共查询到20条相似文献,搜索用时 31 毫秒
1.
Ilya S. Molchanov 《Scandinavian Journal of Statistics》1998,25(1):235-242
Let H ( p ) be the set { x ∈ X : h ( x ) ≤ p } where h is a real-valued lower semicontinuous function on a locally compact separable metric space X . This paper presents a general limit theorem for the sequence of random sets H n ( p ) = { x ∈ X : h n ( x ) ≤ p } n ≥ 1, where h n , n ≥ 1, are functions that estimate h 相似文献
2.
Gie-Whan Kim 《Scandinavian Journal of Statistics》1997,24(3):387-406
The objective of this paper is to investigate exact slopes of test statistics { Tn } when the random vectors X 1 , ..., Xn are distributed according to an unknown member of an exponential family { P θ ; θ∈Ω. Here Ω is a parameter set. We will be concerned with the hypothesis testing problem of H 0 θ∈Ω0 vs H 1 : θ∉Ω0 where Ω0 is a subset of Ω. It will be shown that for an important class of problems and test statistics the exact slope of { Tn } at η in Ω−Ω0 is determined by the shortest Kullback–Leibler distance from {θ: Tn (λ(θ)) = Tn (λ(π))} to Ω0 , λθ = E θ )( X ). 相似文献
3.
Let X 1 , X 2 , ... be a sequence of i.i.d. random variables, X i ∼ F θ , θ∈Θ. Let N 1 and N 2 be two stopping rules. For a class of exponential families { F θ : θ∈Θ} we show that the experiment Y 1 = ( X 1 , ..., X N1 ) carries more statistical information than Y 2 = ( X 1 , ..., x N2 ) only if N 1 is stochastically larger then N 2 相似文献
4.
Non-parametric Regression with Dependent Censored Data 总被引:1,自引:0,他引:1
Abstract. Let ( X i , Y i ) ( i = 1 ,…, n ) be n replications of a random vector ( X , Y ), where Y is supposed to be subject to random right censoring. The data ( X i , Y i ) are assumed to come from a stationary α -mixing process. We consider the problem of estimating the function m ( x ) = E ( φ ( Y ) | X = x ), for some known transformation φ . This problem is approached in the following way: first, we introduce a transformed variable , that is not subject to censoring and satisfies the relation , and then we estimate m ( x ) by applying local linear regression techniques. As a by-product, we obtain a general result on the uniform rate of convergence of kernel type estimators of functionals of an unknown distribution function, under strong mixing assumptions. 相似文献
5.
It is shown that the least squares estimators of B and Σ in the multivariate linear model {E Y i = X 1 B , D ( Y i ) =Σ, 1 ≤ i ≤ n , Y 1 Y n uncorrelated} subject to the constraints Y i M = X i N are just the usual least squares estimators = ( X'X )-1 X'Y and ΣC = 1/n( Y-X )( Y-X ) in the unconstrained model where Σ has full rank. Tests of hypotheses concerning B are discussed for situations in which each Y i has a multivariate normal distribution, and examples of the applicability of the model reviewed. 相似文献
6.
In sequential analysis it is often necessary to determine the distributions of √t Y t and/or √a Y t , where t is a stopping time of the form t = inf{ n ≥ 1 : n+Sn +ξn > a }, Y n is the sample mean of n independent and identically distributed random variables (iidrvs) Yi with mean zero and variance one, Sn is the partial sum of iidrvs Xi with mean zero and a positive finite variance, and { ξn } is a sequence of random variables that converges in distribution to a random variable ξ as n →∞ and ξn is independent of ( Xn+1 , Yn+1 ), (Xn+2 , Yn+2 ), . . . for all n ≥ 1. Anscombe's (1952) central limit theorem asserts that both √t Y t and √a Y t are asymptotically normal for large a , but a normal approximation is not accurate enough for many applications. Refined approximations are available only for a few special cases of the general setting above and are often very complex. This paper provides some simple Edgeworth approximations that are numerically satisfactory for the problems it considers. 相似文献
7.
