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对齐秩次过程的两端固定维纳过程近似及应用AI 解读

For independent random variables distributed symmetrically around an unknown location parameter, aligned rank order statistics are constructed by using an estimator of the location parameter based on suitable rank statistics. The sequence of these aligned rank order statistics is then incorporated in the construction of suitable stochastic processes which converge weakly to some Gaussian functions, and, in particular, to tied-down Wiener processes in the most typical cases.…

检测时间序列模型参数变化的序贯程序AI 解读

Procedures are proposed for monitoring forecast errors in order to detect changes in a time-series model. These procedures are based on likelihood ratio statistics which consist of cumulative sums. An extension of Page's method is presented which tests for changes in the parameter values of autoregressive integrated moving average (arima) models. The distributional properties of the statistics are approximated under the assumption that the series follows an integrated…

观测序列位置参数突变的检验AI 解读

A possible alternative to the hypothesis that the sequence X 1, X 2, …, Xn are iid N(ξ, σ2) random variables is that at some unknown instant the expectation ξ shifts. The likelihood ratio test for the alternative of a location shift is studied and its distribution under the null hypothesis found. Tables of standard fractiles are given, along with asymptotic results.

检验回归系数稳定性的两种方法AI 解读

This paper investigates the power of two methodologies, the tests of Brown, Durbin, and Evans [2] and variable parameter regression, to detect several varieties of instability in the coefficients of a linear regression model. The study reported by Khan [10] on the stability of the demand for money is replicated with variable parameter regression, and his results are in part questioned and in part sharpened.

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利用汇总数据估计时变马尔可夫过程AI 解读

The exact stochastic character of observed data from a Markov process is derived for the case where only aggregate stocks, as opposed to individual transitions, are observed. Particular attention is devoted to the distinction between data generated by a panel study, where a single group of individuals is followed over time, and that generated by random sampling, where the observed groups are not identical over time. Several alternative estimators are developed which take…

回归中检测结构变化或异常值的若干“最优”方法AI 解读

A Neyman-Pearson approach is taken to the problem of detecting structural shifts in naturally ordered regression problems. When the variance is known, backwards CUSUM methods are shown to maximize average power, and their application is discussed. Two methods with optimality properties for outlier detection are developed, assuming that the observations may be divided into two parts, where the first part satisfies the model assumptions, while outliers may be present in the…

荒野地区游憩使用量的计量经济分析AI 解读

Although outdoor recreational use fluctuates daily, this time-varying feature has received little attention by economists and statisticians. In this paper, wilderness recreational use relationships are estimated, based on daily observations over the length of a given season, by (i) traditional econometric techniques and via (ii) time series analysis procedures promoted by Box and Jenkins [3]. In applying both sets of estimated relationships for forecasting purposes, the…

荒野地区游憩使用的计量经济分析AI 解读

Although outdoor recreational use fluctuates daily, this time-varying feature has received little attention by economists and statisticians. In this paper, wilderness recreational use relationships are estimated, based on daily observations over the length of a given season, by (i) traditional econometric techniques and via (ii) time series analysis procedures promoted by Box and Jenkins [3]. In applying both sets of estimated relationships for forecasting purposes, the…

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关于“随机变量序列变点推断的贝叶斯方法”的文献提示AI 解读

The author's attention has been drawn to a similar approach: BROEMELING, L. D. (1974). Bayesian inferences about a changing sequence of random variables. Comm. Statist. 3, 243–55.

切换回归与随机系数回归模型的贝叶斯及非贝叶斯分析AI 解读

Quandt [20] analyzed the problem of discontinuous shifts in regression regimes at unknown points in the data series. We note that Quandt's statistical approach based solely on the likelihood function can be misleading, whereas the Bayesian method based on a proper prior distribution of the unknown parameters yields sensible results. However, the exact evaluation of the posterior distribution is unusually burdensome and cannot be simplified even in large samples. To avoid…

随机变量序列变点推断的贝叶斯方法AI 解读

A Bayesian approach is considered to the problem of making inferences about the point in a sequence of random variables at which the underlying distribution changes. Inferences are based on the posterior probabilities of the possible change-points. Detailed analyses are given for cases in which the distributions are binomial and normal, and numerical illustrations are provided. An informal sequential procedure is also noted.

