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若干非参数问题的贝叶斯视角AI 解读

We study the Bayesian approach to nonparametric function estimation problems such as nonparametric regression and signal estimation. We consider the asymptotic properties of Bayes procedures for conjugate (= Gaussian) priors. We show that so long as the prior puts nonzero measure on the very large parameter set of interest then the Bayes estimators are not satisfactory. More specifically, we show that these estimators do not achieve the correct minimax rate over norm bounded…

后验分布的收敛速率AI 解读

We consider the asymptotic behavior of posterior distributions and Bayes estimators for infinite-dimensional statistical models. We give general results on the rate of convergence of the posterior measure. These are applied to several examples, including priors on finite sieves, log-spline models, Dirichlet processes and interval censoring.

曲线估计的尺度空间视角AI 解读

Scale space theory from computer vision leads to an interesting and novel approach to nonparametric curve estimation. The family of smooth curve estimates indexed by the smoothing parameter can be represented as a surface called the scale space surface. The smoothing parameter here plays the same role as that played by the scale of resolution in a visual system. In this paper, we study in detail various features of that surface from a statistical viewpoint. Weak convergence…

广义线性模型中的置信带AI 解读

Generalized linear models (GLM) include many useful models. This paper studies simultaneous confidence regions for the mean response function in these models. The coverage probabilities of these regions are related to tail probabilities of maxima of Gaussian random fields, asymptotically, and hence, the so-called tube formula is applicable without any modification. However, in the generalized linear models, the errors are often nonadditive and non-Gaussian and may be…

摘要暂缺

日频股票波动率的长程依赖AI 解读

Recent empirical studies show that the squares of high-frequency stock returns are long-range dependent and can be modeled as fractionally integrated processes, using, for example, long-memory stochastic volatility models. Are such long-range dependencies common among stocks? Are they caused by the same sources of variation? In this article, we classify daily stock returns of Standard and Poor 500 companies on the basis of a company's size and its business or industrial…

使用迭代自助法对广义基尼指数进行推断AI 解读

Inference using the iterated-bootstrap method proposed by Hall is appealing for cases in which the percentile method needs to be used but the nominal level of a confidence interval has to be adjusted. One natural application is for generalized Gini indices of income inequality. When applying these theoretical inequality measures directly to sample data for the purpose of statistical inference, economists must come up with some measure of sampling variation. This is…

动态双变量混合模型的贝叶斯分析：能否解释收益与交易量的行为？AI 解读

Bivariate mixture models attribute the well-known positive correlation between return volatility and trading volume in financial markets to stochastic changes in a single latent variable representing the number of information arrivals. In this article, dynamic bivariate mixture models that allow for autocorrelation in the latent variable are analyzed by a Bayesian method via Markov-chain Monte Carlo techniques. The results, based on daily data from the Nikkei 225 stock-index…

高频数据分析的若干思考AI 解读

Finance is arguably the most empirically oriented of all the social sciences. This is in part due to the deliberate practical orientation and the ready availability of high-quality financial market data. In recent years, the ever lower costs of data recording and storage have driven the phenomenon to the ultimate limit for some markets: We may have access to time-stamped observations on all quotes and transactions, denoted ultra-high-frequency data by Engle (in press). These…

基于平稳性检验的协整系数置信集合AI 解读

Standard methods for inference in cointegrating systems require all the variables to have exact unit roots and are not at all robust even to slight violations of this condition. In this article, I consider an alternative approach to inference in a cointegrating system. This involves testing the hypothesis that a cointegrating vector takes on a specified value by testing for the stationarity of the associated residual. Confidence sets for the cointegrating vector can be…

GARCH 与 EGARCH 模型的完整贝叶斯推断AI 解读

A full Bayesian analysis of GARCH and EGARCH models is proposed consisting of parameter estimation, model selection, and volatility prediction. The Bayesian paradigm is implemented via Markov-chain Monte Carlo methodologies. We provide implementation details and illustrations using the General Index of the Athens stock exchange.

ARFIMA 模型中基于似然的小样本推断AI 解读

The autoregressive fractionally integrated moving average (ARFIMA) model has become a popular approach for analyzing time series that exhibit long-range dependence. For the Gaussian case, there have been substantial advances in the area of likelihood-based inference, including development of the asymptotic properties of the maximum likelihood estimates and formulation of procedures for their computation. Small-sample inference, however, has not to date been studied. Here we…

异方差与自相关一致协方差矩阵估计量的强一致性证明AI 解读

A strong consistency result for heteroskedasticity and autocorrelation consistent covariance matrix estimators is proven in this paper. In addition, an error in a weak consistency proof for such estimators in the econometrics literature and a correction of that result is provided.

