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1.
We report on an empirical investigation of the modified rescaled adjusted range or R/S statistic that was proposed by Lo, 1991. Econometrica 59, 1279–1313, as a test for long-range dependence with good robustness properties under ‘extra’ short-range dependence. In contrast to the classical R/S statistic that uses the standard deviation S to normalize the rescaled range R, Lo's modified R/S-statistic Vq is normalized by a modified standard deviation Sq which takes into account the covariances of the first q lags, so as to discount the influence of the short-range dependence structure that might be present in the data. Depending on the value of the resulting test-statistic Vq, the null hypothesis of no long-range dependence is either rejected or accepted. By performing Monte-Carlo simulations with ‘truly’ long-range- and short-range dependent time series, we study the behavior of Vq, as a function of q, and uncover a number of serious drawbacks to using Lo's method in practice. For example, we show that as the truncation lag q increases, the test statistic Vq has a strong bias toward accepting the null hypothesis (i.e., no long-range dependence), even in ideal situations of ‘purely’ long-range dependent data.  相似文献   

2.
Let X1,X2,… be a sequence of iid random variables having a continuous distribution; by R1,R2,… denote the corresponding record values. All the distributions allowing linearity of regressions either E(Rm+k|Rm) or E(Rm|Rm+k) are identified.  相似文献   

3.
Assume that in independent two-dimensional random vectors (X11),…,(Xnn), each θi is distributed according to some unknown prior density function g. Also, given θi=θ, Xi has the conditional density function q(x−θ), x,θ(−∞,∞) (a location parameter case), or θ−1q(x/θ), x,θ(0,∞) (a scale parameter case). In each pair the first component is observable, but the second is not. After the (n+1)th pair (Xn+1n+1) is obtained, the objective is to construct an empirical Bayes (EB) estimator of θ. In this paper we derive the EB estimators of θ based on a wavelet approximation with Meyer-type wavelets. We show that these estimators provide adaptation not only in the case when g belongs to the Sobolev space H with an unknown , but also when g is supersmooth.  相似文献   

4.
Let (ψii) be independent, identically distributed pairs of zero-one random variables with (possible) dependence of ψi and φi within the pair. For n pairs, both variables are observed, but for m1 additional pairs only ψi is observed and for m2 others φi is observed. If π = Pi = 1} and π·1=Pi, the problem is to test π·1. Maximum likelihood estimates of π and π·1 are obtained via the EM algorithm. A test statistic is developed whose null distribution is asymptotically chi-square with one degree of freedom (as n and either m1 or m2 tend to infinity). If m1 = m2 = 0 the statistic reduces to that of McNemar's test; if n = 0, it is equivalent to the statistic for testing equality of two independent proportions. This test is compared with other tests by means of Pitman efficiency. Examples are presented.  相似文献   

5.
Consider predicting the integral of a diffusion process Z in a bounded interval A, based on the observations Z(t1n),…,Z(tnn), where t1n,…,tnn is a dense triangular array of points (the step of discretization tends to zero as n increases) in the bounded interval. The best linear predictor is generally not asymptotically optimal. Instead, we predict using the conditional expectation of the integral of the diffusion process, the optimal predictor in terms of minimizing the mean squared error, given the observed values of the process. We obtain that, conditioning on the observed values, the order of convergence in probability to zero of the mean squared prediction error is Op(n−2). We prove that the standardized conditional prediction error is approximately Gaussian with mean zero and unit variance, even though the underlying diffusion is generally non-Gaussian. Because the optimal predictor is hard to calculate exactly for most diffusions, we present an easily computed approximation that is asymptotically optimal. This approximation is a function of the diffusion coefficient.  相似文献   

6.
7.
This paper presents a method for assessing the sensitivity of predictions in Bayesian regression analyses. In parametric Bayesian analyses there is a family s0 of regression functions, parametrized by a finite-dimensional vector B. The family s0 is a subset of R, the set of all possible regression functions. A prior π0 on B induces a prior on R. This paper assesses sensitivity by computing bounds on the predictive probability of a fixed set K over a class of priors, Γ, induced by a class of families of regression functions, Γs, and a class of priors, Γπ. This paper is divided into three parts which (1) define Γ, (2) describe an algorithm for finding accurate bounds on predictive probabilities over Γ and (3) illustrate the method with two examples. It is found that sensitivity to the family of regression functions can be much more important than sensitivity to π0.  相似文献   