ELISA M. MOLANES LOPEZ INGRID VAN KEILEGOM NOËL VERAVERBEKE 《Scandinavian Journal of Statistics》2009,36(3):413-432
Abstract. Suppose that X 1 ,…, X n is a sequence of independent random vectors, identically distributed as a d -dimensional random vector X . Let be a parameter of interest and be some nuisance parameter. The unknown, true parameters ( μ 0 , ν 0 ) are uniquely determined by the system of equations E { g ( X , μ 0 , ν 0 )} = 0 , where g = ( g 1 ,…, g p + q ) is a vector of p + q functions. In this paper we develop an empirical likelihood (EL) method to do inference for the parameter μ 0 . The results in this paper are valid under very mild conditions on the vector of criterion functions g . In particular, we do not require that g 1 ,…, g p + q are smooth in μ or ν . This offers the advantage that the criterion function may involve indicators, which are encountered when considering, e.g. differences of quantiles, copulas, ROC curves, to mention just a few examples. We prove the asymptotic limit of the empirical log-likelihood ratio, and carry out a small simulation study to test the performance of the proposed EL method for small samples. 相似文献
8.
T. A. Severini 《Journal of the Royal Statistical Society. Series B, Statistical methodology》1999,61(1):115-126
Let Y 1 , . . ., Yn denote independent random variables such that Yj has a one-parameter exponential family distribution with canonical parameter θ j =λ+ψ Xj ; here X 1 , . . ., Xn are known constants. Consider a test of the null hypothesis ψ=0. Under the null hypothesis, A =Σ Yj is sufficient for λ and, hence, a test of ψ=0 may be based on the conditional distribution of T =Σ Xj Yj given A , which is independent of λ. In this paper, the effects of overdispersion due to a mixture model on the conditional distribution of T given A are considered. 相似文献
9.
Olle Nerman 《Scandinavian Journal of Statistics》1998,25(3):569-572
Suppose that {( X n , Y n )} is a sequence of pairs of cector-valued stochastic variables which converges weakly to ( X , Y ), and that { y n } converges to y . Sufficient conditions for the conditional distribution of X n given Y = y are given in terms of stochastic monotonicity. Conditions, which guarantee that also moments of the conditional distributions converge to the moments of the ones of the limit, are also derived. 相似文献
10.
Andrzej S. Kozek 《Australian & New Zealand Journal of Statistics》1998,40(3):317-334
Let X 1 , . . ., Xn be independent identically distributed random variables with a common continuous (cumulative) distribution function (d.f.) F , and F^n the empirical d.f. (e.d.f.) based on X 1 , . . ., Xn . Let G be a smooth d.f. and Gθ = G (·–θ) its translation through θ∈ R . Using a Kolmogorov-Lévy type metric ρα defined on the space of d.f.s. on R , the paper derives both null and non-null limiting distributions of √ n [ ρα ( Fn , Gθn ) – ρα ( F, Gθ )], √ n (θ n –θ) and √ nρα ( Gθ , Gθ ), where θ n and θ are the minimum ρα -distance parameters for Fn and F from G , respectively. These distributions are known explicitly in important particular cases; with some complementary Monte Carlo simulations, they help us clarify our understanding of estimation using minimum distance methods and supremum type metrics. We advocate use of the minimum distance method with supremum type metrics in cases of non-null models. The resulting functionals are Hadamard differentiable and efficient. For small scale parameters the minimum distance functionals are close to medians of the parent distributions. The optimal small scale models result in minimum distance estimators having asymptotic variances very competitive and comparable with best known robust estimators. 相似文献
11.
Charles F. Dunkl & Donald E. Ramirez 《Australian & New Zealand Journal of Statistics》2001,43(1):21-31
Exact expressions for the cumulative distribution function of a random variable of the form ( α 1 X 1 + α 2 X 2 )/ Y are given where X 1 , X 2 and Y are independent chi-squared random variables. The expressions are applied to the detection of joint outliers and Hotelling's mis-specified T 2 distribution. 相似文献
12.
