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Bayesian Methods: An Analysis for Statisticians and Interdisciplinary Researchers

贝叶斯方法:面向统计学家与跨学科研究者的分析

1. Introductory statistical concepts 2. The discrete version of Bayes' theorem 3. Models with a single unknown parameter 4. The expected utility hypothesis and its alternatives 5. Models with several unknown parameters 6. Prior structures, posterior smoothing, and Bayes-Stein estimation Guide to worked examples Guide to self-study exercises.

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Two-Sample Multistate Accelerated Sojourn Times Model

两样本多状态加速停留时间模型

Many medical studies involve observations of patients experiencing multiple consecutive states during their follow-up. Since treatments may have differential effects on these states, comparison is of interest with respect to individual sojourn times. In this article I generalize the univariate accelerated failure time model for multistate processes and model the treatment effects as state-specific time scale changes. I propose a two-sample inference procedure that…

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Asymptotic Behavior of Linear Permutation Tests under General Alternatives, with Application to Test Selection and Study Design

一般备择下线性置换检验的渐近行为及其检验选择与研究设计应用

Tests based on the permutation of observations are a common and attractive method of comparing two groups of outcomes, in part because they retain proper test size with minimal assumptions and can have high efficiency toward specific alternatives of interest. In addition, permutation tests may be used with discrete or categorical outcomes, for which linear rank tests are not designed. Permutation tests are now increasingly used to analyze discrete or continuous responses…

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Risk Assessment via a Robust Probit Model, with Application to Toxicology

稳健 Probit 风险评估模型及其毒理学应用

Various frameworks have been suggested for assessing the risk associated with continuous toxicity outcomes. The first formulates the effect of exposure on the adverse effect via a simple normal model and then computes the risk function using tail probabilities from the standard normal distribution. Because this risk function depends heavily on the assumed model, it may be sensitive to model misspecification. Recently, a semiparametric approach that utilizes an alternative…

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A Bayesian Approach to Combining Information from a Census, a Coverage Measurement Survey, and Demographic Analysis

融合人口普查、覆盖测量调查与人口学分析的贝叶斯方法

Demographic analysis of data on births, deaths, and migration and coverage measurement surveys that use capture-recapture methods have both been used to assess U.S. Census counts. These approaches have established that unadjusted Census counts are seriously flawed for groups such as young and middle-aged African-American men. There is considerable interest in methods that combine information from the Census, coverage measurement surveys, and demographic information to…

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Modelling Stock Market Volatility: Bridging the Gap to Continuous Time

股票市场波动率建模:连接离散时间与连续时间

Understanding And Specifying The Discrete Time Model: D.B. Nelson, Modelling Stock Market Volatility Changes. D.B. Nelson, Stationarity and Persistence in the GARCH(I,I) Model. D.B. Nelson, Conditional Heteroskedasticity in Asset Returns: A New Approach. P.A. Braun, D.B. Nelson and A.M. Sunier, Good News, Bad News, Volatility, and Betas. Continuous Time Limits And Optimal Filtering For ARCH Models: D.B. Nelson, ARCH Models as Diffusion Approximations. D.B. Nelson, Filtering…

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THE POWER OF SINGLE EQUATION TESTS FOR COINTEGRATION WHEN THE COINTEGRATING VECTOR IS PRESPECIFIED

预先指定协整向量时单方程协整检验的功效

In this paper I present an alternative derivation of the asymptotic distribution of Kremers, Ericsson, and Dolado's (1992, Oxford Bulletin of Economics and Statistics 54, 325–348) conditional error correction model (ECM)–based t -test for cointegration with a single prespecified cointegrating vector. This alternative distribution, which is identical to the distribution of Hansen's (1995, Econometric Theory 11, 1148–1171) covariate augmented t -test for a unit root, is valid…

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TESTING FOR THE COINTEGRATING RANK OF A VAR PROCESS WITH AN INTERCEPT

含截距 VAR 过程的协整秩检验

Testing the cointegrating rank of a vector autoregressive process with an intercept is considered. In addition to the likelihood ratio (LR) tests developed by Johansen and Juselius (1990, Oxford Bulletin of Economics and Statistics , 52, 169–210) and others we also consider an alternative class of tests that is based on estimating the trend parameters of the deterministic term in a different way. The asymptotic local power of these tests is derived and compared to that of…

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ESTIMATING TRENDING VARIABLES IN THE PRESENCE OF FRACTIONALLY INTEGRATED ERRORS

分数单整误差下趋势变量的估计

This paper considers the problems of estimation and inference in the linear regression model with fractionally integrated errors. The ordinary least squares (OLS) and the first differenced (FD) estimators are studied. Relative to the OLS estimators, a substantial increase in the convergence rates of the coefficient estimator for the stochastic regressor can be achieved by the FD estimators when the error term is nonstationary. However, the preceding decisive results can not…

