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半正态图最大值的渐近理论AI 解读

We study approximations to the distribution of the largest Walsh-Fourier coefficient obtained by transforming i.i.d. observations from a non-normal parent distribution. The study is inspired by the use of half-normal plots in screening studies and in the analysis of molecular sequence data. In the latter context, we indicate why continuity corrections are needed.

线性过程自相关的序贯估计AI 解读

This paper considers sequential point estimation of the autocorrelations of stationary linear processes within the framework of the sequential procedure initiated by Robbins. The sequential estimator proposed here is based on the usual sample autocorrelations and is shown to be risk efficient in the sense of Starr as the cost per observation approaches zero. To achieve the asymptotic risk efficiency, we are led to study the uniform integrability and random central limit…

规模依赖序贯搜索的最优停止AI 解读

In many areas of application, one searches within finite populations for items of interest, where the probability of sampling an item is proportional to a random size attribute from an i.i.d. superpopulation of attributes which may or may not be observable upon discovery. Here we treat the problem of asymptotically optimal stopping rules for size-dependent searches of this type, as the size of the underlying population grows, where the loss function includes an…

满足误报概率界的分布变化检测动态抽样策略AI 解读

We show that if dynamic sampling is feasible, then there exist surveillance schemes that satisfy a probability constraint on false alarm. Procedures are suggested for detecting a change of a normal mean from 0 to a (unknown) positive value. These procedures are optimal (up to a constant term) when the post-change mean is known, and almost optimal [up to an $o(\log(1/\alpha))$ term when the post-change mean is unknown.

稀疏概率表的贝叶斯模型AI 解读

We wish to make inferences about the conditional probabilities $p(y|x)$, many of which are zero, when the distribution of X is unknown and one observes only a multinomial sample of the Y variates. To do this, fixed likelihood ratio models and quasi-incremental distributions are defined. It is shown that quasi-incremental distributions are intimately linked to decomposable graphs and that these graphs can guide us to transformations of X and Y which admit a conjugate Bayesian…

有理函数模型的最优实验设计AI 解读

In this paper, experimental designs for a rational model, $Y = P(x)/Q(x) + \varepsilon$, are investigated, where $P(x) = \theta_0 + \theta_1 x + \dots + \theta_p x^p$ and $Q(x) = 1 + \theta_{p + 1} x + \dots + \theta_{p+q} x^q$ are polynomials and $\varepsilon$ is a random error. Two approaches, Bayesian D-optimal and Bayesian optimal design for extrapolation, are examined. The first criterion maximizes the expected increase in Shannon information provided by the experiment…

部分指定异方差结构模型的最优贝叶斯设计AI 解读

We consider the problem of finding a nonsequential optimal design for estimating parameters in a generalized exponential growth model. This problem is solved by first considering polynomial regression models with error variances that depend on the covariate value and unknown parameters. A Bayesian approach is adopted, and optimal Bayesian designs supported on a minimal number of support points for estimating the coefficients in the polynomial model are found analytically.…

处理—对照设计的可容许性与最优性AI 解读

The relationship between admissible incomplete block designs for confidence intervals with maximal coverage probability for treatment-control contrasts and optimal designs for estimation is investigated. For certain types of designs, admissible designs are shown to be precisely those with the number of replications of the control less than or equal to that of an optimal design. Moreover, admissible designs are the Bayes optimal designs for a class of priors.

论拉丁超立方抽样AI 解读

This paper contains a collection of results on Latin hypercube sampling. The first result is a Berry-Esseen-type bound for the multivariate central limit theorem of the sample mean $\hat{\mu}_n$ based on a Latin hypercube sample. The second establishes sufficient conditions on the convergence rate in the strong law for $\hat{\mu}_n$. Finally motivated by the concept of empirical likelihood, a way of constructing nonparametric confidence regions based on Latin hypercube…

空间抽样方案下的最大似然估计AI 解读

It is shown that the maximum likelihood estimator in a model used in the statistical analysis of computer experiments is asymptotically efficient.

锥序关联、随机锥排序及其在序约束检验中的应用AI 解读

Cohen, Sackrowitz and Samuel-Cahn introduced the notion of cone order association and established a necessary and sufficient condition for a normal random vector to be cone order associated (COA). In this paper we provide the following: (1) a necessary and sufficient condition for a multinomial distribution to be COA when the cone is a pairwise contrast cone; (2) a relationship between COA and regular association; (3) a notion of stochastic cone ordering (SCO) of random…

数据驱动 Neyman 均匀性检验的渐近最优性AI 解读

Data-driven Neyman's tests resulting from a combination of eyman' smooth tests for uniformity and Schwarz's selection procedure are nvestigated. Asymptotic intermediate efficiency of those tests with respect to the Neyman-Pearson test is shown to be 1 for a large set of converging alternatives. The result shows that data-driven Neyman's tests, contrary to classical goodness-of-it tests, are indeed omnibus tests adapting well to the data at hand.