Konul Bayramoglu 《统计学通讯:模拟与计算》2013,42(10):2173-2185
Let (X, Y) be a bivariate random vector with joint distribution function FX, Y(x, y) = C(F(x), G(y)), where C is a copula and F and G are marginal distributions of X and Y, respectively. Suppose that (Xi, Yi), i = 1, 2, …, n is a random sample from (X, Y) but we are able to observe only the data consisting of those pairs (Xi, Yi) for which Xi ? Yi. We denote such pairs as (X*i, Yi*), i = 1, 2, …, ν, where ν is a random variable. The main problem of interest is to express the distribution function FX, Y(x, y) and marginal distributions F and G with the distribution function of observed random variables X* and Y*. It is shown that if X and Y are exchangeable with marginal distribution function F, then F can be uniquely determined by the distributions of X* and Y*. It is also shown that if X and Y are independent and absolutely continuous, then F and G can be expressed through the distribution functions of X* and Y* and the stress–strength reliability P{X ? Y}. This allows also to estimate P{X ? Y} with the truncated observations (X*i, Yi*). The copula of bivariate random vector (X*, Y*) is also derived. 相似文献
13.
George S. Fishman 《Journal of the Royal Statistical Society. Series B, Statistical methodology》1999,61(3):623-641
Convergence rates, statistical efficiency and sampling costs are studied for the original and extended Swendsen–Wang methods of generating a sample path { S j , j ≥1} with equilibrium distribution π , with r distinct elements, on a finite state space X of size N 1 . Given S j -1 , each method uses auxiliary random variables to identify the subset of X from which S j is to be randomly sampled. Let πmin and πmax denote respectively the smallest and largest elements in π and let Nr denote the number of elements in π with value πmax . For a single auxiliary variable, uniform sampling from the subset and ( N 1 − Nr )πmin + Nr πmax ≈1, our results show rapid convergence and high statistical efficiency for large πmin /πmax or Nr / N 1 and slow convergence and poor statistical efficiency for small πmin /πmax and Nr / N1 . Other examples provide additional insight. For extended Swendsen–Wang methods with non-uniform subset sampling, the analysis identifies the properties of a decomposition of π( x ) that favour fast convergence and high statistical efficiency. In the absence of exploitable special structure, subset sampling can be costly regardless of which of these methods is employed. 相似文献
14.
B. U. Park W. C. Kim D. Ruppert M. C. Jones D. F. Signorini & R. Kohn 《Scandinavian Journal of Statistics》1997,24(2):145-163
We propose and investigate two new methods for achieving less bias in non- parametric regression. We show that the new methods have bias of order h 4 , where h is a smoothing parameter, in contrast to the basic kernel estimator's order h 2 . The methods are conceptually very simple. At the first stage, perform an ordinary non-parametric regression on { xi , Yi } to obtain m^ ( xi ) (we use local linear fitting). In the first method, at the second stage, repeat the non-parametric regression but on the transformed dataset { m^ ( xi , Yi )}, taking the estimator at x to be this second stage estimator at m^ ( x ). In the second, and more appealing, method, again perform non-parametric regression on { m^ ( xi , Yi )}, but this time make the kernel weights depend on the original x scale rather than using the m^ ( x ) scale. We concentrate more of our effort in this paper on the latter because of its advantages over the former. Our emphasis is largely theoretical, but we also show that the latter method has practical potential through some simulated examples. 相似文献
15.
Kentaro Nomakuchi 《Australian & New Zealand Journal of Statistics》1998,40(1):103-109
van der Vaart (1953, 1955) introduced the orthoscheme probability Rn (c 1 ,..., cn−1 ), meaning the orthant probability of an n -dimensional normal random vector with zero mean and tridiagonal correlation matrix with elements c 1 ,..., cn−1 on the upper diagonal. Childs (1967) conjectured and Moran (1983) proved that the generating function of { Rn (½,...,½)} equals tan z + sin z . This paper derives the generating function of { Rn (τ,½,...,½)}. 相似文献
16.
