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非平稳与单位根情形下的局部Whittle估计AI 解读

Asymptotic properties of the local Whittle estimator in the nonstationary case (d>½) are explored. For ½ 1 and when the process has a polynomial trend of order α>½, the estimator is shown to be inconsistent and to converge in probability to unity.

用U统计量估计线性过程的平稳分布泛函AI 解读

Suppose we observe an invertible linear process with independent mean-zero innovations and with coefficients depending on a finite-dimensional parameter, and we want to estimate the expectation of some function under the stationary distribution of the process. The usual estimator would be the empirical estimator. It can be improved using the fact that the innovations are centered. We construct an even better estimator using the representation of the observations as…

时变波动率模型的统计推断AI 解读

This paper offers a new approach for estimating and forecasting the volatility of financial time series. No assumption is made about the parametric form of the processes. On the contrary, we only suppose that the volatility can be approximated by a constant over some interval. In such a framework, the main problem consists of filtering this interval of time homogeneity; then the estimate of the volatility can be simply obtained by local averaging. We construct a locally…

高斯回归中的置信球AI 解读

Starting from the observation of an ℝn-Gaussian vector of mean f and covariance matrix σ2In (In is the identity matrix), we propose a method for building a Euclidean confidence ball around f, with prescribed probability of coverage. For each n, we describe its nonasymptotic property and show its optimality with respect to some criteria.

基于平稳过程归一化距离加权和的房价空间建模AI 解读

Hedonic models are used almost universally for modeling house prices. Recognizing the importance of location, the past decade has seen increasing effort to introduce spatial considerations into such modeling. When spatial process models are used to capture association between locations, isotropic specifications have been used almost exclusively despite the fact that they seem unlikely to be appropriate in practice. The contribution of this article is to offer a novel,…

时间序列模型的广义 Portmanteau 拟合优度检验AI 解读

We present a goodness-of-fit test for time series models based on the discrete spectral average estimator. Unlike current tests of goodness of fit, the asymptotic distribution of our test statistic allows the null hypothesis to be either a short- or long-range dependence model. Our test is in the frequency domain, is easy to compute, and does not require the calculation of residuals from the fitted model. This is especially advantageous when the fitted model is not a…

部分根接近一时完全修正 VAR 假设检验的稳健性AI 解读

This paper proves that the fully modified vector autoregression (FM-VAR) estimator has second-order bias effects when some roots are local to unity. These bias effects are shown to result in potentially severe size distortions in FM-VAR testing when the hypothesis involves near unit root variables. In addition, the paper reveals that with the FM-VAR method near unit roots become estimated as exact unit roots with convergence speed faster than the order of the sample size.…

协整平滑转换回归AI 解读

This paper studies the smooth transition regression model where regressors are I(1) and errors are I(0). The regressors and errors are assumed to be dependent both serially and contemporaneously. Using the triangular array asymptotics, the nonlinear least squares estimator is shown to be consistent, and its asymptotic distribution is derived. It is found that the asymptotic distribution involves a bias under the regressor-error dependence, which implies that the nonlinear…

半参数广义可加模型中的 Bootstrap 推断AI 解读

Semiparametric generalized additive models are a powerful tool in quantitative econometrics. With response Y, covariates X,T, the considered model is E(Y |X;T) = G{XTβ + α + m1(T1) + ··· + md(Td)}. Here, G is a known link, α and β are unknown parameters, and m1,…,md are unknown (smooth) functions of possibly higher dimensional covariates T1,…,Td. Estimates of m1,…,md, α, and β are presented, and asymptotic distributions are given for both the nonparametric and the parametric…

基于经验似然的推断及其在若干计量模型中的应用AI 解读

This paper uses the concept of dual likelihood to develop some higher order asymptotic theory for the empirical likelihood ratio test for parameters defined implicitly by a set of estimating equations. The resulting theory is likelihood based in the sense that it relies on methods developed for ordinary parametric likelihood models to obtain valid Edgeworth expansions for the maximum dual likelihood estimator and for the dual/empirical likelihood ratio statistic. In…

稳健单位根检验不应被“修改”AI 解读

The rank-based unit root tests proposed by Hasan and Koenker (1997, Econometrica 65, 133–161) have power equal to size for normal innovations. Unit root tests based on M-estimators exhibit the same behavior. The problem occurs because the test statistics are transformed to obtain computationally convenient critical values. I describe a convenient way to compute critical values without transforming the test statistics. The resulting tests are almost as powerful as least…

