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1.
《统计学通讯:模拟与计算》2013,42(3):773-785
Summary The concepts of D-, A- and E-minimax optimality criteria of designs for estimating the slopes of a response surface are considered for situations where the region of interest may not be identical to the experimental region. Optimal second-order designs are derived for the situation where the experimental region and the region of interest are both hyperspherical with a common centre. The dependence of the optimal design on the relative sizes of the regions is investigated. Further, the perfomance of designs optimal for one region in estimating slopes in other regions is also examined. 相似文献
2.
Response surface methodology is widely used for developing, improving, and optimizing processes in various fields. In this article, we present a method for constructing three-level designs in order to explore and optimize response surfaces combining orthogonal arrays and covering arrays in a particular manner. The produced designs achieve the properties of rotatability, predictive performance and efficiency for the estimation of a second-order model. 相似文献
3.
This article considers the second-order response surface model in which the experimental units, i.e., plots experience the neighbor effects from immediate left and right neighboring plots assuming the plots to be placed adjacent linearly with no gaps. Conditions have been derived for the estimation of coefficients of second-order response surface model. A method of constructing designs for fitting second-order response surface in the presence of neighbor effects has been developed. The designs so obtained are found to be rotatable. 相似文献
4.
Edwin Choi & Peter Hall 《Journal of the Royal Statistical Society. Series B, Statistical methodology》2000,62(2):461-477
Given a linear time series, e.g. an autoregression of infinite order, we may construct a finite order approximation and use that as the basis for confidence regions. The sieve or autoregressive bootstrap, as this method is often called, is generally seen as a competitor with the better-understood block bootstrap approach. However, in the present paper we argue that, for linear time series, the sieve bootstrap has significantly better performance than blocking methods and offers a wider range of opportunities. In particular, since it does not corrupt second-order properties then it may be used in a double-bootstrap form, with the second bootstrap application being employed to calibrate a basic percentile method confidence interval. This approach confers second-order accuracy without the need to estimate variance. That offers substantial benefits, since variances of statistics based on time series can be difficult to estimate reliably, and—partly because of the relatively small amount of information contained in a dependent process—are notorious for causing problems when used to Studentize. Other advantages of the sieve bootstrap include considerably greater robustness against variations in the choice of the tuning parameter, here equal to the autoregressive order, and the fact that, in contradistinction to the case of the block bootstrap, the percentile t version of the sieve bootstrap may be based on the 'raw' estimator of standard error. In the process of establishing these properties we show that the sieve bootstrap is second order correct. 相似文献
5.
ABSTRACTA quantile autoregresive model is a useful extension of classical autoregresive models as it can capture the influences of conditioning variables on the location, scale, and shape of the response distribution. However, at the extreme tails, standard quantile autoregression estimator is often unstable due to data sparsity. In this article, assuming quantile autoregresive models, we develop a new estimator for extreme conditional quantiles of time series data based on extreme value theory. We build the connection between the second-order conditions for the autoregression coefficients and for the conditional quantile functions, and establish the asymptotic properties of the proposed estimator. The finite sample performance of the proposed method is illustrated through a simulation study and the analysis of U.S. retail gasoline price. 相似文献
6.
《随机性模型》2013,29(3):381-389
Abstract Self-similarity in discrete second-order stationary processes is defined as a fixed point of a renormalisation operator consisting of aggregation normalised by the variance, rather than by the traditional power-law factor. This broader definition reveals a new class of self-similar processes. 相似文献
7.
Nitis Mukhopadhyay Tumulesh K. S. Solanky 《Journal of statistical planning and inference》2002,100(2):209-220
We consider the problem of constructing a set of fixed-width simultaneous confidence intervals for the treatment-control differences of means for several independent normal populations with a common unknown variance. Taking c observations from the control population instead of the usual vector-at-a-time approach, purely sequential estimation methodology is developed and asymptotic second-order characteristics are provided. Brief remarks on the accelerated sequential and three-stage methodologies have been added. Next, with the help of simulations, performances of the purely sequential, accelerated sequential and three-stage estimation techniques are compared. Overall, the second-order asymptotics are found to provide useful approximations even for moderate sample sizes. 相似文献
8.
Sharma (1977) and Aggarwal et al. (2006) considered non circular construction of first- and second-order balanced repeated measurements designs. Sharma et al. (2002) constructed circular first- and second-order balanced repeated measurements designs only for a class with parameters (v, p = 3n, n = v 2) and also showed its universal optimality. In this article, we consider circular construction of first- and second-order balanced repeated measurements designs and strongly balanced repeated measurements designs by using the method of cyclic shifts. Some new circular designs with parameters (v, p, n) for cases p = v, p < v and p > v are given. 相似文献
9.
In this article, we propose the local linear estimators of the drift coefficient and diffusion coefficient in the second-order jump-diffusion model. We also show the consistency and asymptotic normality of these estimators under mild conditions. 相似文献
10.
Fan Yang 《统计学通讯:理论与方法》2013,42(3):520-532
The tail distortion risk measure at level p was first introduced in Zhu and Li (2012), where the parameter p ∈ (0, 1) indicates the confidence level. They established first-order asymptotics for this risk measure, as p↑1, for the Fréchet case. In this article, we extend their work by establishing both first-order and second-order asymptotics for the Fréchet, Weibull, and Gumbel cases. Numerical studies are also carried out to examine the accuracy of both asymptotics. 相似文献