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Analysis of Binary Data from a Multicentre Clinical Trial

多中心临床试验的二元数据分析

We develop several methods for estimating the treatment effect difference defined as the overall log-odds ratio of favourable response in a multicentre clinical trial comparing two treatments with binary response. A simulation study compares the bias and mean squared error of the point estimates and the exact coverage probabilities of confidence intervals obtained distributions.

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An Efficient Semiparametric Estimator for Binary Response Models

二元响应模型的有效半参数估计量

This paper proposes an estimator for discrete choice models that makes no assumption concerning the functional form of th e choice probability function where this function can be characterized by an index. The estimator is shown to be consistent, asymptotically normally distributed, and to achieve the semiparametric efficiency bound. Monte Carlo evidence indicates that there may be only modest efficiency losses relative to maximum likelihood estimation when the distribution…

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The Assumptions on Which Causal Inferences Rest

因果推断所依赖的假设

SUMMARY Statisticians commonly make causal inferences from the results of randomized experiments, but usually question causal inferences from observational studies on the grounds that untestable assumptions are required. This paper explains the basis for this situation and examines, within quite a general framework, various assumptions that appear in the literature. It is demonstrated how the role of each assumption is intimately related to the sort of causal inference being…

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The Limiting Distribution of the Maximum Rank Correlation Estimator

最大秩相关估计量的极限分布

Han's maximum rank correlation estimator is shown to be square-root n-consistent and asymptotically normal. The proof rests on a general method for determining the asymptotic distribution of a maximization estimator, a simple U-statistic decomposition, and a uniform bound for degenerate U-processes. A consistent estimator of the asymptotic covariance matrix is provided, along with a result giving the explicit form of this matrix for any model within the scope of the maximum…

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Seminonparametric Estimation of Binary-Choice Models With an Application to Labor-Force Participation

二元选择模型的半非参数估计及其劳动参与应用

The authors adapt the estimation method proposed by A. R. Gallant and D. N. Nychka (1987) to binary-choice models. They present Monte Carlo and asymptotic comparisons with the probit estimator and discuss optimization algorithms, choice of starting values, and strategies f or choosing the number of parameters used in approximating the density. Seminonparametric estimation is almost as efficient as probit estimation in normal samples and performs better in nonnormal sample s.…

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Optimal Rates of Convergence of Parameter Estimators in the Binary Response Model with Weak Distributional Assumptions

弱分布假设下二元响应模型参数估计的最优收敛速度

The smoothed maximum score estimator of the coefficient vector of a binary response model is consistent and, after centering and suitable normalization, asymptotically normally distributed under weak assumptions [5]. Its rate of convergence in probability is N − h /(2 h +1) , where h ≥ 2 is an integer whose value depends on the strength of certain smoothness assumptions. This rate of convergence is faster than that of the maximum score estimator of Manski [11,12], which…

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Likelihood analysis for probit regression with measurement errors

含测量误差的 probit 回归似然分析

Likelihood analysis is proposed for a probit regression model when one of the explanatory variables is measured with error and replicate measurements of that variable are available on some of the subjects. The distribution of the measurement error and of the unknown explanatory variable, conditional on the known variables, are both taken to be normal. The maximum likelihood estimates can be computed exactly with the EM algorithm. Likelihood ratio tests and confidence…

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Using surrogate failure time data to increase cost effectiveness in clinical trials

利用替代失效时间数据提高临床试验的成本效益

In clinical trials with failure time, outcomes, the cost of follow-up for the endpoint of primary interest is sometimes expensive. In many of these settings, one or more secondary or surrogate failure time outcomes are also available which either occur much earlier or are much less expensive to follow than the primary outcome. This paper presents a method for using these secondary outcomes to increase the power of detecting a treatment effect on the primary outcome only,…

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A proportional odds model with subject-specific effects for repeated ordered categorical responses

含个体特定效应的重复有序类别响应比例优势模型

Suppose subjects make repeated responses on the same ordered categorical scale. We propose a generalization of the Rasch model that expresses the cumulative logit of the response distribution using subject parameters and a proportional odds structure for item effects. Parameters in the model describe subject-specific, rather than population averaged, effects. Consistent estimation of the effects requires eliminating the subject parameters. We accomplish this by simultaneous…

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Goodness-of-fit tests in two-state processes

两状态过程的拟合优度检验

Binary data in which successive outcomes may be dependent frequently arise in a medical and social sciences context. A simple model for such data is a homogeneous 2-state Markov chain. Under this model one would usually treat the first observation in each sequence, Y1, as fixed. In the case of panel data this may constitute a substantial loss of information. In this paper we propose goodness-of-fit tests for the 2-state Markov model under several likely alternative…

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A kernel method for estimating finite population distribution functions using auxiliary information

