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1.
Kaiyong Wang 《统计学通讯:理论与方法》2013,42(5):830-837
Let {S n : n ≥ 0} be a random walk with light-tailed increments and negative drift, and let τ(x) be the first time when the random walk crosses a given level x ≥ 0. Tang (2007) obtained the asymptotics of P(S τ(x) ? x > y, τ(x) < ∞) as x → ∞, which is uniform for y ≥ f(x) for any positive function f(x) → ∞ as x → ∞. In this article, the uniform asymptotics of P(S τ(x) ? x > y, τ(x) < ∞) as x → ∞, for 0 ≤ y ≤ N for any positive number N will be given. Using the above two results, the uniform asymptotics of P(S τ(x) ? x > y, τ(x) < ∞) as x → ∞, for y ≥ 0, is presented. 相似文献
2.
Let X = (X, Y) be a pair of lifetimes whose dependence structure is described by an Archimedean survival copula, and let X t = [(X ? t, Y ? t) | X > t, Y > t] denotes the corresponding pair of residual lifetimes after time t ≥ 0. Multivariate aging notions, defined by means of stochastic comparisons between X and X t , with t ≥ 0, were studied in Pellerey (2008), who considered pairs of lifetimes having the same marginal distribution. Here, we present the generalizations of his results, considering both stochastic comparisons between X t and X t+s for all t, s ≥ 0 and the case of dependent lifetimes having different distributions. Comparisons between two different pairs of residual lifetimes, at any time t ≥ 0, are discussed as well. 相似文献
3.
4.
《统计学通讯:理论与方法》2013,42(10):2031-2042
Abstract If the random variable X denotes the lifetime (X ≥ 0, with probability one) of a unit, then the random variable X t = (t ? X|X ≤ t), for a fixed t > 0, is known as `time since failure', which is analogous to the residual lifetime random variable used in reliability and survival analysis. The reversed hazard rate function, which is related to the random variable X t , has received the attention of many researchers in the recent past [(cf. Shaked, M., Shanthikumar, J. G., 1994). Stochastic Orders and Their Applications. New York: Academic Press]. In this paper, we define some new classes of distributions based on the random variable X t and study their interrelations. We also define a new ordering based on the mean of the random variable Xt and establish its relationship with the reversed hazard rate ordering. 相似文献
5.
《随机性模型》2013,29(1):41-69
Let { X n ,n≥1} be a sequence of iid. Gaussian random vectors in R d , d≥2, with nonsingular distribution function F. In this paper the asymptotics for the sequence of integrals I F,n (G n )?n∫ R d G n n?1( X ) dF( X ) is considered with G n some distribution function on R d . In the case G n =F the integral I F,n (F)/n is the probability that a record occurs in X 1,…, X n at index n. [1] obtained lower and upper asymptotic bounds for this case, whereas [2] showed the rate of convergence if d=2. In this paper we derive the exact rate of convergence of I F,n (G n ) for d≥2 under some restrictions on the distribution function G n . Some related results for multivariate Gaussian tails are discussed also. 相似文献
6.
Czesław Ste¸pniak 《统计学通讯:理论与方法》2013,42(13):2405-2412
Canonical form plays a similar role in linear models to spectral decomposition in matrix analysis. Let X = (X 1,…, X n )′ be a random vector with expectation Aβ and the variance–covariance matrix σV, where V is positive definite and let rank(A) = r. Then there exists a nonsingular linear transformation from X to T = (T 1,…, T n )′, such that ET i = η i , for i = 1,…, r and zero for i > r, while cov(T i , T j ) = δ ij σ. This canonical form, introduced by Ko?odziejczyk (1935), was used, among others, by Scheffé (1959) and by Lehmann (1959, 1986). This technique is extended here for arbitrary (possibly singular) V and for simultaneous canonization of two models of this type. 相似文献
7.
This study is mainly concerned with estimating a shift parameter in the two-sample location problem. The proposed Smoothed Mann–Whitney–Wilcoxon method smooths the empirical distribution functions of each sample by using convolution technique, and it replaces unknown distribution functions F(x) and G(x ? Δ0) with the new smoothed distribution functions F s (x) and G s (x ? Δ0), respectively. The unknown shift parameter Δ0 is estimated by solving the gradient function S n (Δ) with respect to an arbitrary variable Δ. The asymptotic properties of the new estimator are established under some conditions that are similar to the Generalized Wilcoxon procedure proposed by Anderson and Hettmansperger (1996). Some of these properties are asymptotic normality, asymptotic level confidence interval, and hypothesis testing for Δ0. Asymptotic relative efficiency of the proposed method with respect to the least squares, Generalized Wilcoxon and Hodges and Lehmann (1963) procedures are also calculated under the contaminated normal model. 相似文献
8.
