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边际均值效应与边际分位数效应估计的半参数方法AI 解读

We consider a semiparametric generalized linear model and study estimation of both marginal mean effects and marginal quantile effects in this model. We propose an approximate maximum likelihood estimator, and rigorously establish the consistency, the asymptotic normality, and the semiparametric efficiency of our method in both the marginal mean effect and the marginal quantile effect estimation. Simulation studies are conducted to illustrate the finite sample performance,…

空间面板数据模型的鞍点近似AI 解读

We develop new higher-order asymptotic techniques for the Gaussian maximum likelihood estimator in a spatial panel data model, with fixed effects, time-varying covariates, and spatially correlated errors. Our saddlepoint density and tail area approximation feature relative error of order O(1/(n(T−1))) with n being the cross-sectional dimension and T the time-series dimension. The main theoretical tool is the tilted-Edgeworth technique in a nonidentically distributed setting.…

短记忆与长记忆时间序列的鞍点近似：频域方法AI 解读

Saddlepoint techniques provide numerically accurate, small sample approximations to the distribution of estimators and test statistics. Except for a few simple models, these approximations are not available in the framework of stationary time series. We contribute to fill this gap. Under short or long range serial dependence, for Gaussian and non Gaussian processes, we show how to derive and implement saddlepoint approximations for two relevant classes of frequency domain…

高维广义线性模型中的稳健一致变量选择AI 解读

Generalized linear models are popular for modelling a large variety of data. We consider variable selection through penalized methods by focusing on resistance issues in the presence of outlying data and other deviations from assumptions. We highlight the weaknesses of widely-used penalized M-estimators, propose a robust penalized quasilikelihood estimator, and show that it enjoys oracle properties in high dimensions and is stable in a neighbourhood of the model. We…

样本选择模型中的稳健推断AI 解读

Summary The problem of non-random sample selectivity often occurs in practice in many fields. The classical estimators introduced by Heckman are the backbone of the standard statistical analysis of these models. However, these estimators are very sensitive to small deviations from the distributional assumptions which are often not satisfied in practice. We develop a general framework to study the robustness properties of estimators and tests in sample selection models. We…

稳健滤波AI 解读

Filtering methods are powerful tools to estimate the hidden state of a state-space model from observations available in real time. However, they are known to be highly sensitive to the presence of small misspecifications of the underlying model and to outliers in the observation process. In this article, we show that the methodology of robust statistics can be adapted to sequential filtering. We define a filter as being robust if the relative error in the state distribution…

高阶无穷小稳健性AI 解读

Using the von Mises expansion, we study the higher-order infinitesimal robustness of a general M-functional and characterize its second-order properties. We show that second-order robustness is equivalent to the boundedness of both the estimator’s estimating function and its derivative with respect to the parameter. It implies, at the same time, (i) variance robustness and (ii) robustness of higher-order saddlepoint approximations to the estimator’s finite sample density.…

测量误差模型中的鞍点检验AI 解读

We develop second-order hypothesis testing procedures in functional measurement error models for small or moderate sample sizes, where the classical first-order asymptotic analysis often fails to provide accurate results. In functional models no distributional assumptions are made on the unobservable covariates and this leads to semiparametric models. Our testing procedure is derived using saddlepoint techniques and is based on an empirical distribution estimation subject to…

广义线性潜变量模型的拟合优度检验AI 解读

Generalized Linear Latent Variables Models (GLLVM) enable the modeling of relationships between manifest and latent variables, where the manifest variables are distributed according to a distribution of the exponential family (e.g., binomial or normal) and to the multinomial distribution (for ordinal manifest variables). These models are widely used in social sciences. To test the appropriateness of a particular model, one needs to define a goodness-of-fit test statistic…

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广义线性潜变量模型的估计AI 解读

Summary Generalized linear latent variable models (GLLVMs), as defined by Bartholomew and Knott, enable modelling of relationships between manifest and latent variables. They extend structural equation modelling techniques, which are powerful tools in the social sciences. However, because of the complexity of the log-likelihood function of a GLLVM, an approximation such as numerical integration must be used for inference. This can limit drastically the number of variables in…

