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EDGEWORTH AND SADDLEPOINT EXPANSIONS FOR NONLINEAR ESTIMATORS

非线性估计量的 Edgeworth 展开与鞍点展开

Simple methods are developed for deriving Edgeworth, saddlepoint, and related expansions for the estimators of multivariate and nonlinear models. Illustrations are provided. Simulations are reported indicating the methods work well compared to standard asymptotic and bootstrapped approaches.

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A COMPARISON OF ALTERNATIVE APPROACHES TO SUPREMUM-NORM GOODNESS-OF-FIT TESTS WITH ESTIMATED PARAMETERS

含估计参数的上确界范数拟合优度检验:不同方法的比较

Goodness-of-fit tests based on parametric empirical processes have nonstandard limiting distributions when the null hypothesis is composite — that is, when parameters of the null model are estimated. Several analytic solutions to this problem have been suggested, including the calculation of adjusted critical values for these nonstandard distributions and the transformation of the empirical process such that statistics based on the transformed process are asymptotically…

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TAIL INDEX OF AN AR(1) MODEL WITH ARCH(1) ERRORS

具有 ARCH(1) 误差的 AR(1) 模型的尾指数

Relevant sample quantities such as the sample autocorrelation function and extremes contain useful information about autoregressive time series with heteroskedastic errors. As these quantities usually depend on the tail index of the underlying heteroskedastic time series, estimating the tail index becomes an important task. Since the tail index of such a model is determined by a moment equation, one can estimate the underlying tail index by solving the sample moment equation…

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Nonparametric estimation of the mean function for recurrent event data with missing event category

事件类别缺失时复发事件均值函数的非参数估计

Recurrent event data frequently arise in longitudinal studies when study subjects possibly experience more than one event during the observation period. Often, such recurrent events can be categorized. However, part of the categorization may be missing due to technical difficulties. If the event types are missing completely at random, then a complete case analysis may provide consistent estimates of regression parameters in certain regression models, but estimates of the…

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Inverse probability weighting with error-prone covariates

含测量误差协变量的逆概率加权

Inverse probability-weighted estimators are widely used in applications where data are missing due to nonresponse or censoring and in the estimation of causal effects from observational studies. Current estimators rely on ignorability assumptions for response indicators or treatment assignment and outcomes being conditional on observed covariates which are assumed to be measured without error. However, measurement error is common for the variables collected in many…

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More efficient estimators for case-cohort studies

病例—队列研究的更高效估计量

The case-cohort study design, used to reduce costs in large cohort studies, is a random sample of the entire cohort, named the subcohort, augmented with subjects having the disease of interest but not in the subcohort sample. When several diseases are of interest, several case-cohort studies may be conducted using the same subcohort, with each disease analyzed separately, ignoring the additional exposure measurements collected on subjects with the other diseases. This is not…

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Robust estimation of optimal dynamic treatment regimes for sequential treatment decisions

序贯治疗决策中最优动态治疗方案的稳健估计

A dynamic treatment regime is a list of sequential decision rules for assigning treatment based on a patient's history. Q- and A-learning are two main approaches for estimating the optimal regime, i.e., that yielding the most beneficial outcome in the patient population, using data from a clinical trial or observational study. Q-learning requires postulated regression models for the outcome, while A-learning involves models for that part of the outcome regression…

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Automatic declustering of rare events

罕见事件的自动去簇

The analysis of events with low probability but disastrous impact entails understanding how they cluster in time. We present an automatic three-step procedure for identifying clusters, estimating the cluster size distribution and constructing confidence intervals for the extremal index, which measures the degree of clustering of rare events. The third step combines empirical likelihood and parametric likelihood approaches. Simulations show that our new procedure performs…

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A unified approach to robust estimation in finite population sampling

有限总体抽样中稳健估计的统一方法

We argue that the conditional bias associated with a sample unit can be a useful measure of influence in finite population sampling. We use the conditional bias to derive robust estimators that are obtained by downweighting the most influential sample units. Under the model-based approach to inference, our proposed robust estimator is closely related to the well-known estimator of Chambers (1986). Under the design-based approach, it possesses the desirable feature of being…

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Robust analysis of semiparametric renewal process models

半参数更新过程模型的稳健分析

A rate model is proposed for a modulated renewal process comprising a single long sequence, where the covariate process may not capture the dependencies in the sequence as in standard intensity models. We consider partial likelihood-based inferences under a semiparametric multiplicative rate model, which has been widely studied in the context of independent and identical data. Under an intensity model, gap times in a single long sequence may be used naively in the partial…

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Dimension reduction and predictor selection in semiparametric models

半参数模型中的降维与预测变量选择

Dimension reduction in semiparametric regressions includes construction of informative linear combinations and selection of contributing predictors. To reduce the predictor dimension in semiparametric regressions, we propose an ℓ1-minimization of sliced inverse regression with the Dantzig selector, and establish a non-asymptotic error bound for the resulting estimator. We also generalize the regularization concept to sliced inverse regression with an adaptive Dantzig…

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Survival analysis without survival data: connecting length-biased and case-control data

没有生存数据的生存分析:连接长度偏倚与病例对照数据

We show that relative mean survival parameters of a semiparametric log-linear model can be estimated using covariate data from an incident sample and a prevalent sample, even when there is no prospective follow-up to collect any survival data. Estimation is based on an induced semiparametric density ratio model for covariates from the two samples, and it shares the same structure as for a logistic regression model for case-control data. Likelihood inference coincides with…

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Large Covariance Estimation by Thresholding Principal Orthogonal Complements

