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Testing for a unit root in the presence of moving average errors

移动平均误差下的单位根检验

In this paper we propose a new approach to testing for unit roots in a time series {yt} with moving average innovations based on an instrumental variable estimator. If {yt} is a random walk with moving average innovations, we derive the limiting distribution of the instrumental variable estimator when the estimated model is either (i) the true model, (ii) a random walk with shift in mean, or (iii) a random walk with shift in mean and a linear time trend. These distributions…

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Mixtures of Distributions: A Topological Approach

Identifiability problems have previously precluded a general approach to testing the hypothesis of a "pure" distribution against the alternative of a mixture of distributions. Three types of identifiability are defined, and it is shown that $B$-identifiability allows a Bayesian solution to the testing problem. First, an equivalence relation is defined over parametrizations of probability functions. Then the projection onto the quotient space is shown to give a $B$-identifiabl…

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Rank-Based Tests for Randomness against First-Order Serial Dependence

针对一阶序列依赖的随机性秩检验

Optimal rank-based procedures were derived in Hallin, Ingenbleek, and Puri (1985, 1987) and Hallin and Puri (1988) for some fundamental testing problems arising in time series analysis. The optimality properties of these procedures are of an asymptotic nature, however, whereas much of the attractiveness of rank-based methods lies in their small-sample applicability and robustness features. Accordingly, the objective of this article is twofold: (a) a study of the…

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The Effect of Truncation on the Identifiability of Regression Coefficients

截断对回归系数可识别性的影响

When data are truncated and hence partly unobservable, parameters identifiable under the complete observation may not be identifiable. A class of distributions is characterized, under which regression coefficients are unidentifiable by truncation of a dependent variable in the regression model. In a class of strongly unimodal densities regression coefficients are shown to be unidentifiable only when the underlying distribution is proportional to the exponential distribution…

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Rank-Based Tests for Randomness Against First-Order Serial Dependence

针对一阶序列依赖的基于秩的随机性检验

Optimal rank-based procedures were derived in Hallin, Ingenbleek, and Puri (1985, 1987) and Hallin and Puri (1988) for some fundamental testing problems arising in time series analysis. The optimality properties of these procedures are of an asymptotic nature, however, whereas much of the attractiveness of rank-based methods lies in their small-sample applicability and robustness features. Accordingly, the objective of this article is twofold: (a) a study of the…

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Limit Theorems for Stochastic Processes.

随机过程的极限定理

I. The General Theory of Stochastic Processes, Semimartingales and Stochastic Integrals.- II. Characteristics of Semimartingales and Processes with Independent Increments.- III. Martingale Problems and Changes of Measures.- IV. Hellinger Processes, Absolute Continuity and Singularity of Measures.- V. Contiguity, Entire Separation, Convergence in Variation.- VI. Skorokhod Topology and Convergence of Processes.- VII. Convergence of Processes with Independent Increments.- VIII.…

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On the Use of Covariates for Rodent Bioassay and Screening Experiments

啮齿动物生物测定与筛查实验中的协变量使用

Consider a three-state compartmental model with an initial, an absorbing and an intermediate state which may or may not be entered before absorption. Observable data are time to absorption and an indication of whether the intermediate state was entered, but not the time of transition. The transition rates characterizing the process are nonidentifiable without simplifying assumptions or additional information on the prevalence function, defined as the time specific proportion…

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Asymptotic Normality, When Regressors Have a Unit Root

回归变量具有单位根时的渐近正态性

Under fairly general conditions, ordinary least squares and linear instrumental variables estimators are asymptotically normal when a regression equation has nonstationary right hand side variables. Standard formulas may be used to calculate a consistent estimate of the asymptotic variance-covariance matrix of the estimated parameter vector, even if the disturbances are conditionally heteroskedastic and autocorrelated. So inference may proceed in the usual way. The key…

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Estimating Vector Autoregressions with Panel Data

利用面板数据估计向量自回归模型

This paper considers estimation and testing of vector autoregressio n coefficients in panel data, and applies the techniques to analyze the dynamic relationships between wages an d hours worked in two samples of American males. The model allows for nonstationary individual effects and is estimated by applying instrumental variables to the quasi-differenced autoregressive equations. The empirical results suggest the absence of lagged hours in the wage forecasting equation.…

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Disclosure Risk and Disclosure Avoidance for Microdata

Under given concrete exogenous conditions, the fraction of identifiable records in a microdata file without positive identifiers such as name and address is estimated. The effect of possible noise in the data, as well as the sample property of microdata files, is taken into account. Using real microdata files, it is shown that there is no risk of disclosure if the information content of characteristics known to the investigator (additional knowledge) is limited. Files with…

