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潜变量模型的在线期望最大化算法AI 解读

Summary We propose a generic on-line (also sometimes called adaptive or recursive) version of the expectation–maximization (EM) algorithm applicable to latent variable models of independent observations. Compared with the algorithm of Titterington, this approach is more directly connected to the usual EM algorithm and does not rely on integration with respect to the complete-data distribution. The resulting algorithm is usually simpler and is shown to achieve convergence to…

Logistic 项目反应模型的非线性序贯设计及计算机自适应测验应用AI 解读

Computerized adaptive testing is becoming increasingly popular due to advancement of modern computer technology. It differs from the conventional standardized testing in that the selection of test items is tailored to individual examinee’s ability level. Arising from this selection strategy is a nonlinear sequential design problem. We study, in this paper, the sequential design problem in the context of the logistic item response theory models. We show that the adaptive…

对数凹密度最大似然估计的极限分布理论AI 解读

We find limiting distributions of the nonparametric maximum likelihood estimator (MLE) of a log-concave density, i.e. a density of the form f(0) = exp varphi(0) where varphi(0) is a concave function on R. Existence, form, characterizations and uniform rates of convergence of the MLE are given by Rufibach (2006) and Dümbgen and Rufibach (2007). The characterization of the log-concave MLE in terms of distribution functions is the same (up to sign) as the characterization of…

主成分限制最大似然估计量的一致性AI 解读

In this paper we consider two closely related problems: estimation of eigenvalues and eigenfunctions of the covariance kernel of functional data based on (possibly) irregular measurements, and the problem of estimating the eigenvalues and eigenvectors of the covariance matrix for high-dimensional Gaussian vectors. In [A geometric approach to maximum likelihood estimation of covariance kernel from sparse irregular longitudinal data (2007)], a restricted maximum likelihood…

面板计数数据的多样本非参数检验新方法AI 解读

This paper considers the problem of multi-sample nonparametric comparison of counting processes with panel count data, which arise naturally when recurrent events are considered. Such data frequently occur in medical follow-up studies and reliability experiments, for example. For the problem considered, we construct two new classes of nonparametric test statistics based on the accumulated weighted differences between the rates of increase of the estimated mean functions of…

多元随机波动率的Wishart自回归过程AI 解读

The Wishart Autoregressive (WAR) process is a dynamic model for time series of multivariate stochastic volatility. The WAR naturally accommodates the positivity and symmetry of volatility matrices and provides closed-form non-linear forecasts. The estimation of the WAR is straighforward, as it relies on standard methods such as the Method of Moments and Maximum Likelihood. For illustration, the WAR is applied to a sequence of intraday realized volatility-covolatility…

非平稳面板离散选择建模及其汇率制度选择应用AI 解读

This paper develops a regression limit theory for discrete choice nonstationary panels with large cross section (N) and time series (T) dimensions. Some results emerging from this theory are directly applicable in the wider context of M-estimation. This includes an extension of work by Wooldridge [Wooldridge, J.M., 1994. Estimation and Inference for Dependent Processes. In: Engle, R.F., McFadden, D.L. (Eds.). Handbook of Econometrics, vol. 4, North-Holland, Amsterdam] on the…

共同随机趋势的提取：理论与应用AI 解读

This paper investigates the statistical properties of estimators of the parameters and unobserved series for state space models with integrated time series. In particular, we derive the full asymptotic results for maximum likelihood estimation using the Kalman filter for a prototypical class of such models--those with a single latent common stochastic trend. Indeed, we establish the consistency and asymptotic mixed normality of the maximum likelihood estimator and show that…

交易噪声污染股价时的结构信用风险模型估计AI 解读

The transformed-data maximum likelihood estimation (MLE) method for structural credit risk models developed by Duan [Duan, J.-C., 1994. Maximum likelihood estimation using price data of the derivative contract. Mathematical Finance 4, 155-167] is extended to account for the fact that observed equity prices may have been contaminated by trading noises. With the presence of trading noises, the likelihood function based on the observed equity prices can only be evaluated via…

基于两阶段已实现波动率的离散观测扩散过程估计AI 解读

This paper motivates and introduces a two-stage method of estimating diffusion processes based on discretely sampled observations. In the first stage we make use of the feasible central limit theory for realized volatility, as developed in [Jacod, J., 1994. Limit of random measures associated with the increments of a Brownian semiartingal. Working paper, Laboratoire de Probabilities, Universite Pierre et Marie Curie, Paris] and [Barndorff-Nielsen, O., Shephard, N., 2002.…

存在干扰参数时基于伪似然的先验分布AI 解读

Consider a model parameterized by θ == (ψ, λ), where ψ is the parameter of interest. The problem of eliminating the nuisance parameter λ can be tackled by resorting to a pseudo-likelihood function L**(ψ) for ψ—namely, a function of ψ only and the data y with properties similar to those of a likelihood function. If one treats L**(ψ) as a true likelihood, the posterior distribution π**(ψ | y) ∝ π(ψ)L**(ψ) for ψ can be considered, where π(ψ) is a prior distribution on ψ. The…

基于潜在马尔可夫异质性结构的多元纵向动态Logit模型AI 解读

For the analysis of multivariate categorical longitudinal data, we propose an extension of the dynamic logit model. The resulting model is based on a marginal parameterization of the conditional distribution of each vector of response variables given the covariates, the lagged response variables, and a set of subject-specific parameters for the unobserved heterogeneity. The latter ones are assumed to follow a first-order Markov chain. For the maximum likelihood estimation of…

