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GARCH(1,1) 模型的闭式估计量AI 解读

We propose a closed-form estimator for the linear GARCH(1,1) model. The estimator has the advantage over the often used quasi-maximum likelihood estimator (QMLE) that it can be easily implemented and does not require the use of any numerical optimization procedures or the choice of initial values of the conditional variance process. We derive the asymptotic properties of the estimator, showing T(κ−1)/κ-consistency for some κ ∈ (1,2) when the fourth moment exists and…

正态混合 GARCH(1,1)：汇率建模应用AI 解读

Abstract Some recent specifications for GARCH error processes explicitly assume a conditional variance that is generated by a mixture of normal components, albeit with some parameter restrictions. This paper analyses the general normal mixture GARCH(1,1) model which can capture time variation in both conditional skewness and kurtosis. A main focus of the paper is to provide evidence that, for modelling exchange rates, generalized two‐component normal mixture GARCH(1,1)…

分组数据下的稳健与有效估计AI 解读

The minimum Hellinger distance estimator is known to have desirable properties in terms of robustness and efficiency. We propose an approximate minimum Hellinger distance estimator by adapting the approach to grouped data from a continuous distribution. It is easier to compute the approximate version for either the continuous data or the grouped data. Given certain conditions on the model distribution and reasonable grouping rules, the approximate minimum Hellinger distance…

疫苗对感染后二元结局的因果效应AI 解读

The effects of vaccine on postinfection outcomes, such as disease, death, and secondary transmission to others, are important scientific and public health aspects of prophylactic vaccination. As a result, evaluation of many vaccine effects condition on being infected. Conditioning on an event that occurs posttreatment (in our case, infection subsequent to assignment to vaccine or control) can result in selection bias. Moreover, because the set of individuals who would become…

遗传关联研究中单倍型效应的似然推断AI 解读

A haplotype is a specific sequence of nucleotides on a single chromosome. The population associations between haplotypes and disease phenotypes provide critical information about the genetic basis of complex human diseases. Standard genotyping techniques cannot distinguish the two homologous chromosomes of an individual, so only the unphased genotype (i.e., the combination of the two homologous haplotypes) is directly observable. Statistical inference about…

混合线性模型的高崩溃点稳健推断AI 解读

Mixed linear models are used to analyze data in many settings. These models have a multivariate normal formulation in most cases. The maximum likelihood estimator (MLE) or the residual MLE (REML) is usually chosen to estimate the parameters. However, the latter are based on the strong assumption of exact multivariate normality. Welsh and Richardson have shown that these estimators are not robust to small deviations from multivariate normality. This means that in practice a…

计数数据分布AI 解读

In this article we characterize all two-parameter count distributions (satisfying very general conditions) that are partially closed under addition. We also find those for which the maximum likelihood estimator of the population mean is the sample mean. Mixed Poisson models satisfying these properties are completely determined. Among these models are the negative binomial, Poisson-inverse Gaussian, and other known distributions. New count distributions can also be…

不同长度时间序列的多变量模型估计AI 解读

Abstract We consider the problem of estimating parametric multivariate density models when unequal amounts of data are available on each variable. We focus in particular on the case that the unknown parameter vector may be partitioned into elements relating only to a marginal distribution and elements relating to the copula. In such a case we propose using a multi‐stage maximum likelihood estimator (MSMLE) based on all available data rather than the usual one‐stage maximum…

鞅变换的稳定极限及其在 GARCH 参数估计中的应用AI 解读

In this paper we study the asymptotic behavior of the Gaussian quasi maximum likelihood estimator of a stationary GARCH process with heavy-tailed innovations. This means that the innovations are regularly varying with index α∈(2,4). Then, in particular, the marginal distribution of the GARCH process has infinite fourth moment and standard asymptotic theory with normal limits and $\sqrt{n}$-rates breaks down. This was recently observed by Hall and Yao [Econometrica 71 (2003)…

惩罚最大似然与半参数二阶效率AI 解读

We consider the problem of estimation of a shift parameter of an unknown symmetric function in Gaussian white noise. We introduce a notion of semiparametric second-order efficiency and propose estimators that are semiparametrically efficient and second-order efficient in our model. These estimators are of a penalized maximum likelihood type with an appropriately chosen penalty. We argue that second-order efficiency is crucial in semiparametric problems since only the…

单一监测时间下的双变量现时状态数据AI 解读

For bivariate current status data with univariate monitoring times, the identifiable part of the joint distribution is three univariate cumulative distribution functions, namely the two marginal distributions and the bivariate cumulative distribution function evaluated on the diagonal. We show that smooth functionals of these univariate cumulative distribution functions can be efficiently estimated with easily computed nonparametric maximum likelihood estimators based on…

逆高斯分布参数最大似然估计量分布的另一种推导AI 解读

We provide a simpler derivation of the sampling properties of the maximum likelihood estimators of the parameters in an inverse Gaussian distribution.

