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利用定性约束的 bootstrap 方法降低变异性AI 解读

Parametric methods are often attractive for small to moderate samples, since, relative to nonparametric techniques, they reduce variability of a wide range of statistical procedures. However, when sample size is small there is often little empirical evidence to support a particular model, and so, while variance can be reduced, bias may be increased. In theory, smoothing can be used to reduce variability of nonparametric procedures, but the difficulty of choosing the…

自相关数据的逻辑回归及其重复测量应用AI 解读

A stochastic model is proposed for the study of the influence of time-dependent covariates on the marginal distribution of the binary response in serially correlated binary data. Markov chains are expressed in terms of transitional rather than marginal probabilities. We show how to construct the model so that the covariates relate only to the mean value of the process, independently of the association parameter. After formulating the stochastic model for a simple sequence of…

利用非参数回归检查模型AI 解读

The use of nonparametric regression is explored to check the fit of a parametric regression model. The principal aim is to check the validity of the regression curve rather than necessarily to detect outliers. A pseudo likelihood ratio test is developed to provide a global assessment of fit and simulation bands are used to indicate the nature of departures from the model. The types of data considered include discrete response variables, where standard diagnostic techniques…

非参数回归在模型检验中的应用AI 解读

The use of nonparametric regression is explored to check the fit of a parametric regression model. The principal aim is to check the validity of the regression curve rather than necessarily to detect outliers. A pseudo likelihood ratio test is developed to provide a global assessment of fit and simulation bands are used to indicate the nature of departures from the model. The types of data considered include discrete response variables, where standard diagnostic techniques…

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《自回归时间序列集合的估计与假设检验》的公式更正AI 解读

Formulae for ψ^(α) and σ^2(α) on p. 87 do not hold for all α, since they may not satisfy the constraint σ^2(α)≤ψ^(α) induced by the parameterization. Then the expressions do not give maximum likelihood estimates for given α. When the inequality fails, the maximum likelihood estimates are on the boundary of the parameter space, namely where σ2=ψ⁠. The maximum then occurs for σ^2(α)=ψ^(α) both equal to σ^2(α) given at p. 88, shortly after (7). Formula (6) still applies,…

多条自回归时间序列的估计与假设检验AI 解读

The analysis of a number of independent first-order autoregressive time series is considered in a normal theory context. A model is studied which allows for nonstation-ary and nonidentical distribution of the series caused by both fixed effect and random effect components.

多组自回归时间序列的估计与假设检验AI 解读

The analysis of a number of independent first-order autoregressive time series is considered in a normal theory context. A model is studied which allows for nonstation-ary and nonidentical distribution of the series caused by both fixed effect and random effect components.

用核方法估计分布函数与分位数的札记AI 解读

A distribution function is estimated by integrating a kernel estimator of the density. Quantiles are estimated by inverting the estimate of the distribution function. Second-order properties of both these estimators are studied.