共查询到20条相似文献,搜索用时 578 毫秒
1.
Consider a family of distributions which is invariant under a group of transformations. In this paper, we define an optimality
criterion with respect to an arbitrary convex loss function and we prove a characterization theorem for an equivariant estimator
to be optimal. Then we consider a linear model Y=Xβ+ε, in which ε has a multivariate distribution with mean vector zero and
has a density belonging to a scale family with scale parameter σ. Also we assume that the underlying family of distributions
is invariant with respect to a certain group of transformations. First, we find the class of all equivariant estimators of
regression parameters and the powers of σ. By using the characterization theorem we discuss the simultaneous equivariant estimation
of the parameters of the linear model. 相似文献
2.
The paper derives bounds on the distribution of the quadratic forms Z = y H ( X Γ X H )−1 y and W = y H (σ2 I + X Γ X H )−1 y , where the elements of the M × 1 vector y and the M × N matrix X are independent identically distributed (i.i.d.) complex zero mean Normal variables, Γ is some N × N diagonal matrix with positive diagonal elements, I , is the identity, σ2 is a constant and H denotes the Hermitian transpose. The bounds are convenient for numerical work and appear to be tight for small values of M . This work has applications in digital mobile radio for a specific channel where M antennas are used to receive a signal with N interferers. Some of these applications in radio communication systems are discussed. 相似文献
3.
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
4.
Estimation of an Ergodic Diffusion from Discrete Observations 总被引:6,自引:0,他引:6
Mathieu Kessler 《Scandinavian Journal of Statistics》1997,24(2):211-229
We consider a one-dimensional diffusion process X , with ergodic property, with drift b ( x , θ) and diffusion coefficient a ( x , σ) depending on unknown parameters θ and σ. We are interested in the joint estimation of (θ, σ). For that purpose, we dispose of a discretized trajectory, observed at n equidistant times tn i = ihn , 1 ≤ i ≤ n . We assume that hn ← 0 and nhn ←∞. Under the condition nhn p ← 0 for an arbitrary integer p , we exhibit a contrast dependent on p which provides us with an asymptotically normal and efficient estimator of (θ, σ). 相似文献
5.
We consider estimation of β in the semiparametric regression model y ( i ) - x T ( i )β + f ( i / n ) + ε( i ) where x ( i ) = g ( i )/ n ) + e ( i , f and g are unknown smooth functions and the processes ε( i ) and e ( i ) are stationary with short- or long-range dependence. For the case of i.i.d. errors, Speckman (1988) proposed a √ n –consistent estimator of β. In this paper it is shown that, under suitable regularity conditions, this estimator is asymptotically unbiased and √ n –consistent even if the errors exhibit long-range dependence. The orders of the finite sample bias and of the required bandwidth depend on the long-memory parameters. Simulations and a data example illustrate the method 相似文献
6.
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
7.
Abstract. Let Ω be a space of densities with respect to some σ -finite measure μ and let Π be a prior distribution having support Ω with respect to some suitable topology. Conditional on f , let X n = ( X 1 ,…, X n ) be an independent and identically distributed sample of size n from f . This paper introduces a Bayesian non-parametric criterion for sample size determination which is based on the integrated squared distance between posterior predictive densities. An expression for the sample size is obtained when the prior is a Dirichlet mixture of normal densities. 相似文献
8.
M. L. Tiku 《Australian & New Zealand Journal of Statistics》1967,9(2):49-54
Replacing f (x)/F (x) by α+β(x- θ)/σ in the maximum likelihood equations ∂L/∂θ and ∂L/∂σ calculated from a censored sample, a pair of estimators θ
9.
MOULINATH BANERJEE PINAKI BISWAS DEBASHIS GHOSH 《Scandinavian Journal of Statistics》2006,33(4):673-697
Abstract. We study a binary regression model using the complementary log–log link, where the response variable Δ is the indicator of an event of interest (for example, the incidence of cancer, or the detection of a tumour) and the set of covariates can be partitioned as ( X , Z ) where Z (real valued) is the primary covariate and X (vector valued) denotes a set of control variables. The conditional probability of the event of interest is assumed to be monotonic in Z , for every fixed X . A finite-dimensional (regression) parameter β describes the effect of X . We show that the baseline conditional probability function (corresponding to X = 0 ) can be estimated by isotonic regression procedures and develop an asymptotically pivotal likelihood-ratio-based method for constructing (asymptotic) confidence sets for the regression function. We also show how likelihood-ratio-based confidence intervals for the regression parameter can be constructed using the chi-square distribution. An interesting connection to the Cox proportional hazards model under current status censoring emerges. We present simulation results to illustrate the theory and apply our results to a data set involving lung tumour incidence in mice. 相似文献
10.