空间统计中两种渐近框架的协调AI 解读

Two asymptotic frameworks, increasing domain asymptotics and infill asymptotics, have been advanced for obtaining limiting distributions of maximum likelihood estimators of covariance parameters in Gaussian spatial models with or without a nugget effect. These limiting distributions are known to be different in some cases. It is therefore of interest to know, for a given finite sample, which framework is more appropriate. We consider the possibility of making this choice on…

曲线样本结构均值的非参数最大似然估计AI 解读

A random sample of curves can be usually thought of as noisy realisations of a compound stochastic process X(t) = Z{W(t)}, where Z(t) produces random amplitude variation and W(t) produces random dynamic or phase variation. In most applications it is more important to estimate the so-called structural mean μ(t) = E{Z(t)} than the crosssectional mean E{X(t)}, but this estimation problem is difficult because the process Z(t) is not directly observable. In this paper we propose…

多类型分枝过程的识别AI 解读

We solve the problem of constructing an asymptotic global confidence region for the means and the covariance matrices of the reproduction distributions involved in a supercritical multitype branching process. Our approach is based on a central limit theorem associated with a quadratic law of large numbers performed by the maximum likelihood or the multidimensional Lotka–Nagaev estimator of the reproduction law means. The extension of this approach to the least squares…

线性移动平均模型对门限移动平均模型的检验AI 解读

This paper investigates the (conditional) quasi-likelihood ratio test for the threshold in MA models. Under the hypothesis of no threshold, it is shown that the test statistic converges weakly to a function of the centred Gaussian process. Under local alternatives, it is shown that this test has nontrivial asymptotic power. The results are based on a new weak convergence of a linear marked empirical process, which is independently of interest. This paper also gives an…

This paper derives second‐order expansions for the distributions of the Whittle and profile plug‐in maximum likelihood estimators of the fractional difference parameter in the ‘Autoregressive Fractionally Integrated Moving Average of order (0, d, 0)’ with unknown mean and variance. Both estimators are shown to be second‐order pivotal. This extends earlier findings of Lieberman and Phillips (2004a, Econometric Theory, 20, 464–84), who derived expansions for the Gaussian…

多变量观测的线性解混AI 解读

In many fields of science there are multivariate observations that may be assumed to be generated by a (physical) linear mixing process of contributions from different sources. If the compositions of the sources are constant for different observations, then these observations are, up to a random error term, nonnegative linear combinations of a fixed set of so-called “source profiles” that characterize the sources. The goal of linear unmixing is to recover both the source…

圆周上的一族对称分布AI 解读

We propose a new family of symmetric unimodal distributions on the circle that contains the uniform, von Mises, cardioid, and wrapped Cauchy distributions, among others, as special cases. The basic form of the densities of this family is very simple, although its normalization constant involves an associated Legendre function. The family of distributions can also be derived by conditioning and projecting certain bivariate spherically and elliptically symmetric distributions…

似然推断中的分部最大化AI 解读

This article presents and examines a new algorithm for solving a score equation for the maximum likelihood estimate in certain problems of practical interest. The method circumvents the need to compute second-order derivatives of the full likelihood function. It exploits the structure of certain models that yield a natural decomposition of a very complicated likelihood function. In this decomposition, the first part is a log-likelihood from a simply analyzed model, and the…

含协变量误差的半参数生存回归：伪偏似然方法AI 解读

This article presents an estimator for the regression coefficient vector in the Cox proportional hazards model with covariate error. The estimator is obtained by maximizing a likelihood-type function similar to the Cox partial likelihood. The likelihood function involves the cumulative baseline hazard function, for which a simple estimator is substituted. The method is capable of handling general covariate error structures; it is not restricted to the independent additive…

二元 ARCH 模型：QML 估计的有限样本性质及 LM 型检验应用AI 解读

This paper provides two main new results: the first shows theoretically that large biases and variances can arise when the quasi-maximum likelihood (QML) estimation method is employed in a simple bivariate structure under the assumption of conditional heteroskedasticity; and the second demonstrates how these analytical theoretical results can be used to improve the finite-sample performance of a test for multivariate autoregressive conditional heteroskedastic (ARCH) effects,…

估计分布端点的贝叶斯似然方法AI 解读

Summary We consider maximum likelihood methods for estimating the end point of a distribution. The likelihood function is modified by a prior distribution that is imposed on the location parameter. The prior is explicit and meaningful, and has a general form that adapts itself to different settings. Results on convergence rates and limiting distributions are given. In particular, it is shown that the limiting distribution is non-normal in non-regular cases. Parametric…

Summary We develop a new class of time continuous autoregressive fractionally integrated moving average (CARFIMA) models which are useful for modelling regularly spaced and irregu-larly spaced discrete time long memory data. We derive the autocovariance function of a stationary CARFIMA model and study maximum likelihood estimation of a regression model with CARFIMA errors, based on discrete time data and via the innovations algorithm. It is shown that the maximum likelihood…