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自回归序列拟合的简化方法
Summary The set of k equations arising from the asymptotic least-squares estimation procedure for fitting the unknown parameters in kth-order autoregressive models is shown to degenerate into two subsets, each of m equations for the even case (k = 2m), or two subsets, one of m equations and one of (m + 1) equations for the odd case (k = 2m + 1).
非平稳时间序列中多项预测器与控制器的多项式投影性质
Summary Box and Jenkins (1962, 1963) introduce a practical predictor for handling non-stationary types of time series and they show it to be optimal for a particular class of stochastic processes. As a consequence the predictor can be shown to follow stochastic as well as deterministic polynomial trends in the series. The present paper sets out to evaluate the bias term in the expression for the error when applying this predictor, and shows how the bias can be reduced…
未知方差正态总体均值的序贯置信区间
Summary A modified sequential procedure is put forward for the problem of estimating the mean of a normal population by a confidence interval of prescribed width and confidence coefficient, when the population variance is unknown. Certain problems akin to the latter are discussed and wherever possible comparison is made with some results of Anscombe based on his asymptotic theory.