamination. We propose a modification of the sign test (and its associated confidence interval) which attains the nominal significance level (probability coverage) for any distribution in the contamination neighborhood of a continuous distribution. We also define some…

非参数置信区间的适应性理论AI 解读

A nonparametric adaptation theory is developed for the construction of confidence intervals for linear functionals. A between class modulus of continuity captures the expected length of adaptive confidence intervals. Sharp lower bounds are given for the expected length and an ordered modulus of continuity is used to construct adaptive confidence procedures which are within a constant factor of the lower bounds. In addition, minimax theory over nonconvex parameter spaces is…

单位根与阈值设定的检验：购买力平价关系的应用AI 解读

We consider modeling the real exchange rate by a stationary three-regime self-exciting threshold autoregressive (SETAR) model with possibly a unit root in the middle regime. This representation is consistent with purchasing power parity in the presence of trading costs. Our main contribution is to provide statistical tools for testing unit root versus a SETAR. First, we show that a SETAR with a unit root in the middle regime is stationary and mixing under reasonable…

利用协偏度检验资产定价模型AI 解读

In this article we investigate portfolio coskewness using a quadratic market model as a return-generating process. We show that the portfolios of small (large) firms have negative (positive) coskewness with the market. We test an asset pricing model including coskewness by checking the validity of the restrictions that it imposes on the return-generating process. We find evidence of an additional component in expected excess returns, which is not explained by either…

CAViaR：条件自回归风险价值模型AI 解读

Value at risk (VaR) is the standard measure of market risk used by financial institutions. Interpreting the VaR as the quantile of future portfolio values conditional on current information, the conditional autoregressive value at risk (CAViaR) model specifies the evolution of the quantile over time using an autoregressive process and estimates the parameters with regression quantiles. Utilizing the criterion that each period the probability of exceeding the VaR must be…

摘要暂缺

摘要暂缺

Consistent standard errors for target variance approach to GARCH estimation.

多元统计量的变换AI 解读

This paper derives transformations for multivariate statistics that eliminate asymptotic skewness, extending the results of Niki and Konishi (1986, Annals of the Institute of Statistical Mathematics 38, 371–383). Within the context of valid Edgeworth expansions for such statistics we first derive the set of equations that such a transformation must satisfy and second propose a local solution that is sufficient up to the desired order. Application of these results yields two…

伪回归中具有极限分布的 t 统计量AI 解读

This paper investigates the asymptotic properties of the t-statistic in spurious regressions when the bandwidth in the estimation of the heteroskedasticity and autocorrelation consistent (HAC) standard error is set proportional to the sample size. Using autocovariances of large lags, the so-defined HAC estimator is capable of capturing the high persistence of the regressor and regression residuals. It is shown that the resulting t-statistic converges to a nondegenerate…

门限模型的工具变量估计AI 解读

Threshold models (sample splitting models) have wide application in economics. Existing estimation methods are confined to regression models, which require that all right-hand-side variables are exogenous. This paper considers a model with endogenous variables but an exogenous threshold variable. We develop a two-stage least squares estimator of the threshold parameter and a generalized method of moments estimator of the slope parameters. We show that these estimators are…

离散观测莱维过程的偏斜参数估计AI 解读

We consider models for financial data by Lévy processes, including hyperbolic, normal inverse Gaussian, and Carr, Geman, Madan, and Yor (CGMY) processes. They are given by their Lévy triplet (μ(θ),σ2,eθxg(x)ν(dx)), where μ denotes the drift, σ2 the diffusion, and eθxg(x)ν(dx) the Lévy measure, and the unknown parameter θ models the skewness of the process. We provide local asymptotic normality results and construct efficient estimators for the skewness parameter θ taking…

带长期约束的脉冲响应函数的渐近分布AI 解读

This paper adopts a two-step technique to estimate structural vector error correction models and provides the asymptotic distribution of the impulse response functions of such a system. The method combines two popular tools in econometrics, namely, vector autoregressive cointegration analysis in the first step and structural vector autoregression analysis in the second. The proposed structural model structure is very general in the sense that all just-identifying or…

连续时间扩散模型中的自适应检验AI 解读

We propose an optimal test procedure for testing the marginal density functions of a class of nonlinear diffusion processes. The proposed test is not only an optimal one but also avoids undersmoothing. An adaptive test is constructed, and its asymptotic properties are investigated. To show the asymptotic properties, we establish some general results for moment inequalities and asymptotic distributions for strictly stationary processes under the α-mixing condition. These…

组序贯临床试验设计中的功效、样本量与适应性AI 解读

A class of flexible and asymptotically efficient group sequential designs is developed herein for one-sided and two-sided tests of the parameter of an exponential family. Efficiency is measured in terms of the expected sample size and power function, under prespecified constraints on the maximum sample size and Type I error probability. It is shown how these designs achieve asymptotic efficiency by adapting to the information about the unknown parameter during the course of…

关于由边际密度构造伪似然的说明AI 解读

For likelihood‐based inference involving distributions in which high‐dimensional dependencies are present it may be useful to use approximate likelihoods based, for example, on the univariate or bivariate marginal distributions. The asymptotic properties of formal maximum likelihood estimators in such cases are outlined. In particular, applications in which only a single q×1 vector of observations is observed are examined. Conditions under which consistent estimators of…

时间过程回归AI 解读

We consider regression for response and covariates which are temporal processes observed over intervals. A functional generalised linear model is proposed which includes extensions of standard models in multi‐state survival analysis. Simple nonparametric estimators of time‐indexed parameters are developed using ‘working independence’ estimating equations and are shown to be uniformly consistent and to converge weakly to Gaussian processes. The procedure does not require…

半变系数模型的有效估计AI 解读

Motivated by two practical problems, we propose a new procedure for estimating a semivarying‐coefficient model. Asymptotic properties are established which show that the bias of the parameter estimator is of order h3 when a symmetric kernel is used, where h is the bandwidth, and the variance is of order n−1 and efficient in the semiparametric sense. Undersmoothing is unnecessary for the root‐n consistency of the estimators. Therefore, commonly used bandwidth selection…