参考值与估计方差对CUSUM检验平均运行长度的影响AI 解读

Summary An approximation, based on the Wiener process, is applied to Page's cusum statistic. Based on the average run length, the optimal reference value is determined analytically and shown to agree with results from studies using numerically determined run lengths. Next, we study the effect of using an estimate for variance and how this interacts with the choice of a reference value.

检验回归关系随时间保持稳定的方法AI 解读

Summary Methods for studying the stability over time of regression relationships are considered. Recursive residuals, defined to be uncorrelated with zero means and constant variance, are introduced and tests based on the cusum and cusum of squares of recursive residuals are developed. Further techniques based on moving regressions, in which the regression model is fitted from a segment of data which is moved along the series, and on regression models whose coefficients are…

检测均值变化的检验AI 解读

Procedures are considered for testing whether the means of each variable in a sequence of independent random variables can be taken to be the same, against alternatives that a shift might have occurred after some point $r$. Bayesian test statistics as well as some statistics depending on estimates of $r$ are presented and their powers compared. Exact and asymptotic distribution functions are derived for some of the Bayesian statistics.

未知时点的参数变化检验及相关布朗运动泛函的分布AI 解读

Statistics are derived for testing a sequence of observations from an exponential-type distribution for no change in parameter against possible two-sided alternatives involving parameter changes at unknown points. The test statistic can be chosen to have high power against certain of a variety of alternatives. Conditions on functionals on $C\lbrack 0,1\rbrack$ are given under which one can assert that the large sample distribution of the test statistic under the…

推断与排队问题中的 Wiener–Hopf 积分方程AI 解读

The solution is presented to an integral equation of Wiener-Hopf type which has been recently treated numerically by Hinkley in connexion with the problem of inference about the change-point in a sequence of random variables. The closed form solution given here enables results to be obtained easily in situations where the numerical method fails. A similar integral equation arises in a queueing problem where the difference between inter-arrival and service time of a customer…

异方差下 Chow 检验的使用AI 解读

the assumption of equality of variances of error terms between two separate sample regimes. It is shown that the test is well behaved when there are variations of variances if at least one of two sample sizes is very large. However, if two samples are of small size, even moderate heteroscedasticity has considerable effect on the level of significance of the test. In what follows, it is assumed that T1 samples belong to the first regime and T2 samples to the second regime;…

推断与排队问题中的一个 Wiener–Hopf 积分方程AI 解读

The solution is presented to an integral equation of Wiener-Hopf type which has been recently treated numerically by Hinkley in connexion with the problem of inference about the change-point in a sequence of random variables. The closed form solution given here enables results to be obtained easily in situations where the numerical method fails. A similar integral equation arises in a queueing problem where the difference between inter-arrival and service time of a customer…

使用三次样条的分段回归AI 解读

Spline theory and piecewise regression theory are integrated to provide a framework in which structural change is viewed as occurring in a smooth fashion. Specifically, structural change occurs at given points through jump discontinuities in the third derivative of a continuous piecewise cubic estimating function. Testing procedures are developed for detecting structural change as well as linear or quadratic segments. Finally, the techniques developed are illustrated…

传递函数时间依赖性的若干检验AI 解读

In studies of linear open loop systems, the assumption of time invariance is often tacitly made. In this paper we exploit a convenient frequency-domain approach to furnish tests for the time dependence of a transfer function, which is the most crucial notion in the case of linear systems. An extension of Tukey's test for nonadditivity is given in § 4. The proposed tests are illustrated numerically with both simulated and real data.

切换回归估计的一种新方法AI 解读

In recent years much attention has been focussed on the problem of discontinuous shifts in regression regimes at unknown points in the data series. This article approaches this problem by assuming that nature chooses between regimes with probabilities λ and 1 — λ. This allows formulation of the appropriate likelihood function maximized with respect to the parameters in the regression equations and λ. The method is compared to another recent procedure in some sampling…

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