利用辅助信息估计有限总体分布函数的核方法

This paper considers the use of auxiliary information to improve the estimation of the distribution function of a finite population. A method is proposed which combines the known distribution of the auxiliary variable with a kernel estimate of the conditional distribution of the survey variable given the value of the auxiliary variable. The resulting estimator compares favourably with existing estimators in terms of efficiency, conditional behaviour and robustness. The…

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A likelihood-based method for analysing longitudinal binary responses

纵向二元响应的似然分析方法

In this paper, we discuss a likelihood-based method for analysing correlated binary responses based on a multivariate model. It is related to the pseudo-maximum likelihood approach suggested recently by Zhao & Prentice (1990). Their parameterization results in a simple pairwise model, in which the association between responses is modelled in terms of correlations, while the present paper uses conditional log odds-ratios. With this approach, higher-order associations can be…

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Analysis of binary data from a multicentre clinical trial

多中心临床试验二元数据的分析

We develop several methods for estimating the treatment effect difference defined as the overall log-odds ratio of favourable response in a multicentre clinical trial comparing two treatments with binary response. A simulation study compares the bias and mean squared error of the point estimates and the exact coverage probabilities of confidence intervals obtained distributions.

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Estimating Conditional Quantiles at the Root of a Regression Function

回归函数根处的条件分位数估计

The Robbins-Monro process $X_{n+1} = X_n - c_n Y_n$ is a standard stochastic approximation method for estimating the root $\theta$ of an unknown regression function. There is a vast literature on the convergence properties of $X_n$ to $\theta$. In practice, one is also interested in the conditional distribution of the system under the sequential control when the control is set at $\theta$ or near $\theta$. This problem appears to have received no attention in the literature.…

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Linear Regression Analysis for Multivariate Failure Time Observations

多元失效时间观测的线性回归分析

In this article we consider the case that each patient in a longitudinal study may experience two or more distinct failures. The corresponding failure times, which are possible censored, are recorded for each patient. The logarithm of each marginal failure time is assumed to be linearly related to its covariates; however, the distributional form of the error term in the model does not have to be specified in the analysis. Furthermore, no specific structure of dependence…

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Estimation Using Multiyear Rotation Design Sampling in Agricultural Surveys

农业调查中利用多年轮换抽样设计进行估计

In the annual June Enumerative Surveys (JES) of the U.S. Department of Agriculture (USDA), the area frame sampling involves multiyear rotation designs with 20% replacement of sample units each year. Currently, USDA uses the latest year sample data almost exclusively in its estimation procedure. We propose that the multiyear sample survey data should be used for estimation of crop acreages and livestock. We develop a multiyear estimation method based on an analysis of…

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Estimating the Proportion of Immunes in a Censored Sample

An estimator for the proportion of ‘immunes’ in a population is proposed, when a sample of censored failure times is available. Our suggestion is to use one minus the maximum observed value of the Kaplan-Meier empirical distribution function. This estimator is shown to be consistent and asymptotically normal, under modest conditions on the censoring mechanism. Simulations suggest that the estimator is approximately normal for quite small sample sizes, provided the immune…

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On Efficiency of Methods of Simulated Moments and Maximum Simulated Likelihood Estimation of Discrete Response Models

离散响应模型中模拟矩与最大模拟似然估计的效率

This article considers methods of simulated moments for estimation of discrete response models. It is possible to use the same set of random numbers to simulate the choice probabilities for each individual in the sample. In addition to the method of simulated moments of McFadden, we have considered also maximum simulated likelihood estimation methods. An asymptotic theory for such procedures is provided. The estimators are shown to be consistent and asymptotically normal by…

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Simultaneous Density Estimation of Several Income Distributions

多个收入分布的同时密度估计

The size distributions of net income in Great Britain changed systematically in the 1970s. This can be shown by visual comparison of nonparametric density estimates. Typical bandwidth selection methods, such as least squares and biased cross-validation, tend to hinder comparison, because of too much variability across curves. Hence, a method for finding an appropriate pooled bandwidth is developed. It is seen that this method is much more reliable than single curve…

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Engel's Law and Cointegration

恩格尔定律与协整

A time-series counterpart of Engel's law is that the expenditure share on food declines as the economy grows. The main purpose of this paper is to test whether Houthakker's addilog utility function can simultaneously explain this time-series observation and cross-sectional observations concerning Engel's law. Masao Ogaki and Joon Y. Park's cointegration approach is used to estimate parameters of the utility function from time-series data. Total expenditure elasticities…

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Estimation Under Profit-Driven Loss Functions

利润导向损失函数下的估计

Consider the problem of estimating a price-sensitivity parameter in a demand model. Depending on the context in which the estimate will be used, traditional squared-error loss may be inappropriate. The authors consider the situation in which the estimate will be used by a manufacturer to set the price. Effectively, the manufacturer's goal of profit maximization induces a loss function that turns out to be asymmetric. Estimates that perform well with respect to such loss…

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