离散线性系统的盲反卷积AI 解读

We study the blind deconvolution problem in the case where the input noise has a finite discrete support and the transfer linear system is not necessarily minimum phase. We propose a new family of estimators built using algebraic considerations. The estimates are consistent under very wide assumptions: The input signal need not be independently distributed; the cardinality of the finite support may be estimated simultaneously. We consider in particular AR systems: In this…

时间序列比值统计量的频域自助法AI 解读

The asymptotic properties of the bootstrap in the frequency domain based on Studentized periodogram ordinates are studied. It is proved that this bootstrap approximation is valid for ratio statistics such as autocorrelations. By using Edgeworth expansions it is shown that the bootstrap approximation even outperforms the normal approximation. The results carry over to Whittle estimates. In a simulation study the behavior of the bootstrap is studied for empirical correlations…

平稳观测下分块自助法的二阶正确性AI 解读

We show that the blockwise bootstrap approximation for the distribution of a studentized statistic computed from dependent data is second-order correct provided we choose an appropriate variance estimator. We also show how to adapt the $BC_a$ confidence interval of Efron to the a dependent case. For the proofs we extend the results of Götze and Hipp on the validity of the formal Edgeworth expansion for a sum to the studentized mean.

无限方差分数 ARIMA 模型的参数估计AI 解读

Consider the fractional ARIMA time series with innovations that have infinite variance. This is a finite parameter model which exhibits both long-range dependence (long memory) and high variability. We prove the consistency of an estimator of the unknown parameters which is based on the periodogram and derive its asymptotic distribution. This shows that the results of Mikosch, Gadrich, Klüppelberg and Adler for ARMA time series remain valid for fractional ARIMA with…

规则序列采样设计的渐近最优性AI 解读

We study linear estimators for the weighted integral of a stochastic process. The process may only be observed on a finite sampling design. The error is defined in a mean square sense, and the process is assumed to satisfy Sacks-Ylvisaker regularity conditions of order $r \epsilon \mathbb{N}_0$. We show that sampling at the quantiles of a particular density already yields asymptotically optimal estimators. Hereby we extend the results of Sacks and Ylvisaker for regularity $r = 0$…

Ritov 贝叶斯方法与 CUSUM 极小极大性质的连续时间札记AI 解读

We consider, in a Bayesian framework, the model $W_t = B_t + \theta (t - \nu)^+$, where B is a standard Brownian motion, $\theta$ is arbitrary but known and $\nu$ is the unknown change-point. We transfer the construction of Ritov to this continuous time setup and show that the corresponding Bayes problems can be reduced to generalized parking problems.

双参数指数族分布中的预设比例精度估计AI 解读

We propose a sequential procedure for estimating with prescribed proportional accuracy one parameter in a class of two-parameter exponential family of distributions. We study the properties of the resulting stopping time and provide second-order analysis of the coverage probability associated with it by using Edgeworth expansion.

双侧删失数据的自洽估计与极大似然估计算法AI 解读

The paper investigates the structure of the self-consistent estimators (SCE) and the nonparametric maximum likelihood estimator (NPMLE) for doubly censored data. An explicit sufficient and necessary condition for an SCE to be the NPMLE is given. Based on this, algorithms for computing the SCE and the NPMLE are provided. The relation between our algorithms and the EM algorithm is studied.

平均剩余寿命过程AI 解读

Yang and Hall and Wellner initiated investigations of the asymptotic uniform behaviour of mean residual life (MRL) processes. They obtained results holding true over fixed and expanding compact subintervals of $[0, \infty)$. In this exposition we study MRL processes over the whole positive half-line $[0, \infty)$. We describe classes of weight functions which enable us to establish the (a) strong uniform-over-$[0, \infty)$ consistency and (b)weak uniform-over-$[0, \infty)$ ap…

序约束下生存曲线非参数估计的渐近理论AI 解读

We consider two problems in nonparametric survival analysis under the restriction of stochastic ordering. The first problem is that of estimating a survival function $\overline{F}(t)$ under the restriction $\overline{F}(t) \geq $\overline{F}_0 (t)$, all t, where $\overline{F}_0 (t)$ is known. The second problem consists of estimating two unknown survival functions $\overline{F}^{(1)}(t)$ and $\overline{F}^{(2)}(t)$ when it is known that $\overline{F}^{(1)}(t) \geq…

利用非参数回归估计变点AI 解读

We consider a regression model in which the mean function may have a discontinuity at an unknown point. We propose an estimate of the location of the discontinuity based on one-side nonparametric regression estimates of the mean function. The change point estimate is shown to converge in probability at rate $O(n^{-1})$ and to have the same asymptotic distribution as maximum likelihood estimates considered by other authors under parametric regression models. Confidence…

图像分析与非参数回归中中位数平滑器的渐近表现AI 解读

For d-dimensional images and regression functions the true object is estimated by median smoothing. The mean square error of the median smoother is calculated using the framework of M-estimation, and an expression for the asymptotic rate of convergence of the mean square error is given. It is shown that the median smoother performs asymptotically as well as the local mean. The optimal window size and the bandwidth of the median smoother are given in terms of the sample size…