主正交补阈值化方法与高维协方差估计

Summary The paper deals with the estimation of a high dimensional covariance with a conditional sparsity structure and fast diverging eigenvalues. By assuming a sparse error covariance matrix in an approximate factor model, we allow for the presence of some cross-sectional correlation even after taking out common but unobservable factors. We introduce the principal orthogonal complement thresholding method ‘POET’ to explore such an approximate factor structure with sparsity.…

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Smoothing Parameter Selection in two Frameworks for Penalized Splines

惩罚样条两种框架下的平滑参数选择

Summary There are two popular smoothing parameter selection methods for spline smoothing. First, smoothing parameters can be estimated by minimizing criteria that approximate the average mean-squared error of the regression function estimator. Second, the maximum likelihood paradigm can be employed, under the assumption that the regression function is a realization of some stochastic process. The asymptotic properties of both smoothing parameter estimators for penalized…

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Asymptotics of the Discrete Log-Concave Maximum Likelihood Estimator and Related Applications

离散对数凹最大似然估计的渐近理论及应用

Summary The assumption of log-concavity is a flexible and appealing non-parametric shape constraint in distribution modelling. In this work, we study the log-concave maximum likelihood estimator of a probability mass function. We show that the maximum likelihood estimator is strongly consistent and we derive its pointwise asymptotic theory under both the well-specified and misspecified settings. Our asymptotic results are used to calculate confidence intervals for the true…

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Probabilistic Causality and Detecting Collections of Interdependence Patterns

概率因果性与相互依赖模式集合的检测

Summary Interdependent effects are usually distinguished from statistical interaction by using the sufficient causes framework. This almost always involves expressing probability distributions as deterministic logic functions, where certain conditions invariably produce or prevent an outcome. Using an idea from the philosophy literature, that a cause is defined as an event which increases the probability of an outcome, a probabilistic sufficient causes framework is developed…

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Semiparametric estimation in triangular system equations with nonstationarity

含非平稳性的三角方程系统半参数估计

A system of multivariate semiparametric nonlinear time series models is studied with possible dependence structures and nonstationarities in the parametric and nonparametric components. The parametric regressors may be endogenous while the nonparametric regressors are assumed to be strictly exogenous. The parametric regressors may be stationary or nonstationary and the nonparametric regressors are nonstationary integrated time series. Semiparametric least squares (SLS)…

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What model for entry in first-price auctions? A nonparametric approach

第一价格拍卖应采用何种进入模型?一种非参数方法

We develop a selective entry model for first-price auctions that nests two polar models often estimated in the empirical literature on auctions, Levin and Smith (1994), and Samuelson (1985). The selective entry model features a pro-competitive selection effect. The selection effect is shown to be nonparametrically identifiable, and a nonparametric test for its presence is proposed. This test can be used to discriminate between the two polar models.

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Testing for a break in trend when the order of integration is unknown

积分阶数未知时的趋势突变检验

Harvey, Leybourne and Taylor [Harvey, D.I., Leybourne, S.J., Taylor, A.M.R. 2009. Simple, robust and powerful tests of the breaking trend hypothesis. Econometric Theory 25, 995–1029] develop a test for the presence of a broken linear trend at an unknown point in the sample whose size is asymptotically robust as to whether the (unknown) order of integration of the data is either zero or one. This test is not size controlled, however, when this order assumes fractional values;…

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Principal components estimation and identification of static factors

静态因子的主成分估计与识别

It is known that the principal component estimates of the factors and the loadings are rotations of the underlying latent factors and loadings. We study conditions under which the latent factors can be estimated asymptotically without rotation. We derive the limiting distributions for the estimated factors and factor loadings when N and T are large and make precise how identification of the factors affects inference based on factor augmented regressions. We also consider…

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The dark side of analyst coverage: The case of innovation

分析师覆盖的负面影响:企业创新的证据

We examine the effects of financial analysts on the real economy in the case of innovation. Our baseline results show that firms covered by a larger number of analysts generate fewer patents and patents with lower impact. To establish causality, we use a difference-in-differences approach that relies on the variation generated by multiple exogenous shocks to analyst coverage, as well as an instrumental variable approach. Our identification strategies suggest a negative…

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Using Secondary Outcomes to Sharpen Inference in Randomized Experiments With Noncompliance

利用次要结局改进存在不依从的随机实验推断

We develop new methods for analyzing randomized experiments with noncompliance and, by extension, instrumental variable settings, when the often controversial, but key, exclusion restriction assumption is violated. We show how existing large-sample bounds on intention-to-treat effects for the subpopulations of compliers, never-takers, and always-takers can be tightened by exploiting the joint distribution of the outcome of interest and a secondary outcome, for which the…

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Wavelet-Variance-Based Estimation for Composite Stochastic Processes

基于小波方差的复合随机过程参数估计

This article presents a new estimation method for the parameters of a time series model. We consider here composite Gaussian processes that are the sum of independent Gaussian processes which, in turn, explain an important aspect of the time series, as is the case in engineering and natural sciences. The proposed estimation method offers an alternative to classical estimation based on the likelihood, that is straightforward to implement and often the only feasible estimation…

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Nonparametric Mixture of Regression Models

非参数有限混合回归模型

Motivated by an analysis of US house price index data, we propose nonparametric finite mixture of regression models. We study the identifiability issue of the proposed models, and develop an estimation procedure by employing kernel regression. We further systematically study the sampling properties of the proposed estimators, and establish their asymptotic normality. A modified EM algorithm is proposed to carry out the estimation procedure. We show that our algorithm…

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