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简单随机传染病模型感染率极大似然估计的近似AI 解读

Hill & Severo (1969) and Kryscio (1972) present approximations to the maximum likelihood estimator of the infection rate of the simple stochastic epidemic model. These approximations, valid under some restrictions on the data set, use a table published by Hill & Severo (1969). We give here an algebraically simpler approximation, which does not use an auxiliary table and may be applied to all data sets.

鱼类标记实验中自然死亡率估计方法的比较AI 解读

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.

The paper presents general second-order approximate formulae for the Fisher information of asymptotically normal statistics, and applies the formulae to a stationary time-series model as well as to an econometric simultaneous equation model. Also the second-order conditional information is evaluated for the exponential family and the location family. Conditioned on a second-order ancillary statistic, the second-order information loss of the maximum likelihood estimate is…

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分类面板数据中的不可忽略无回答：劳动力总流量估计AI 解读

Many large-scale sample surveys use panel designs under which sampled individuals are interviewed several times before being dropped from the sample. The longitudinal data bases available from such surveys could be used to provide estimates of gross change over time. One problem in using these data to estimate gross change is how to handle the period-to-period nonresponse. This nonresponse is typically nonrandom and, furthermore, may be nonignorable in that it cannot be…

联立回归方程系统参数的最大似然估计AI 解读

Procedures for computing the full information maximum likelihood (FIML) estimates of the parameters of a system of simultaneous regression equations have been described by Koopmans, Rubin, and Leipnik, Chernoff and Divinsky, Brown, and Eisenpress. However, all of these methods are rather complicated since they are based on estimating equations that are expressed in an inconvenient form. In this paper, a transformation of the maximum likelihood (ML) equations is developed…

异频存量与流量数据下连续时间 ARMAX 模型的高斯似然AI 解读

For purposes of maximum likelihood estimation, we show how to compute the Gaussian likelihood function when the data are generated by a higher-order continuous-time vector ARMAX model and are observed as stocks and flows at different frequencies. Continuous-time ARMAX models are analogous to discrete-time autoregressive moving-average models with distributed-lag exogenous variables. Stocks are variables observed at points in time and flows are variables observed as integrals…

存在结构变化时单个结构方程的估计AI 解读

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.

参数维数趋于无穷时指数族似然方法的渐近行为AI 解读

Consider a sample of size $n$ from a regular exponential family in $p_n$ dimensions. Let $\hat\theta_n$ denote the maximum likelihood estimator, and consider the case where $p_n$ tends to infinity with $n$ and where $\{\theta_n\}$ is a sequence of parameter values in $R^{p_n}$. Moment conditions are provided under which $\|\hat\theta_n - \theta_n\| = O_p(\sqrt{p_n/n})$ and $\|\hat\theta_n - \theta_n - \overline{X}_n\| = O_p (p_n/n)$, where $\overline{X}_n$ is the sample…

对协方差及其逆矩阵均为线性的协方差假设AI 解读

It is proved in this paper that covariance hypotheses which are linear in both the covariance and the inverse covariance are products of models each of which consists of either (i) independent identically distributed random vectors which have a covariance with a real, complex or quaternion structure or (ii) independent identically distributed random vectors with a parametrization of the covariance which is given by means of the Clifford algebra. The models (i) are well…

非线性函数关系的估计AI 解读

Estimation of the parameters of the nonlinear functional model with known error covariance matrix is discussed. Asymptotic properties of the maximum likelihood estimator for the implicit functional model are presented. The approximate bias in the maximum likelihood estimator due to the nonlinearity of the relationship is given and a bias-adjusted estimator is suggested. Numerical and theoretical results support the superiority of the bias-adjusted estimator relative to the…

地震学与神经生理学随机过程数据的若干统计方法AI 解读

Examples are presented of statistical techniques for the analysis of random process data and of their uses in the substantive fields of seismology and neurophysiology. The problems addressed include frequency estimation for decaying cosinusoids, signal estimation, association measurement, causal connection assessment, estimation of speed and direction and structural modeling. The techniques employed include complex demodulation, nonlinear regression, probit analysis,…

Pearson型拟合优度检验：单变量情形AI 解读

Chi-squared tests are proposed for testing goodness of fit when the data may or may not be subject to random censoring. Both the simple and compositive null hypotheses are considered. For the simple null hypothesis the resulting test statistic in the uncensored case differs from Pearson's statistic only in that the expected frequency for cell Aj is taken to be , where is the empirical distribution function, instead of n ∫ A j d F o ; this results in k df instead of the usual…