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Identification of Nonzero Elements in the Polynomial Matrices of Mixed Varma Processes

混合VARMA过程多项式矩阵中非零元素的识别

S. G. Koreisha, T. M. Pukkila; Identification of Nonzero Elements in the Polynomial Matrices of Mixed Varma Processes, Journal of the Royal Statistical Soc

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Large Sample Theory of Empirical Distributions in Biased Sampling Models

有偏抽样模型中经验分布的大样本理论

Vardi (1985a) introduced an $s$-sample model for biased sampling, gave conditions which guarantee the existence and uniqueness of the nonparametric maximum likelihood estimator $\mathbb{G}_n$ of the common underlying distribution $G$ and discussed numerical methods for calculating the estimator. Here we examine the large sample behavior of the NPMLE $\mathbb{G}_n$, including results on uniform consistency of $\mathbb{G}_n$, convergence of $\sqrt n (\mathbb{G}_n - G)$ to a…

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Identification of Binary Response Models

二元反应模型的识别

This article studies identification of the threshold-crossing model of binary response. Most research on binary response has considered specific estimators and tests. The study of identification exposes the foundations of binary response analysis by making explicit the assumptions needed to justify different methods. It also clarifies the connections between reduced-form and structural analyses of binary response data. Assume that the binary outcome z is determined by an…

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A Model for Ex Ante Real Interest Rates and Derived Inflation Forecasts

事前实际利率模型及其导出的通胀预测

A methodology for estimating expected real interest rates and making inflation forecasts, together with appropriate confidence intervals, is presented. The role of price expectations in determining real interest rates is also analyzed. Structural breaks in the process generating real interest rates are detected in 1980 and 1983 by tracking the accuracy of interest-rate forecasts. Analysis of these structural breaks reveals that the break at the beginning of 1983 returns the…

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Nonparametric Analysis of Truncated Survival Data, with Application to AIDS

截断生存数据的非参数分析及其艾滋病应用

One source of data for the induction distribution of aids arises from persons infected by the aids virus from contaminated blood transfusions. Analyses of these data are complicated because the number of individuals infected by transfusion is unknown; information is available only for those who are infected and develop aids within a certain chronologic time interval. The statistical problem is one of making inferences about a stochastic process of infection and disease for…

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Higher-Order Approximations to the Null Distributions of Test Statistics for Nonlinear Restrictions on Regression Coefficients

回归系数非线性约束检验统计量零假设分布的高阶近似

Asymptotic expansions of the distributions of likelihood ratio and Lagrange multiplier test statistics for nonlinear restrictions on regression coefficients are derived under the null hypothesis. Nonlinear restrictions include, as a special case, the identifiability restrictions in the simultaneous equations models. Our analyses of simultaneous equations deal not only with single equations but also subsystems and complete systems. The asymptotic expansions we derive are…

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Root-N-Consistent Semiparametric Regression

根号 N 一致的半参数回归

One type of semiparametric regression is b8X A u(Z), where b and u(Z) are an unknown slope coefficient vector and function. Estimates of b based on incorrect parametrization of u are generally inconsist ent, whereas consistent nonparametric estimates converge slowly. An e stimate, bC, is constructed by inserting nonpar-ametric regression es timates in the nonlinear orthogonal projection on Z. Under regularity conditions bC is shown to be N1/2-consistent for b and…

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The Asymptotic Normal Distribution of Estimators in Factor Analysis under General Conditions

一般条件下因子分析估计量的渐近正态分布

Asymptotic properties of estimators for the confirmatory factor analysis model are discussed. The model is identified by restrictions on the elements of the factor loading matrix; the number of restrictions may exceed that required for identification. It is shown that a particular centering of the maximum likelihood estimator derived under assumed normality of observations yields an asymptotic normal distribution that is common to a wide class of distributions of the factor…

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A Comparison of Estimates of Natural Mortality from Fish Tagging Experiments

鱼类标记实验中自然死亡率估计方法的比较

Tagging experiments in which recaptures have to be made by professional fishermen are considered. The methods put forward are shown to be maximum likelihood solutions, and expressions are derived for the variances of the estimators. Optimal conditions for the experiment are found, and cases of questionable behaviour are identified.

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Estimation of a Single Structural Equation with Structural Change

存在结构变化时单个结构方程的估计

Estimation of a single structural equation when there exists structural change is considered. Equality of structural variances in different samples is shown to affect the identification condition and asymptotic efficiency of best asymptotically normal estimators when the reduced-form covariance matrices differ by the structural change. The limited information maximum likelihood estimator is presented with its asymptotic property and compared with an alternative estimator.

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