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带迁入分枝过程的序贯估计AI 解读

For the critical and subcritical Galton-Watson processes with immigration, it is shown that if the data were collected according to an appropriate stopping rule, the natural sequential estimator of the offspring mean $m$ is asymptotically normally distributed for each fixed $m \in (0, 1\rbrack.$ Furthermore, the sequential estimator is shown to be asymptotically normally distributed uniformly over a class of offspring distributions with $m \in (0, 1\rbrack$ bounded variance…

不稳定一阶自回归过程的自助法AI 解读

Consider a first-order autoregressive process $X_t = \beta X_{t - 1} + \varepsilon_t$, where $\{\varepsilon_t\}$ are independent and identically distributed random errors with mean 0 and variance 1. It is shown that when $\beta = 1$ the standard bootstrap least squares estimate of $\beta$ is asymptotically invalid, even if the error distribution is assumed to be normal. The conditional limit distribution of the bootstrap estimate at $\beta = 1$ is shown to converge to a…

爆炸性自回归过程的 BootstrapAI 解读

Asymptotic validity of the bootstrap is established for the least squares estimate of the parameter of an explosive first-order autoregressive process. It is noted that nonnormal limit distributions are obtained for both the traditional and the bootstrap estimates. The theoretical bootstrap validity results are supported by appropriate simulation.

自相关误差回归模型的大样本推断AI 解读

Based on intermittent observations from several independent regression models with autocorrelated errors, we derive tests of homogeneity, and the maximum likelihood estimate of the common regression parameter. The estimate for the regression parameter is based on aggregated data in the form of sample means at each time point. The limit distributions of the test statistics, and the estimate are considered.

自相关误差回归模型的大样本推断AI 解读

SUMMARY Based on intermittent observations from several independent regression models with autocorrelated errors, we derive tests of homogeneity, and the maximum likelihood estimate of the common regression parameter. The estimate for the regression parameter is based on aggregated data in the form of sample means at each time point. The limit distributions of the test statistics, and the estimate are considered. Basawa, Billard & Srinivasan (1984) discussed testing the…

非平稳过程预测误差的渐近分布及相关拟合检验AI 解读

Limit distributions of prediction errors when the parameters are estimated are obtained for a general class of nonstationary processes that includes supercritical branching processes and explosive autoregressive processes as typical examples. The estimated prediction errors are used to construct new tests of fit whose limit distributions are also derived.

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时间序列的稳健检验及其在一阶自回归过程中的应用AI 解读

Robust analogues of the Wald and the Rao score statistics are presented for testing composite hypotheses in time series models involving dependent observations. Asymptotic efficiency and empirical power comparisons using moderate size samples are given for first-order autoregressive processes. Our method of robustifying the estimating equation gives a simple and unified approach which is useful in a large class of problems including regression with dependent errors, and…

时间序列模型同质性的大样本检验AI 解读

Limit distributions both under the null and a sequence of alternative hypotheses are derived for the likelihood ratio and related statistics for testing the homogeneity of several autoregressive processes. These results are extended to mixed autoregressive and moving average processes.

正则非遍历模型的渐近条件推断及其自回归应用AI 解读

A conditional limit theorem is derived for a certain class of stochastic processes whose distributions constitute a nonergodic family. The limit theorem allows us to study the asymptotic behaviour under the conditional model of some standard statistical procedures by making use of results for ergodic families. Explosive Gaussian autoregressive processes are studied in some detail. Here the conditional process is shown to be a nonexplosive Gaussian autoregression bearing a…

时间序列模型同质性的大样本检验AI 解读

Limit distributions both under the null and a sequence of alternative hypotheses are derived for the likelihood ratio and related statistics for testing the homogeneity of several autoregressive processes. These results are extended to mixed autoregressive and moving average processes.

非递减 Lévy 过程的非参数估计AI 解读

Summary Three non-parametric estimates of the measure corresponding to a non-decreasing Lévy process are discussed. Consistency and the limit distributions of the estimates are studied. The empirical process corresponding to one of the estimates is briefly discussed with an anticipation of an application to goodness-of-fit tests.

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混合试验的有效条件检验及其在出生与分枝过程中的应用AI 解读

Conditional tests, which are efficient in the sense of being uniformly most powerful unbiased for any sample size and are also asymptotically efficient with reference to a relevant likelihood in the sense of maximizing asymptotic power at alternatives converging to the null hypothesis, are derived for mixture experiments involving dependent observations. As simple applications efficient tests in birth processes, branching processes, stable additive processes, etc. are…

指数族混合模型中条件最大似然估计与置信限的效率AI 解读

In a previous paper (Basawa, 1981) efficient conditional tests were discussed for mixture experiments involving dependent observations. The present paper is devoted to a study of the performance, in large samples, of a conditional maximum likelihood estimator and of a confidence limit for a parameter in a model specified by a mixture of a two-parameter exponential family. The conditional estimator proposed in the paper is free from the mixing distribution, and is efficient…

Conditional tests, which are efficient in the sense of being uniformly most powerful unbiased for any sample size and are also asymptotically efficient with reference to a relevant likelihood in the sense of maximizing asymptotic power at alternatives converging to the null hypothesis, are derived for mixture experiments involving dependent observations. As simple applications efficient tests in birth processes, branching processes, stable additive processes, etc. are…

伽马过程与稳定过程参数估计的一则札记AI 解读

Maximum likelihood estimators of the parameters of nondecreasing pure-jump gamma and stable processes based on the jumps of size greater than or equal to ε were studied in a previous paper (Basawa & Brockwell, 1978). In particular, for a single realization {X( u ), 0 ≤ u ≤ t }, the estimators for the stable process are consistent as ε ↓ 0, but this is not so for the gamma process. In the present note we derive asymptotic distributions as ε ↓ 0 for these estimators, centred…

关于伽马过程与稳定过程估计的一个注记AI 解读

Maximum likelihood estimators of the parameters of nondecreasing pure-jump gamma and stable processes based on the jumps of size greater than or equal to ε were studied in a previous paper (Basawa & Brockwell, 1978). In particular, for a single realization {X( u ), 0 ≤ u ≤ t }, the estimators for the stable process are consistent as ε ↓ 0, but this is not so for the gamma process. In the present note we derive asymptotic distributions as ε ↓ 0 for these estimators, centred…

Gamma 与稳定过程的统计推断AI 解读

Problems of estimation and testing for nondecreasing pure jump gamma and stable additive processes are considered. The inference is based on a single realization of the process on a given time interval [0,t]. The maximum likelihood estimators of the parameters based on observation of the jumps of size greater than or equal to ε are found to be consistent as ε tends to 0 for the stable process but not for the gamma process.

伽马过程与稳定过程的统计推断AI 解读

Problems of estimation and testing for nondecreasing pure jump gamma and stable additive processes are considered. The inference is based on a single realization of the process on a given time interval [0,t]. The maximum likelihood estimators of the parameters based on observation of the jumps of size greater than or equal to ε are found to be consistent as ε tends to 0 for the stable process but not for the gamma process.

分枝过程的有效检验AI 解读

This paper is concerned with efficiency in testing for the mean of the offspring distribution of a supercritical Galton-Watson process. It is suggested that the maximum likelihood estimator is generally inefficient for this problem in the sense that asymptotically it is not an optimum discriminator between alternative values of the parameter. Three competing tests are discussed and their efficiency compared via an example.

简单马尔可夫链自相关系数的估计AI 解读

Four estimates of the autocorrelation in simple Markov chains are given and their asymptotic normality established. Exact moment generating functions of two of the estimates are obtained. These estimates are compared with the maximum likelihood estimate.

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