Let X = (X1 , - Xp )prime; ˜ Np (μ, Σ) where μ= (μ1 , -, μp )' and Σ= diag (Σ2 1 , -, Σ2 p ) are both unknown and p3. Let (ni - 2) wi /Σ2 i ! X2 ni , independent. of wi (I ≠ j = 1, -, p). Assume that (w1 , -, wp ) and X are independent. Define W = diag (w1 , -, wp ) and ¶ X ¶2 w = X'W-1 Q-1 W-1 X where Q = diag (q1 , -,n qp ), qi > 0, i = 1, -, p. In this paper, the minimax estimator of Berger & Bock (1976), given by δ (X, W) = [Ip - r(X, W) ¶ X ¶-2 w Q-1 W-1 ] X, is shown to be minimax relative to the convex loss (δ - μ)'[αQ + (1 - α) Σ-1 ] δ - μ)/C, where C =α tr (Σ) + (1 - α)p and 0 α 1, under certain conditions on r(X, W). This generalizes the above mentioned result of Berger & Bock. 相似文献
17.
Rong Chen Lijian Yang Christian Hafner 《Journal of the Royal Statistical Society. Series B, Statistical methodology》2004,66(3):669-686
Summary. We consider the problem of multistep-ahead prediction in time series analysis by using nonparametric smoothing techniques. Forecasting is always one of the main objectives in time series analysis. Research has shown that non-linear time series models have certain advantages in multistep-ahead forecasting. Traditionally, nonparametric k -step-ahead least squares prediction for non-linear autoregressive AR( d ) models is done by estimating E ( X t + k | X t , …, X t − d +1 ) via nonparametric smoothing of X t + k on ( X t , …, X t − d +1 ) directly. We propose a multistage nonparametric predictor. We show that the new predictor has smaller asymptotic mean-squared error than the direct smoother, though the convergence rate is the same. Hence, the predictor proposed is more efficient. Some simulation results, advice for practical bandwidth selection and a real data example are provided. 相似文献
18.
B. C. Arnold 《Australian & New Zealand Journal of Statistics》1979,21(2):166-169
If X and Y are independent standard Cauchy random variables then (i) Y and (X+Y)/(1-Xu) are independent, (ii) X and (X + Y)/(1 -XU) are identically distributed, and (iii) X and 2X/(1-X2 ) are identically distributed. Each of these three properties is shown to characterize the Cauchy distribution among absolutely continuous distributions. Some related uniform characterizations are discussed. 相似文献
19.
Jing Qin 《Scandinavian Journal of Statistics》1998,25(4):681-691
We use Owen's (1988, 1990) empirical likelihood method in upgraded mixture models. Two groups of independent observations are available. One is z 1 , ..., z n which is observed directly from a distribution F ( z ). The other one is x 1 , ..., x m which is observed indirectly from F ( z ), where the x i s have density ∫ p ( x | z ) dF ( z ) and p ( x | z ) is a conditional density function. We are interested in testing H 0 : p ( x | z ) = p ( x | z ; θ ), for some specified smooth density function. A semiparametric likelihood ratio based statistic is proposed and it is shown that it converges to a chi-squared distribution. This is a simple method for doing goodness of fit tests, especially when x is a discrete variable with finitely many values. In addition, we discuss estimation of θ and F ( z ) when H 0 is true. The connection between upgraded mixture models and general estimating equations is pointed out. 相似文献
20.
Abstract. Consider the model Y = β ' X + ε . Let F 0 be the unknown cumulative distribution function of the random variable ε . Consistency of the semi-parametric Maximum likelihood estimator of ( β , F 0 ), denoted by , has not been established under any interval censorship (IC) model. We prove in this paper that is consistent under the mixed case IC model and some mild assumptions. 相似文献