非正态误差分布下的 LM 检验AI 解读

The paper considers different versions of the Lagrange multiplier (LM) tests for autocorrelation and/or for conditional heteroskedasticity. These versions differ in terms of the residuals, and of the functions of the residuals, used to build the tests. In particular, we compare ordinary least squares versus least absolute deviation (LAD) residuals, and we compare squared residuals versus their absolute value. We show that the LM tests based on LAD residuals are…

近积分季节自回归模型中单位根检验统计量的渐近分布AI 解读

Seasonal autoregressive models with an intercept or linear trend are discussed. The main focus of this paper is on the models in which the intercept or trend parameters do not depend on the season. One of the most important results from this study is the asymptotic distribution for the ordinary least squares estimator of the autoregressive parameter obtained under nearly integrated condition, and another is the approximation to the limiting distribution of the t -statistic…

共同随机趋势检验AI 解读

This paper is concerned with tests in multivariate time series models made up of random walk (with drift) and stationary components. When the stationary component is white noise, a Lagrange multiplier test of the hypothesis that the covariance matrix of the disturbances driving the multivariate random walk is null is shown to be locally best invariant, something that does not automatically follow in the multivariate case. The asymptotic distribution of the test statistic is…

矩阵秩的检验AI 解读

This paper considers tests for the rank of a matrix for which a root- T consistent estimator is available. However, in contrast to tests associated with the minimum chi-square and asymptotic least squares principles, the estimator's asymptotic variance matrix is not required to be either full or of known rank. Test statistics based on certain estimated characteristic roots are proposed whose limiting distributions are a weighted sum of independent chi-squared variables.…

面板数据半参数模型的统计推断AI 解读

In a longitudinal study, suppose that, for each subject, repeated measurements of the response variable and covariates are collected at a set of distinct, irregularly spaced time points. We consider a semiparametric model which relates the mean of the response variable at each time point proportionally to a function of a time-dependent covariate vector to analyse such panel data. Inference procedures for regression parameters are proposed without involving any nonparametric…

一类双重删失现时状态模型的非参数极大似然估计及伴侣研究应用AI 解读

The California Partners' Study is an ongoing investigation of heterosexual HIV transmission in partners of infected index cases (Padian, et al., 1987; Shiboski & Jewell, 1990). In addition to the HIV-status of the partner at the recruiting time one also observes the initial time of the partnership and a lower bound for the infection time of the index case. Following Jewell, Malani & Vittinghoff (1994) we assume that the infection time of the index case is uniformly…

复杂抽样调查数据的 Cox 比例风险模型拟合AI 解读

Binder (1992) proposed a method of fitting Cox's proportional hazards to models to survey data with complex sampling designs. He defined the regression parameter of interest as the solution to the partial likelihood score equation based on all the data values of the survey population under study, and developed heuristically a procedure to estimate the regression parameter and the corresponding variance. In this paper, we provide a formal justification of Binder's method.…

向量自回归谱的渐近同时置信带AI 解读

Asymptotic simultaneous confidence bands for all ω in [0, 0.5] are obtained for each scalar function in a spectral density matrix, as well as for the logarithm of the autospectra, the squared coherence and the phase spectra. The bands are illustrated using a simulation study and surface elevation data.

插补估计量的统计推断AI 解读

We derive an estimator of the asymptotic variance of both single and multiple imputation estimators. We assume a parametric imputation model but allow for non- and semiparametric analysis models. Our variance estimator, in contrast to the estimator proposed by Rubin (1987), is consistent even when the imputation and analysis models are misspecified and incompatible with one another.

病例队列设计的竞争风险分析AI 解读

The case-cohort design has been put forward as an alternative design in epidemiological follow-up studies which is less expensive than a full-scale cohort study. In this design, all cases are assembled together with a randomly selected sub-cohort which is then used as a comparison group, one advantage being that the same sub-cohort may serve as a comparison group for a number of different case series. However, the fact that all case groups are compared with the same…

回归误差序列独立性的非参数检验AI 解读

A test for serial independence of regression errors is proposed that is consistent in the direction of serial dependence alternatives of first order. The test statistic is a function of a Hoeffding-Blum-Kiefer-Rosenblatt type of empirical process, based on residuals. The resultant statistic converges, surprisingly, to the same limiting distribution as the corresponding statistic based on true errors.