CÉSAR SÁNCHEZ SELLERO WENCESLAO GONZÁLEZ MANTEIGA INGRID VAN KEILEGOM 《Scandinavian Journal of Statistics》2005,32(4):563-581
Abstract. Let X be a d -variate random vector that is completely observed, and let Y be a random variable that is subject to right censoring and left truncation. For arbitrary functions φ we consider expectations of the form E [ φ ( X , Y )], which appear in many statistical problems, and we estimate these expectations by using a product-limit estimator for censored and truncated data, extended to the context where covariates are present. An almost sure representation for these estimators is obtained, with a remainder term that is of a certain negligible order, uniformly over a class of φ -functions. This uniformity is important for the application to goodness-of-fit testing in regression and to inference for the regression depth, which we consider in more detail. 相似文献
11.
We derive a non-parametric test for testing the presence of V(Xi ,εi ) in the non-parametric first-order autoregressive model Xi+1 =T(Xi )+V(Xi ,εi )+U(Xi )εi+1 , where the function T(x) is assumed known. The test is constructed as a functional of a basic process for which we establish a weak invariance principle, under the null hypothesis and under stationarity and mixing assumptions. Bounds for the local and non-local powers are provided under a condition which ensures that the power tends to one as the sample size tends to infinity.The testing procedure can be applied, e.g. to bilinear models, ARCH models, EXPAR models and to some other uncommon models. Our results confirm the robustness of the test constructed in Ngatchou Wandji (1995) and in Diebolt & Ngatchou Wandji (1995). 相似文献
12.
Testing Hypotheses in the Functional Linear Model 总被引:2,自引:0,他引:2
Hervé Cardot Frédéric Ferraty ré Mas Pascal Sarda 《Scandinavian Journal of Statistics》2003,30(1):241-255
The functional linear model with scalar response is a regression model where the predictor is a random function defined on some compact set of R and the response is scalar. The response is modelled as Y =Ψ( X )+ ɛ , where Ψ is some linear continuous operator defined on the space of square integrable functions and valued in R . The random input X is independent from the noise ɛ . In this paper, we are interested in testing the null hypothesis of no effect, that is, the nullity of Ψ restricted to the Hilbert space generated by the random variable X . We introduce two test statistics based on the norm of the empirical cross-covariance operator of ( X , Y ). The first test statistic relies on a χ 2 approximation and we show the asymptotic normality of the second one under appropriate conditions on the covariance operator of X . The test procedures can be applied to check a given relationship between X and Y . The method is illustrated through a simulation study. 相似文献
13.
Let σ1 , …, σk be the covariance matrices of k p -variate normal populations. Let Λij be the j th largest characteristic root of σi (j=1, …, p; i=1, …, k). In this note we obtain simultaneous confidence intervals on (i)Λi+1, p /Λip and by using methods similar to those of Khatri (1965). 相似文献
14.
Abstract. Suppose the random vector (X,Y) satisfies the regression model Y = m(X) + σ (X) ? , where m (?) and σ (?) are unknown location and scale functions and ? is independent of X. The response Y is subject to random right censoring, and the covariate X is completely observed. A new test for a specific parametric form of any scale function σ (?) (including the standard deviation function) is proposed. Its statistic is based on the distribution of the residuals obtained from the assumed regression model. Weak convergence of the corresponding process is obtained, and its finite sample behaviour is studied via simulations. Finally, characteristics of the test are illustrated in the analysis of a fatigue data set. 相似文献
15.
Mark Berman 《Australian & New Zealand Journal of Statistics》1984,26(2):160-168
This paper examines the joint statistical analysis of M independent data sets, the jth of which satisfies the model λj Yj =Xj B +εj , where the λj are unknown and the εi are normally distributed with a known correlation structure. The maximum likelihood equations, their asymptotic covariance matrix, and the likelihood ratio test of the hypothesis that the λj s are all equal are derived. These results are applied to two examples. 相似文献
16.