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LINEARIZATION OF RANDOMLY WEIGHTED EMPIRICALS UNDER LONG RANGE DEPENDENCE WITH APPLICATIONS TO NONLINEAR REGRESSION QUANTILES

长程依赖下随机加权经验过程的线性化及非线性回归分位数应用

This paper discusses some asymptotic uniform linearity results of randomly weighted empirical processes based on long range dependent random variables. These results are subsequently used to linearize nonlinear regression quantiles in a nonlinear regression model with long range dependent errors, where the design variables can be either random or nonrandom. These, in turn, yield the limiting behavior of the nonlinear regression quantiles. As a corollary, we obtain the…

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Behaviour of the standard and symmetric Dickey-Fuller-type tests when there is a break under the null hypothesis

We examine the behaviour of tests of the unit root null hypothesis when the true generating model is I (1) with a break. Asymptotic distributional results are derived predicting that the standard Dickey–Fuller test will in that case yield frequent rejections of the null for relatively early breaks. This phenomenon is most severe for lowest values of the break fraction under a break in level, and for a break in slope occurring about 15% of the way through the series. However,…

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Estimation of a monotone mean residual life

单调平均剩余寿命的估计

In survival analysis and in the analysis of life tables an important biometric function of interest is the life expectancy at age $x, M(x)$, defined by $$M(x) = E[X - x|X > x],$$ where $X$ is a lifetime. $M$ is called the mean residual life function.In many applications it is reasonable to assume that $M$ is decreasing (DMRL) or increasing (IMRL); we write decreasing (increasing) for nonincreasing (non-decreasing). There is some literature on empirical estimators of $M$ and…

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On the asymptotics of constrained local $M$-estimators

约束局部 M 估计量的渐近性质

We discuss in this paper asymptotics of locally optimal solutions of maximum likelihood and,more generally, $M$-estimation procedures in cases where the true value of the parameter vector lies on the boundary of the parameter set $S$.We give a counterexample showing that regularity of $S$ in the sense of Clarke is not sufficient for asymptotic equivalence of $\sqrt{n}$-consistent locally optimal $M$-estimators.We argue further that stronger properties, such as so-called near…

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Sequential testing problems for Poisson processes

泊松过程的序贯检验问题

We present the explicit solution of the Bayesian problem of sequential testing of two simple hypotheses about the intensity of an observed Poisson process. The method of proof consists of reducing the initial problem to a free-boundary differential-difference Stephan problem and solving the latter by use of the principles of smooth and continuous fit. A rigorous proof of the optimality of the Wald’s sequential probability ratio test in the variational formulation of the…

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Two estimators of the mean of a counting process with panel count data

面板计数数据下计数过程均值的两种估计量

We study two estimators of the mean function of a countingprocess based on “panel count data.” The setting for “panel count data” is one in which $n$ independent subjects, each with a counting process with common mean function, are observed at several possibly different times duringa study. Following a model proposed by Schick and Yu, we allow the number of observation times, and the observation times themselves, to be random variables. Our goal is to estimate the mean…

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Finite sample nonparametric inference and large sample efficiency

有限样本非参数推断与大样本效率

Given a sample $X_1,\dots, X_n$ from a distribution $F$, the problem of constructing nonparametric confidence intervals for the mean $\mu(F)$ is considered. Unlike bootstrap procedures or those based on normal approximations, we insist on any procedure being truly nonparametric in the sense that the probability that the confidence interval contains $\mu(F)$ based on a sample of size $n$ from $F$ be at least $1 - \alpha$ for all $F$ and all $n$. Bahadur and Savage proved it…

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Sample Splitting and Threshold Estimation

样本划分与门槛估计

Threshold models have a wide variety of applications in economics. Direct applications include models of separating and multiple equilibria. Other applications include empirical sample splitting when the sample split is based on a continuously-distributed variable such as firm size. In addition, threshold models may be used as a parsimonious strategy for nonparametric function estimation. For example, the threshold autoregressive model (TAR) is popular in the nonlinear time…

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On an empirical Bayes test for a normal mean

正态均值的经验贝叶斯检验

We exhibit an empirical Bayes test $\delta_n^*$ for the normal mean testing problem using a linear error loss. Under the condition that the critical point of a Bayes test is within some known compact interval, $\delta_n^*$ is shown to be asymptotically optimal and its associated regret Bayes risk converges to zero at a rate $O(n^{-1}(\ln n)^{1.5})$, where $n$ is the number of past experiences available when the current component decision problem is considered. Under the same…

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