Dragan Ðorić 《统计学通讯:理论与方法》2013,42(21):3764-3776
The generalized skew-normal distribution introduced by Balakrishnan (2002) is used to obtain new generalizations of univariate Cauchy distribution with two parameters, denoted by GC m, n (a, b) with m and n non-negative integer numbers and a, b ∈ R. For cases (m, n) = (1, 2), (m, n) = (2, 1), (m, n) = (0, 3) and (m, n) = (3, 0) explicit forms of the density functions are derived and compared to previous generalizations of Cauchy and skew-Cauchy distributions. 相似文献
9.
The density level sets of the two types of measures under consideration are l 2, p -circles with p = 1 and p = 2, respectively. The intersection-percentage function (ipf) of such a measure reflects the percentages which the level set corresponding to the p-radius r shares for each r > 0 with a set to be measured. The geometric measure representation formulae in Richter (2009) is based upon these ipf's and will be used here for evaluating exact cdf's and pdf's for the linear combination, the product, and the ratio of the components of two-dimensional simplicial or spherically distributed random vectors. 相似文献
10.
We investigate a self-normalized central limit theorem for a ρ-mixing stationary sequence {Xi, i ? 1} of random variables such that L(x) ? E(X21I{|X1| ? x}) is a slowly varying function as x → ∞. The results obtained generalize the results of Gine, Gotze, and Mason (1997) and Mason (2005) to ρ-mixing sequences. 相似文献
11.
Let ν be a positive Borel measure on ?n and pFq(a1,…, ap; b1,…, bq; s) be a generalized hypergeometric series. We define a generalized hypergeometric measure, μp,q := pFq(a1,…, ap; b1,…, bq;ν), as a series of convolution powers of the measure ν, and we investigate classes of probability distributions which are expressible as such a measure. We show that the Kemp (1968) family of distributions is an example of μp,q in which ν is a Dirac measure on ?. For the case in which ν is a Dirac measure on ?n, we relate μp,q to the diagonal natural exponential families classified by Bar-Lev et al. (1994). For p < q, we show that certain measures μp,q can be expressed as the convolution of a sequence of independent multi-dimensional Bernoulli trials. For p = q, q + 1, we show that the measures μp,q are mixture measures with the Dufresne and Poisson-stopped-sum probability distributions as their mixing measures. 相似文献
12.
Parimal Mukhopadhyay 《统计学通讯:理论与方法》2013,42(10):1867-1876
When there is only one interesting parameter θ1 and one nuisance parameter θ2, Godambe and Thompson (1974) showed that the optimal estimating function for θ1 essentially is a linear function of the θ1-score, the square of the θ2-score, and the derivative of θ2-score with respect to θ2. Mukhopadhyay (2000b) generalized this result to m nuisance parameters. Mukhopadhyay (2000 2002a b) obtained lower bounds to the variance of regular estimating functions in the presence of nuisance parameters. Taking cues from these results we propose a method of finding optimal estimating function for θ1 by taking the multiple regression equation on θ1 score and Bhattacharyya's (1946) scores with respect to θ2. The result is extended to the case of m nuisance parameters. 相似文献
13.
Suchandan Kayal 《统计学通讯:理论与方法》2018,47(20):4938-4957
Several probability distributions such as power-Pareto distribution (see Gilchrist 2000 and Hankin and Lee 2006), various forms of lambda distributions (see Ramberg and Schmeiser 1974 and Freimer et al. 1988), Govindarajulu distribution (see Nair, Sankaran, and Vineshkumar 2012), etc., do not have manageable distribution functions, though they have tractable quantile functions. Hence, analytical study of the properties of Chernoff distance of two random variables associated with these distributions via traditional distribution function-based tool becomes difficult. To make this simple, in this paper, we introduce quantile-based Chernoff distance for (left or right) truncated random variables and study its various properties. Some useful bounds as well as characterization results are obtained. 相似文献
14.