基于自然指数族二次方差函数模型与调查权重的小区域估计AI 解读

We propose pseudo empirical best linear unbiased estimators of small‐area means based on natural exponential family quadratic variance function models when the basic data consist of survey‐weighted estimators of these means, area‐specific covariates and certain summary measures involving the weights. We also provide explicit approximate mean squared errors of these estimators in the spirit of Prasad & Rao (1990), and these estimators can be readily evaluated. A simulation…

利用渐近枢轴估计函数推断无限维参数AI 解读

Suppose that a consistent estimator for an infinite‐dimensional parameter can be readily obtained via a set of estimating functions which has a ‘good’ local linear approximation around the true value of the parameter. However, it may be difficult to estimate the variance function of this estimator well. We show that, if the set of estimating functions evaluated at the true parameter value is ‘asymptotically pivotal’, then the ‘fiducial’ distribution of the parameter can be…

重新考察误差自相关的简单线性回归AI 解读

This paper studies properties of ordinary and generalised least squares estimators in a simple linear regression with stationary autocorrelated errors. Explicit expressions for the variances of the regression parameter estimators are derived for some common time series autocorrelation structures, including a first‐order autoregression and general moving averages. Applications of the results include confidence intervals and an example where the variance of the trend slope…

利用家庭数据估计遗传关联参数AI 解读

We consider the problem of estimating a parameter θ reflecting association between a disease and genotypes of a genetic polymorphism, using nuclear family data. In many applications, some parental genotypes are missing, and the distribution of these genotypes is unknown. Since misspecification of this distribution can bias estimators for θ, we consider estimating functions that are unbiased, regardless of how the distribution is specified. We call the resulting estimators…

谱密度的广义似然比检验AI 解读

There are few techniques available for testing whether or not a family of parametric times series models fits a set of data reasonably well without serious restrictions on the forms of alternative models. In this paper, we consider generalised likelihood ratio tests of whether or not the spectral density function of a stationary time series admits certain parametric forms. We propose a bias correction method for the generalised likelihood ratio test of Fan et al. (2001). In…

聚类与纵向数据非参数回归中平滑样条的等价核AI 解读

For independent data, it is well known that kernel methods and spline methods are essentially asymptotically equivalent (Silverman, 1984). However, recent work of Welsh et al. (2002) shows that the same is not true for clustered/longitudinal data. Splines and conventional kernels are different in localness and ability to account for the within‐cluster correlation. We show that a smoothing spline estimator is asymptotically equivalent to a recently proposed seemingly…

区分嵌套回归模型的序贯与非序贯设计比较AI 解读

SUMMARY Classical regression analysis is usually performed in two steps. In a first step an appro priate model is identified to describe the data-generating process and in a second step statistical inference is performed in the identified model. In this paper we investigate a sequential and a non-sequential design strategy, which take into account these different goals of the analysis for a class of nested models. It is demonstrated that non-sequential designs usually…

病例对照研究贝叶斯分析中前瞻与回顾模型的等价性AI 解读

The natural likelihood to use for a case‐control study is a ‘retrospective’ likelihood, i.e. a likelihood based on the probability of exposure given disease status. Prentice & Pyke (1979) showed that, when a logistic regression form is assumed for the probability of disease given exposure, the maximum likelihood estimators and asymptotic covariance matrix of the log odds ratios obtained from the retrospective likelihood are the same as those obtained from the ‘prospective’…

高斯时间序列中 Whittle 测度的相互毗连性AI 解读

For a stationary time series, Whittle constructed a likelihood for the spectral density based on the approximate independence of the discrete Fourier transforms of the data at certain frequencies. Whittle's likelihood has been widely used in the literature for constructing estimators. In this paper, we show that, for a Gaussian time series, the Whittle measure is mutually contiguous with the actual distribution of the data. As a consequence, most asymptotic properties of…

依赖数据的多峰性检验AI 解读

We propose a test for multimodality with dependent data by resampling from a suitably constructed transition probability kernel, which includes Silverman's test with independent data as a special case. We extend some theoretical properties of Silverman's test with independent and identically distributed data to weakly dependent data, and also discuss the robustness of Silverman's test against departure from independence.

贝叶斯相关系数估计AI 解读

We propose prior probability models for variance‐covariance matrices in order to address two important issues. First, the models allow a researcher to represent substantive prior information about the strength of correlations among a set of variables. Secondly, even in the absence of such information, the increased flexibility of the models mitigates dependence on strict parametric assumptions in standard prior models. For example, the model allows a posteriori different…

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