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参数位于边界时的高阶渐近理论及其GARCH应用AI 解读

Andrews (1999, Econometrica 67, 1341–1383) derived the first-order asymptotic theory for a very general class of estimators when a parameter is on a boundary. We derive the second-order asymptotic theory in this setting in some special cases. We focus on the behavior of the quasi maximum likelihood estimator (QMLE) in stationary and nonstationary generalized autoregressive conditionally heteroskedastic (GARCH) models when constraints are imposed in the maximization…

非零阈值的 Tobit 模型AI 解读

The standard Tobit maximum likelihood estimator under zero censoring threshold produces inconsistent parameter estimates, when the constant censoring threshold γ is non-zero and unknown. Unfortunately, the recording of a zero rather than the actual censoring threshold value is typical of economic data. Non-trivial minimum purchase prices for most goods, fixed cost for doing business or trading, social customs such as those involving charitable donations, and informal…

状态切换检验AI 解读

We analyze use of a quasi-likelihood ratio statistic for a mixture model to test the null hypothesis of one regime versus the alternative of two regimes in a Markov regime-switching context. This test exploits mixture properties implied by the regime-switching process, but ignores certain implied serial correlation properties. When formulated in the natural way, the setting is nonstandard, involving nuisance parameters on the boundary of the parameter space, nuisance…

正则模型中修正带符号似然比统计量近似的高阶渐近正态性AI 解读

Approximations to the modified signed likelihood ratio statistic are asymptotically standard normal with error of order n−1, where n is the sample size. Proofs of this fact generally require that the sufficient statistic of the model be written as (θ̂, a), where θ̂ is the maximum likelihood estimator of the parameter θ of the model and a is an ancillary statistic. This condition is very difficult or impossible to verify for many models. However, calculation of the statistics…

基于变换的鞅估计函数AI 解读

An estimation method is proposed for a wide variety of discrete time stochastic processes that have an intractable likelihood function but are otherwise conveniently specified by an integral transform such as the characteristic function, the Laplace transform or the probability generating function. This method involves the construction of classes of transform-based martingale estimating functions that fit into the general framework of quasi-likelihood. In the parametric…

含协变量面板计数数据的两种基于似然的半参数估计方法AI 解读

We consider estimation in a particular semiparametric regression model for the mean of a counting process with “panel count” data. The basic model assumption is that the conditional mean function of the counting process is of the form E{ℕ(t)|Z}=exp(β0TZ)Λ0(t) where Z is a vector of covariates and Λ0 is the baseline mean function. The “panel count” observation scheme involves observation of the counting process ℕ for an individual at a random number K of random time points;…

固定效应动态面板离散选择模型的估计AI 解读

In this paper, I consider the estimation of dynamic binary choice panel data models with fixed effects. I use a Modified Maximum Likelihood Estimator (MMLE) that reduces the order of the bias in the Maximum Likelihood Estimator from O(T^(-1)) to O(T^(-2)), without increasing the asymptotic variance. I evaluate its performance in finite samples where T is not large, using Monte Carlo simulations. In Probit and Logit models containing lags of the endogenous variable and…

摘要暂缺

平稳分数协整的局部 Whittle 分析及隐含与已实现波动率的关系AI 解读

I consider local Whittle analysis of a stationary fractionally cointegrated model. The local Whittle quasi maximum likelihood estimator is proposed to jointly estimate the integration orders of the regressors, the integration order of the errors, and the cointegration vector. The proposed estimator is semiparametric in the sense that it employs local assumptions on the joint spectral density matrix of the regressors and the errors near the zero frequency. I show that the…

伪最大似然估计量的渐近方差AI 解读

We present an analytical closed-form expression for the asymptotic variance matrix in the misspecified multivariate regression model.I am grateful to Hamparsum Bozdogan of the University of Tennessee for bringing the idea of the sandwich variance matrix within the context of the misspecified multivariate regression model to my attention and to two referees for their constructive and useful comments.

无限方差 ARMA 模型的加权最小绝对偏差估计AI 解读

For autoregressive moving average (ARMA) models with infinite variance innovations, quasi-likelihood-based estimators (such as Whittle estimators) suffer from complex asymptotic distributions depending on unknown tail indices. This makes statistical inference for such models difficult. In contrast, the least absolute deviations estimators (LADE) are more appealing in dealing with heavy tailed processes. In this paper, we propose a weighted least absolute deviations estimator…

删失数据半参数回归模型中的极大似然估计AI 解读

Summary Semiparametric regression models play a central role in formulating the effects of covariates on potentially censored failure times and in the joint modelling of incomplete repeated measures and failure times in longitudinal studies. The presence of infinite dimensional parameters poses considerable theoretical and computational challenges in the statistical analysis of such models. We present several classes of semiparametric regression models, which extend the…