8.
Let (X, Y) be a bivariate random vector and let be the regression function of Y on X that has to be estimated from a sample of i.i.d. random vectors (X1, Y1),…,(Xn, Yn) having the same distribution as (X, Y). In the present paper it is shown that the normalized integrated squared error of a kernel estimator with data-driven bandwidth is asymptotically normally distributed.  相似文献   

9.
Likelihood ratio ordering of order statistics   总被引:1,自引:0,他引:1  
This paper provides an improvement on the work of Bapat and Kochar (1994, Linear Algebra Appl., 199, 281–291) and strengthens the literature on the likelihood ratio ordering of order statistics. For independent (but possibly nonidentically distributed) absolutely continuous random variables X1,…,Xn, it is shown under some weak conditions that
X1:nlrlrXn:n,
where lr stands for the likelihood ratio ordering and Xk:n represents the kth-order statistic.  相似文献   

10.
The determinant of a generalized Hadamard matrix over its group ring factored out by the relation ΣgεG G = 0 is shown to have certain number theoretic properties. These are exploited to prove the non-existence of many generalised Hadamard matrices for groups whose orders are divisible by 3, 5 or 7. For example the GH(15, C15), GH(15, C3) and GH(15, C5) do not exist. Also for certain n and G we find the set of determinants of the GH(n, G) matrices.  相似文献   

11.
Suppose that a Markov process X1,X2,… appears consecutively. There are two random moments of time θ1 and θ2, independent of (Xn). The distribution of the process (Xn) changes for the first time at instant θ1 and for the second time at instant θ2. Our objective is to find a stopping rule based only upon the former values of (Xn) which maximizes the probability that the moment of stopping is between θ1 and θ2. A sufficient condition is given under which an optimal stopping time is finite. The maximal probability corresponding to the optimal rule is found.  相似文献   

12.
A new approach to form multivariate difference estimator is suggested which does not require the knowledge of unknown population parameters as such. It gives minimum variance among the class of multivariate difference estimators. The performance of this estimator with respect to Des Raj's (J. Amer. Statist. Assoc. 60 (1965), 270–277) multivariate difference estimator is illustrated. Using the information on two auxiliary variates, the robustness of Des Raj's estimator yd is studied empirically. Two new estimators to estimate population mean/total are developed on the same lines as that of yd. The performance of these estimators is studied for a wide variety of populations.  相似文献   

13.
A discussion about the estimators proposed by Zhang (1999) for the true standard deviation σof a normal distribution is presented. Those estimators, called by Zhang q 1 and q 2 , are functions of the expected values of the order statistics from a standard normal distribution and they were the basis of the Q statistic used in the derivation of a new test for normality proposed by Zhang. Although the type I error and the power of the test was discussed by Zhang, no study was performed to test the reliability of q 1 and q 2 as estimators of σ. In this paper, it is shown that q 1 is a very poor estimator for σespecially when σis large. On the other hand, the estimator q 2 has a performance very similar to the well-known sample standard deviation S. When some correlation is introduced among the sample units it can be seen that the estimator q 1 is much more affected than the estimators q 2 and S.  相似文献   

14.
A partially balanced nested row-column design, referred to as PBNRC, is defined as an arrangement of v treatments in b p × q blocks for which, with the convention that p q, the information matrix for the estimation of treatment parameters is equal to that of the column component design which is itself a partially balanced incomplete block design. In this paper, previously known optimal incomplete block designs, and row-column and nested row-column designs are utilized to develop some methods of constructing optimal PBNRC designs. In particular, it is shown that an optimal group divisible PBNRC design for v = mn kn treatments in p × q blocks can be constructed whenever a balanced incomplete block design for m treatments in blocks of size k each and a group divisible PBNRC design for kn treatments in p × q blocks exist. A simple sufficient condition is given under which a group divisible PBNRC is Ψf-better for all f> 0 than the corresponding balanced nested row-column designs having binary blocks. It is also shown that the construction techniques developed particularly for group divisible designs can be generalized to obtain PBNRC designs based on rectangular association schemes.  相似文献   