针对中心混合备择的同质性检验AI 解读

A test of homogeneity is derived for a general sampling model. The alternative hypothesis is a mixture over a parameter of the sampling model, centered at the null hypothesis. The test statistic is derived through a score test. Its functional form is independent of the particular mixing distribution. Suppose Yi (i = 1, …, n) are independent random variables with respective probability density (or mass) functions fi (yi ‖ λi). Under the null hypothesis, suppose all λ i…

经典与现代回归及其应用AI 解读

The author emphasizes applications with examples that illustrate nearly all the techniques discussed. Applications have been selected from physical sciences, engineering, biology, management science and economics. Emphasis is also placed on concepts with a blend between illustrations using real data sets and mathematical and conceptual development. Expanded coverage includes: simultaneous influence, maximum likelihood estimation of parameters, and the plotting of residuals,…

有限封闭总体规模精确最大似然估计的说明AI 解读

Using data obtained by the general capture-recapture sequential sampling process, an analytical expression for the maximum likelihood estimate of the population size is introduced. It is shown that the bounded likelihood functions have at most two maxima. For the simple one-to-one case the estimate is unique.

非标准条件下非正则广义极大似然估计的渐近行为AI 解读

In this paper we generalize Huber's (1967) results to include the nonregular case. Resistant estimators which turn out to be asymptotically unbiased in a neighbourhood of the model are given for some univariate models. Their order of consistency achieves the rate of the maximum likelihood estimates. Moreover, some of the estimates are asymptotically efficient under the central model, in the sense that they have the same asymptotic distribution as the maximum likelihood…

区间删失数据线性回归模型中最大似然估计存在性的一个注记AI 解读

SUMMARY For a class of linear regression models with interval-censored data, including the exponential regression model as a special case, a necessary and sufficient condition is given for the existence of the maximum likelihood estimator (MLE). The condition is especially simple to check for simple linear regression. This result is useful for comparing the small sample properties of MLEs from different special cases of interval-censored data.

污染数据的二元回归模型AI 解读

SUMMARY The nature of outliers in the context of binary regression data is discussed. Resistant fitting procedures produce estimated regression coefficients which are numerically larger than maximum likelihood, implying the need for a shrinkage-type correction. A simple model which allows for a small number of the binary responses being misrecorded is proposed, and associated techniques for robust estimation and diagnostics developed.

连续空间过程的参数估计与模型辨识AI 解读

SUMMARY Formal parameter estimation and model identification procedures for continuous domain spatial processes are introduced. The processes are assumed to be adequately described by a linear model with residuals that follow a second-order stationary Gaussian random field and data are assumed to consist of noisy observations of the process at arbitrary sampling locations. A general class of two-dimensional rational spectral density functions with elliptic contours is used…

By replacing the unknown random factors of factor analysis with observed macroeconomic variables, the arbitrage pricing theory (APT) is recast as a multivariate nonlinear regression model with across-equation restrictions. An explicit theoretical justification for the inclusion of an arbitrary, well-diversified market index is given. Using monthly returns on 70 stocks, iterated nonlinear seemingly unrelated regression techniques are employed to obtain joint estimates of…

类间相关系数的估计AI 解读

A noniterative method for estimating the interclass correlation coefficient is derived from the technique of weighted sums of squares. The asymptotic variance of this estimator is derived under the assumption of normality. Through extensive Monte Carlo simulations, the sample variance of this estimator is found not to differ greatly from that of the maximum likelihood estimator.

位置—尺度模型中回归系数估计的一致性与效率AI 解读

The effect on estimation of regression coefficients in linear location-scale models is investigated when the error distribution is misspecified. It is shown that the maximum likelihood estimator under the incorrect model is still consistent. Its asymptotic efficiency relative to that of the maximum likelihood estimator based on the correct model is obtained and the estimation of asymptotic variances for the regression coefficient estimators is addressed.

相关二元数据的条件逻辑回归模型AI 解读

A class of conditional logistic regression models for clustered binary data is considered. This includes the polychotomous logistic model of Rosner (1984) as a special case. Properties such as the joint distribution and pairwise odds ratio are investigated. A class of easily computed estimating functions is introduced which is shown to have high efficiency compared to the computationally intensive maximum likelihood approach. An example on chronic obstructive pulmonary…