位置或距离测量误差下的空间相关稳健推断AI 解读

This paper presents results from a Monte Carlo study concerning inference with spatially dependent data. We investigate the impact of location/distance measurement errors upon the accuracy of parametric and nonparametric estimators of asymptotic variances. Nonparametric estimators are quite robust to such errors, method of moments estimators perform surprisingly well, and MLE estimators are very poor. We also present and evaluate a speci...cation test based on a parametric…

函数型主成分回归与函数型偏最小二乘AI 解读

Regression of a scalar response on signal predictors, such as near-infrared (NIR) spectra of chemical samples, presents a major challenge when, as is typically the case, the dimension of the signals far exceeds their number. Most solutions to this problem reduce the dimension of the predictors either by regressing on components [e.g., principal component regression (PCR) and partial least squares (PLS)] or by smoothing methods, which restrict the coefficient function to the…

广义线性模型类推断的稳健建模AI 解读

Generalized linear models (GLMs) are widely used for data analysis; however, their maximum likelihood estimators can be sensitive to outliers. We propose new statistical models that allow robust inferences from the GLM class of models, including Poisson and binomial GLMs, and their extension to generalized linear mixed models. The likelihood score equations from the new models give estimators with bounded influence, so that the resulting estimators are robust against…

加州电力备用容量市场的效率AI 解读

Abstract We test the efficiency of the California electricity reserves market by examining systematic differences between its day‐ and hour‐ahead prices. We uncover significant day‐ahead premia, which we attribute to market design characteristics. On the demand side, the market design established a principal–agent relationship between the markets' buyers (principal) and their supervisory authority (agent). The agent had very limited incentives to shift reserve purchases to…

基于估计抽样分布的重要性抽样AI 解读

Monte Carlo importance sampling for evaluating numerical integration is discussed. We consider a parametric family of sampling distributions and propose the use of the sampling distribution estimated by maximum likelihood. The proposed method of importance sampling using the estimated sampling distribution is shown to improve the asymptotic variance of the ordinary method using the true sampling distribution. The argument is closely related to the discussion of the paradox…

潜变量情境下二次指数分布的近似AI 解读

Following Cox & Wermuth (1994, 2002), we show that the distribution of a set of binary observable variables, induced by a certain discrete latent variable model, may be approximated by a quadratic exponential distribution. This discrete latent variable model is equivalent to the latent-class version of the two-parameter logistic model of Birnbaum (1968), which may be seen as a generalized version of the Rasch model (Rasch, 1960, 196). On the basis of this result, we develop…

非对称幂分布：理论及风险度量应用AI 解读

Abstract Theoretical literature in finance has shown that the risk of financial time series can be well quantified by their expected shortfall, also known as the tail value‐at‐risk. In this paper, I construct a parametric estimator for the expected shortfall based on a flexible family of densities, called the asymmetric power distribution (APD). The APD family extends the generalized power distribution to cases where the data exhibits asymmetry. The first contribution of the…

单调响应模型的似然推断AI 解读

The behavior of maximum likelihood estimates (MLEs) and the likelihood ratio statistic in a family of problems involving pointwise nonparametric estimation of a monotone function is studied. This class of problems differs radically from the usual parametric or semiparametric situations in that the MLE of the monotone function at a point converges to the truth at rate n1/3 (slower than the usual $\sqrt{n}$ rate) with a non-Gaussian limit distribution. A framework for…

分数随机微积分的统计学问题AI 解读

We apply the techniques of stochastic integration with respect to fractional Brownian motion and the theory of regularity and supremum estimation for stochastic processes to study the maximum likelihood estimator (MLE) for the drift parameter of stochastic processes satisfying stochastic equations driven by a fractional Brownian motion with any level of Hölder-regularity (any Hurst parameter). We prove existence and strong consistency of the MLE for linear and nonlinear…

缺失数据模型的蒙特卡洛似然推断AI 解读

We describe a Monte Carlo method to approximate the maximum likelihood estimate (MLE), when there are missing data and the observed data likelihood is not available in closed form. This method uses simulated missing data that are independent and identically distributed and independent of the observed data. Our Monte Carlo approximation to the MLE is a consistent and asymptotically normal estimate of the minimizer θ* of the Kullback–Leibler information, as both Monte Carlo…

右删失下具有协变量阈值变点的变换模型推断AI 解读

We consider linear transformation models applied to right censored survival data with a change-point in the regression coefficient based on a covariate threshold. We establish consistency and weak convergence of the nonparametric maximum likelihood estimators. The change-point parameter is shown to be n-consistent, while the remaining parameters are shown to have the expected root-n consistency. We show that the procedure is adaptive in the sense that the nonthreshold…

含测量误差的受限因变量模型的两阶段估计AI 解读

This paper deals with censored or truncated regression models where the explanatory variables are measured with additive errors. We propose a two-stage estimation procedure that combines the instrumental variable method and the minimum distance estimation. This approach produces consistent and asymptotically normally distributed estimators for model parameters. When the predictor and instrumental variables are normally distributed, we also propose a maximum likelihood based…