《统计学通讯:理论与方法》2012,41(13-14):2445-2455
In this article, the problem of estimation of the individual weights of three objects using a chemical balance weighing design is considered. We use the criterion of D-optimality. We assume that the covariance matrix of errors is the matrix of first-order autoregressive process. Such problems were discussed in Li and Yang (2005) and also in Yeh and Lo Huang (2005). We present some results of D-optimal designs in certain class of designs with the design matrix X ∈ M n×3(±1) such that each column of matrix X has at least one 1 and one ?1. 相似文献
15.
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
16.
For regression analysis of data with non response, sensitivity analysis is usually recommended. An index of local sensitivity to non ignorability (ISNI) (Troxel et al., 2004) was derived to detect the sensitivity of maximum likelihood estimates to small departures from ignorability. However, ISNI requires specification of a parametric model for the missing-data mechanism. In this article, a local sensitivity index for a pseudolikelihood (PL) method that does not require specification of the mechanism is proposed. For bivariate data (x, y), when the non response mechanism is an arbitrary function of x + λy, this new index is defined as the first derivative of the PL estimate with respect to λ at λ = 0. The closed form was derived for normal regression data when the density function of the predictor x approximated by a kernel estimator in the PL method. The utility of this new local sensitivity index was illustrated through application on one dataset. 相似文献
17.
Recently, the topic of extreme value under random censoring has been considered. Different estimators for the index have been proposed (see Beirlant et al., 2007). All of them are constructed as the classical estimators (without censoring) divided by the proportion of non censored observations above a certain threshold. Their asymptotic normality was established by Einmahl et al. (2008). An alternative approach consists of using the Peaks-Over-Threshold method (Balkema and de Haan, 1974; Smith, 1987) and to adapt the likelihood to the context of censoring. This leads to ML-estimators whose asymptotic properties are still unknown. The aim of this article is to propose one-step approximations, based on the Newton-Raphson algorithm. Based on a small simulation study, the one-step estimators are shown to be close approximations to the ML-estimators. Also, the asymptotic normality of the one-step estimators has been established, whereas in case of the ML-estimators it is still an open problem. The proof of our result, whose approach is new in the Peaks-Over-Threshold context, is in the spirit of Lehmann's theory (1991). 相似文献
18.
Bo Li 《统计学通讯:理论与方法》2013,42(18):2877-2889
Using the framework proposed by Bickel et al. (2006), we provide a score-based testing method to check the exclusion restriction in quantile regression, i.e., H: να(Y|U, V) = να(Y|U) w.p.1, where να denotes the αth (0 < α < 1) quantile. A subsampling method is suggested to acquire the critical values and justified. The tests are all found to be consistent against fixed alternatives and have discriminating power against local alternatives at root-n scale. We address this particular problem as a representative among a wide family of semiparametric model checking problems. The methodology can be carried over to other goodness-of-fit testing of semiparametric models, possibly involve non smooth functions. 相似文献
19.
By assuming that a random variable X possesses an aging property, we provide conditions under which the corresponding weighted version X 1, with weight function w 1(·), would also possess this aging property. Similarly, by assuming that two random variables X and Y are ordered with respect to a stochastic order, we provide conditions under which the corresponding weighted versions X 1 and Y 2, with weight functions w 1(·) and w 2(·), respectively, preserve this stochastic ordering. We also point out fallacies in the similar results claimed by Jain et al. (1989) and Bartoszewicz and Skolimowska (2006) and correct them. 相似文献
20.
Yang Zhao 《统计学通讯:理论与方法》2013,42(20):3736-3744
Statistical analysis for the regression model f β(y | x, z) with missing values in the covariate vector X requires modeling of the covariate distribution g(x | z). Likelihood methods, including Ibrahim (1990), Chen (2004), and Zhao (2005), need either X or Z to be discrete. This article considers extending the likelihood methods to deal with cases where both X and Z may be continuous. We propose modeling the covariate distribution g(x | z) using a piece-wise nonparametric model, then a maximum likelihood estimate (MLE) of β can be computed following the maximum likelihood estimating procedure of Chen (2004) or Zhao (2005). The resulting estimation method is easy to implement and the asymptotic properties of the MLE follow under certain conditions. Extensive simulation studies for different models indicate that the proposed method is acceptable for practical implementation. A real data example is used to illustrate the method. 相似文献