15.
The lower tail dependence λL is a measure that characterizes the tendency of extreme co-movements in the lower tails of a bivariate distribution. It is invariant with respect to strictly increasing transformations of the marginal distribution and is therefore a function of the copula of the bivariate distribution. λL plays an important role in modelling aggregate financial risk with copulas. This paper introduces three non-parametric estimators for λL. They are weakly consistent under mild regularity conditions on the copula and under the assumption that the number k = k(n) of observations in the lower tail, used for estimation, is asymptotically k ≈ √n. The finite sample properties of the estimators are investigated using a Monte Carlo simulation in special cases. It turns out that these estimators are biased, where amount and sign of the bias depend on the underlying copula, on the sample size n, on k, and on the true value of λL.  相似文献   

16.
17.
This paper aims at deriving explicit transient queue length distribution for GI/M/1 system and busy period analysis of bulk queue GIb/M/1 through lattice paths (LPs) combinatorics. The general interarrival time distribution is approximated by two-phase Cox distribution, C2, that has Markovian property, enabling us to represent the processes by two-dimensional LPs. As distributions C2 cover a wide class of distributions that have rational Laplace–Stieltjes transforms (LSTs) with square coefficient of variation lying in , the results obtained are applicable to a large class of real life situations. Some numerical results for the C2b/M/1 model are also given.  相似文献   

18.
Summary.  The method of Bayesian model selection for join point regression models is developed. Given a set of K +1 join point models M 0,  M 1, …,  M K with 0, 1, …,  K join points respec-tively, the posterior distributions of the parameters and competing models M k are computed by Markov chain Monte Carlo simulations. The Bayes information criterion BIC is used to select the model M k with the smallest value of BIC as the best model. Another approach based on the Bayes factor selects the model M k with the largest posterior probability as the best model when the prior distribution of M k is discrete uniform. Both methods are applied to analyse the observed US cancer incidence rates for some selected cancer sites. The graphs of the join point models fitted to the data are produced by using the methods proposed and compared with the method of Kim and co-workers that is based on a series of permutation tests. The analyses show that the Bayes factor is sensitive to the prior specification of the variance σ 2, and that the model which is selected by BIC fits the data as well as the model that is selected by the permutation test and has the advantage of producing the posterior distribution for the join points. The Bayesian join point model and model selection method that are presented here will be integrated in the National Cancer Institute's join point software ( http://www.srab.cancer.gov/joinpoint/ ) and will be available to the public.  相似文献   

19.
In this paper, we show some results of forecasting based on the ARFIMA(p,d,q) and ARIMA(p,d,q) models. We show, by simulation, that the technique of forecasting of the ARIMA(p,d,q) model can also be used when d is fractional, i.e., for the ARFIMA(p,d,q) model. We also conduct a simulation study to compare the two estimators of d obtained through regression methods. They are used in the hypothesis test to decide whether or not the series has long memory property and are compared on the basis of their k-step ahead forecast errors. The properties of long-memory models are also investigated using an actual set of data.  相似文献   

20.
The effects of parameter estimation are examined for the well-known c-chart for attributes data. The exact run length distribution is obtained for Phase II applications, when the true average number of non-conformities, c, is unknown, by conditioning on the observed number of non-conformities in a set of reference data (from Phase I). Expressions for various chart performance characteristics, such as the average run length (ARL), the standard deviation of the run length (SDRL) and the median run length (MDRL) are also obtained. Examples show that the actual performance of the chart, both in terms of the false alarm rate (FAR) and the in-control ARL, can be substantially different from what might be expected when c is known, in that an exceedingly large number of false alarms are observed, unless the number of inspection units (the size of the reference dataset) used to estimate c is very large, much larger than is commonly used or recommended in practice. In addition, the actual FAR and the in-control ARL values can be very different from the nominally expected values such as 0.0027 (or ARL0=370), particularly when c is small, even with large amounts of reference data. A summary and conclusions are offered.  相似文献   

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