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线性回归中多重不等式与等式约束的精确检验AI 解读

In this article we consider the linear regression model y = Xβ + ε, where ε is N(0, σ2I). In this context we derive exact tests of the form H: Rβ ≥ r versus K: β ∈ RK for the case in which θ2 is unknown. We extend these results to consider hypothesis tests of the form H: R1β ≥ r1 and R2β = r2 versus K: (β ∈ RK . For each of these hypotheses tests we derive several equivalent forms of the test statistics using the duality theory of the quadratic programming. For both tests we…

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整数参数模型的统一处理AI 解读

It is shown that there is an analog to the score function (the derivative of the log-likelihood with respect to the parameter), here called the difference score, which plays an important theoretical role in integer parameter models. A unified treatment of integer parameter models can be obtained by recognizing that many commonly used models have a linear difference score (LDS). It is established that many of the exact results available for exponential family models also hold…

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同期季节调整AI 解读

Concurrent seasonal adjustment uses all information up to and including the current month's figure and thus should provide more accurate estimates of final seasonally adjusted data than the prevalent official method where the current month's component is forecasted from data through the preceding December. This article evaluates the expected gain from employing concurrent seasonal adjustment, including the case in which the data contain both nonseasonal and seasonal…

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随机微分方程：入门及应用AI 解读

Some Mathematical Preliminaries.- Ito Integrals.- The Ito Formula and the Martingale Representation Theorem.- Stochastic Differential Equations.- The Filtering Problem.- Diffusions: Basic Properties.- Other Topics in Diffusion Theory.- Applications to Boundary Value Problems.- Application to Optimal Stopping.- Application to Stochastic Control.- Application to Mathematical Finance.

概率与随机变量AI 解读

Probability Conditional probability and independence Random variables Continuous distributions Distribution function Functions of random variables Bivariate distributions Expectation of a random variable Variance of a random variable Moment generating functions Moments of bivariate distributions Probability generating functions Sums of random variables Unbiased estimators Sampling finite populations Generating random variables.

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简单随机抽样下比率估计的条件化调整AI 解读

The usual ratio estimates for a population mean use information on an auxiliary variable to improve the estimation. The standard randomization analysis, however, does not take enough account of the observations on the auxiliary variable, so estimates and estimated variates can be conditionally biased unless the sample is balanced with respect to the auxiliary variable. I propose a method of adjustment for the bias of the estimate and its variance based only on the assumption…

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整数参数模型的统一处理AI 解读

It is shown that there is an analog to the score function (the derivative of the log-likelihood with respect to the parameter), here called the difference score, which plays an important theoretical role in integer parameter models. A unified treatment of integer parameter models can be obtained by recognizing that many commonly used models have a linear difference score (LDS). It is established that many of the exact results available for exponential family models also hold…

同期季节调整AI 解读

Concurrent seasonal adjustment uses all information up to and including the current month's figure and thus should provide more accurate estimates of final seasonally adjusted data than the prevalent official method where the current month's component is forecasted from data through the preceding December. This article evaluates the expected gain from employing concurrent seasonal adjustment, including the case in which the data contain both nonseasonal and seasonal…

用水调查日记记录分析中的贝叶斯方法应用AI 解读

One of the objectives of a comprehensive domestic water use study conducted in Perth, Western Australia, was the quantification of components of water usage. Each household in a sample of about 3,000 was asked to record all water uses in a specially provided diary for a 2-week period, and the total water usage, both in-house and ex-house, was metered daily during this time. This article describes an application of Bayesian methodology to the estimation of usage for each…

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频域中位数时间序列AI 解读

This article discusses the median of a batch of time series. We focus on the frequency-domain median (FDM) series (Zeger 1985), which is calculated from the “mediancenters” (Gower 1974) of the discrete Fourier transforms. Like the univariate median, it has a breakdown value of 50%. Like the mean, the FDM time series of independent realizations from a stationary Gaussian process has a spectrum proportional to that of the component series. Analogs of the univariate median have…

随机删失数据两样本问题的组合秩检验AI 解读

In the two-sample problem under random censorship we consider the uncensored observations and the censored ones as two separate groups. For each group a suitable rank statistic is obtained, and these two are then combined to a final one. This idea, which was first employed in Akritas (1983), is shown here to produce tests that (a) closely resemble the ordinary rank tests for the uncensored case and do not require the calculation of the Kaplan-Meier estimator, (b) are…

加权秩检验的效率与最优性结果AI 解读

The Tukey–Quade method of weighted rankings for the analysis of complete blocks is considered. Assuming only that the within-block error components are exchangeable, the limiting distribution of a large class of test statistics based on this method is obtained under the null hypothesis and under nearby alternatives as the number of blocks increases to infinity. This makes it possible to derive the asymptotic efficiency of the allied tests relative to the maximin most…

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