工具变量数量较大时的最优不变推断AI 解读

This paper studies the asymptotic behavior of a Gaussian linear instrumental variables model in which the number of instruments diverges with the sample size. Asymptotic efficiency bounds are obtained for rotation invariant inference procedures and are shown to be attainable by procedures based on the limited information maximum likelihood estimator. The bounds are obtained by characterizing the limiting experiment associated with the model induced by the rotation invariance…

随机场阵列的中心极限定理与一致大数定律AI 解读

Over the last decades, spatial-interaction models have been increasingly used in economics. However, the development of a sufficiently general asymptotic theory for nonlinear spatial models has been hampered by a lack of relevant central limit theorems (CLTs), uniform laws of large numbers (ULLNs) and pointwise laws of large numbers (LLNs). These limit theorems form the essential building blocks towards developing the asymptotic theory of M-estimators, including maximum…

面板 Probit 模型中结构参数与边际效应的固定效应估计AI 解读

Fixed effects estimators of nonlinear panel models can be severely biased due to the incidental parameters problem. In this paper, I characterize the leading term of a large-T expansion of the bias of the MLE and estimators of average marginal effects in parametric fixed effects panel binary choice models. For probit index coefficients, the former term is proportional to the true value of the coefficients being estimated. This result allows me to derive a lower bound for the…

一类半参数线性模型的平滑参数选择AI 解读

Summary Spline-based approaches to non-parametric and semiparametric regression, as well as to regression of scalar outcomes on functional predictors, entail choosing a parameter controlling the extent to which roughness of the fitted function is penalized. We demonstrate that the equations determining two popular methods for smoothing parameter selection, generalized cross-validation and restricted maximum likelihood, share a similar form that allows us to prove several…

从含加性噪声的数据估计凹分布函数AI 解读

We consider two nonparametric procedures for estimating a concave distribution function based on data corrupted with additive noise generated by a bounded decreasing density on (0, ∞). For the maximum likelihood (ML) estimator and least squares (LS) estimator, we state qualitative properties, prove consistency and propose a computational algorithm. For the LS estimator and its derivative, we also derive the pointwise asymptotic distribution. Moreover, the rate n−2/5 achieved…

线性因子模型中风险溢价的检验AI 解读

We show that statistical inference on the risk premia in linear factor models that is based on the Fama-MacBeth (FM) and generalized least squares (GLS) two-pass risk premia estimators is misleading when the [beta]'s are small and/or the number of assets is large. We propose novel statistics, that are based on the maximum likelihood estimator of Gibbons [Gibbons, M., 1982. Multivariate tests of financial models: A new approach. Journal of Financial Economics 10, 3-27], which…

扩散过程的参数估计与偏差修正AI 解读

This paper considers parameter estimation for continuous-time diffusion processes which are commonly used to model dynamics of financial securities including interest rates. To understand why the drift parameters are more difficult to estimate than the diffusion parameter, as observed in previous studies, we first develop expansions for the bias and variance of parameter estimators for two of the most employed interest rate processes, Vasicek and CIR processes. Then, we…

检验重要性抽样背后的假设AI 解读

Importance sampling is used in many areas of modern econometrics to approximate unsolvable integrals. Its reliable use requires the sampler to possess a variance, for this guarantees a square root speed of convergence and asymptotic normality of the estimator of the integral. However, this assumption is seldom checked. In this paper we use extreme value theory to empirically assess the appropriateness of this assumption. Our main application is the stochastic volatility…

动态模型的模拟非参数估计AI 解读

This paper introduces a new class of parameter estimators for dynamic models, called simulated non-parametric estimators (SNEs). The SNE minimizes appropriate distances between non-parametric conditional (or joint) densities estimated from sample data and non-parametric conditional (or joint) densities estimated from data simulated out of the model of interest. Sample data and model-simulated data are smoothed with the same kernel, which considerably simplifies bandwidth…

半强 GARCH 模型的拟最大似然估计AI 解读

This note proves the consistency and asymptotic normality of the quasi–maximum likelihood estimator (QMLE) of the parameters of a generalized autoregressive conditional heteroskedastic (GARCH) model with martingale difference centered squared innovations. The results are obtained under mild conditions and generalize and improve those in Lee and Hansen (1994, Econometric Theory 10, 29–52) for the local QMLE in semistrong GARCH(1,1) models. In particular, no restrictions on…

因子 GARCH 模型的渐近理论AI 解读

This paper investigates the asymptotic theory for a factor GARCH (generalized autoregressive conditional heteroskedasticity) model. Sufficient conditions for asymptotic stability and existence of moments are established. These conditions allow for volatility spillover and integrated GARCH. We then show the strong consistency and asymptotic normality of the quasi–maximum likelihood estimator (QMLE) of the model parameters. The results are obtained under the finiteness of the…

基于最优预测的稳健响应变量变换AI 解读

Nonlinear regression problems can often be reduced to linearity by transforming the response variable (e.g., using the Box-Cox family of transformations). The classic estimates of the parameter defining the transformation as well as of the regression coefficients are based on the maximum likelihood criterion, assuming homoscedastic normal errors for the transformed response. These estimates are nonrobust in the presence of outliers and can be inconsistent when the errors are…