稳健间接推断AI 解读

In this article we develop robust indirect inference for a variety of models in a unified framework. We investigate the local robustness properties of indirect inference and derive the influence function of the indirect estimator, as well as the level and power influence functions of indirect tests. These tools are then used to design indirect inference procedures that are stable in the presence of small deviations from the assumed model. Although indirect inference was…

广义线性模型的稳健推断AI 解读

By starting from a natural class of robust estimators for generalized linear models based on the notion of quasi-likelihood, we define robust deviances that can be used for stepwise model selection as in the classical framework. We derive the asymptotic distribution of tests based on robust deviances, and we investigate the stability of their asymptotic level under contamination. The binomial and Poisson models are treated in detail. Two applications to real data and a…

GMM 估计量的稳健推断AI 解读

The local robustness properties of generalized method of moments (GMM) estimators and of a broad class of GMM based tests are investigated in a unified framework. GMM statistics are shown to have bounded influence if and only if the function defining the orthogonality restrictions imposed on the underlying model is bounded. Since in many applications this function is unbounded, it is useful to have procedures that modify the starting orthogonality conditions in order to…

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含离群值抽样调查的偏差校准估计AI 解读

Summary We discuss the problem of estimating finite population parameters on the basis of a sample containing representative outliers. We clarify the motivation for Chambers's bias-calibrated estimator of the population total and show that bias calibration is a key idea in constructing estimators of finite population parameters. We then link the problem of estimating the population total to distribution function or quantile estimation and explore a methodology based on the…

通过交叉验证进行稳健线性模型选择AI 解读

This article gives a robust technique for model selection in regression models, an important aspect of any data analysis involving regression. There is a danger that outliers will have an undue influence on the model chosen and distort any subsequent analysis. We provide a robust algorithm for model selection using Shao's cross-validation methods for choice of variables as a starting point. Because Shao's techniques are based on least squares, they are sensitive to outliers.…

分组数据的稳健估计AI 解读

Here we investigate the robustness properties of the class of minimum power divergence estimators for grouped data. This class contains the classical maximum likelihood estimators for grouped data. We find that the bias of these estimators due to deviations from the assumed underlying model can be large. Therefore, we propose a more general class of estimators that allows us to construct robust procedures. By analogy with Hampel's theorem, we define optimal bounded influence…

分组数据的稳健估计AI 解读

Here we investigate the robustness properties of the class of minimum power divergence estimators for grouped data. This class contains the classical maximum likelihood estimators for grouped data. We find that the bias of these estimators due to deviations from the assumed underlying model can be large. Therefore, we propose a more general class of estimators that allows us to construct robust procedures. By analogy with Hampel's theorem, we define optimal bounded influence…

一般参数模型中的稳健有界影响检验AI 解读

We introduce robust tests for testing hypotheses in a general parametric model. These are robust versions of the Wald, scores, and likelihood ratio tests and are based on general M estimators. Their asymptotic properties and influence functions are derived. It is shown that the stability of the level is obtained by bounding the self-standardized sensitivity of the corresponding M estimator. Furthermore, optimally bounded-influence tests are derived for the Wald- and…

多元 M 估计量的经验鞍点近似AI 解读

SUMMARY In this paper, we investigate the use of the empirical distribution function in place of the underlying distribution function F to construct an empirical saddlepoint approximation to the density fn of a general multivariate M-estimator. We obtain an explicit form for the error term in the approximation, investigate the effect of renormalizing the estimator, carry out some numerical comparisons and discuss the regression problem.

Mallows Cp 的稳健版本AI 解读

We present a robust version of Mallows's C P for regression models. It is defined by RC P = W Pσ2 - (U P - V P), where W P = ω i ω2 i r 2 i is a weighted residual sum of squares computed from a robust fit of model P, σ2 is a robust and consistent estimator of σ2 in the full model, and U P and V P are constants depending on the weight function and the number of parameters in model P. Good subset models are those with RC P close to V P or smaller than V P. When the weights are…

多元 M 估计中经验似然与经验鞍点近似的关系AI 解读

By comparing the expansions of the empirical log-likelihood ratio and the empirical cumulant generating function calculated at the saddlepoint, we investigate the relationship between empirical likelihood and empirical saddlepoint approximations. This leads to a nonparametric approximation of the density of a multivariate M-estimator based on the empirical likelihood and, on the other hand, it provides nonparametric confidence regions based on the empirical cumulant…