Peter Hall & Brett Presnell 《Journal of the Royal Statistical Society. Series B, Statistical methodology》1999,61(3):661-680
Contamination of a sampled distribution, for example by a heavy-tailed distribution, can degrade the performance of a statistical estimator. We suggest a general approach to alleviating this problem, using a version of the weighted bootstrap. The idea is to 'tilt' away from the contaminated distribution by a given (but arbitrary) amount, in a direction that minimizes a measure of the new distribution's dispersion. This theoretical proposal has a simple empirical version, which results in each data value being assigned a weight according to an assessment of its influence on dispersion. Importantly, distance can be measured directly in terms of the likely level of contamination, without reference to an empirical measure of scale. This makes the procedure particularly attractive for use in multivariate problems. It has several forms, depending on the definitions taken for dispersion and for distance between distributions. Examples of dispersion measures include variance and generalizations based on high order moments. Practicable measures of the distance between distributions may be based on power divergence, which includes Hellinger and Kullback–Leibler distances. The resulting location estimator has a smooth, redescending influence curve and appears to avoid computational difficulties that are typically associated with redescending estimators. Its breakdown point can be located at any desired value ε∈ (0, ½) simply by 'trimming' to a known distance (depending only on ε and the choice of distance measure) from the empirical distribution. The estimator has an affine equivariant multivariate form. Further, the general method is applicable to a range of statistical problems, including regression. 相似文献
17.
Kai F Yu 《统计学通讯:理论与方法》2013,42(9):3075-3087
Let (?,X) be a random vector such that E(X|?) = ? and Var(x|?) a + b? + c?2 for some known constants a, b and c. Assume X1,…,Xn are independent observations which have the same distribution as X. Let t(X) be the linear regression of ? on X. The linear empirical Bayes estimator is used to approximate the linear regression function. It is shown that under appropriate conditions, the linear empirical Bayes estimator approximates the linear regression well in the sense of mean squared error. 相似文献
18.
《Scandinavian Journal of Statistics》2018,45(3):421-443
Consider a non‐parametric regression model Y =m (X )+ϵ , where m is an unknown regression function, Y is a real‐valued response variable, X is a real covariate, and ϵ is the error term. In this article, we extend the usual tests for homoscedasticity by developing consistent tests for independence between X and ϵ . Further, we investigate the local power of the proposed tests using Le Cam's contiguous alternatives. An asymptotic power study under local alternatives along with extensive finite sample simulation study shows that the performance of the new tests is competitive with existing ones. Furthermore, the practicality of the new tests is shown using two real data sets. 相似文献
19.
Murray Aitkin 《Statistics and Computing》1993,3(1):17-22
In the exponential regression model, Bayesian inference concerning the non-linear regression parameter has proved extremely difficult. In particular, standard improper diffuse priors for the usual parameters lead to an improper posterior for the non-linear regression parameter. In a recent paper Ye and Berger (1991) applied the reference prior approach of Bernardo (1979) and Berger and Bernardo (1989) yielding a proper informative prior for . This prior depends on the values of the explanatory variable, goes to 0 as goes to 1, and depends on the specification of a hierarchical ordering of importance of the parameters.This paper explains the failure of the uniform prior to give a proper posterior: the reason is the appearance of the determinant of the information matrix in the posterior density for . We apply the posterior Bayes factor approach of Aitkin (1991) to this problem; in this approach we integrate out nuisance parameters with respect to their conditional posterior density given the parameter of interest. The resulting integrated likelihood for requires only the standard diffuse prior for all the parameters, and is unaffected by orderings of importance of the parameters. Computation of the likelihood for is extremely simple. The approach is applied to the three examples discussed by Berger and Ye and the likelihoods compared with their posterior densities. 相似文献
20.
S. N. Wood 《Journal of the Royal Statistical Society. Series B, Statistical methodology》2000,62(2):413-428
Penalized likelihood methods provide a range of practical modelling tools, including spline smoothing, generalized additive models and variants of ridge regression. Selecting the correct weights for penalties is a critical part of using these methods and in the single-penalty case the analyst has several well-founded techniques to choose from. However, many modelling problems suggest a formulation employing multiple penalties, and here general methodology is lacking. A wide family of models with multiple penalties can be fitted to data by iterative solution of the generalized ridge regression problem minimize || W 1/2 ( Xp − y ) ||2 ρ+Σ i =1 m θ i p ' S i p ( p is a parameter vector, X a design matrix, S i a non-negative definite coefficient matrix defining the i th penalty with associated smoothing parameter θ i , W a diagonal weight matrix, y a vector of data or pseudodata and ρ an 'overall' smoothing parameter included for computational efficiency). This paper shows how smoothing parameter selection can be performed efficiently by applying generalized cross-validation to this problem and how this allows non-linear, generalized linear and linear models to be fitted using multiple penalties, substantially increasing the scope of penalized modelling methods. Examples of non-linear modelling, generalized additive modelling and anisotropic smoothing are given. 相似文献