共查询到20条相似文献,搜索用时 15 毫秒
1.
《Journal of statistical planning and inference》1997,64(2):283-295
Consider a family of probability 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. We illustrate this theorem under some conditions on convex loss function. 相似文献
2.
INGE S. HELLAND SOLVE SAEBØ HA˚KON TJELMELAND 《Scandinavian Journal of Statistics》2012,39(4):695-713
Abstract. The random x regression model is approached through the group of rotations of the eigenvectors for the x ‐covariance matrix together with scale transformations for each of the corresponding regression coefficients. The partial least squares model can be constructed from the orbits of this group. A generalization of Pitman's Theorem says that the best equivariant estimator under a group is given by the Bayes estimator with the group's invariant measure as the prior. A straightforward application of this theorem turns out to be impossible since the relevant invariant prior leads to a non‐defined posterior. Nevertheless we can devise an approximate scale group with a proper invariant prior leading to a well‐defined posterior distribution with a finite mean. This Bayes estimator is explored using Markov chain Monte Carlo technique. The estimator seems to require heavy computations, but can be argued to have several nice properties. It is also a valid estimator when p>n. 相似文献
3.
Lakshmi Kanta Patra 《统计学通讯:理论与方法》2013,42(19):4861-4873
AbstractIn the present communication, we consider the estimation of the common hazard rate of several exponential distributions with unknown and unequal location parameters with a common scale parameter under a general class of bowl-shaped scale invariant loss functions. We have shown that the best affine equivariant estimator (BAEE) is inadmissible by deriving a non smooth improved estimator. Further, we have obtained a smooth estimator which improves upon the BAEE. As an application, we have obtained explicit expressions of improved estimators for special loss functions. Finally, a simulation study is carried out for numerically comparing the risk performance of various estimators. 相似文献
4.
Eaton and Olkin (1987) discussed the problem of best equivariant estimator of the matrix scale parameter with respect to different
scalar loss functions. Edwin Prabakaran and Chandrasekar (1994) developed simultaneous equivariant estimation approach and
illustrated the method with examples. The problems considered in this paper are simultaneous equivariant estimation of the
parameters of (i) a matrix scale model and (ii) a multivariate location-scale model. By considering matrix loss function (Klebanov,
Linnik and Ruhin, 1971) a characterization of matrix minimum risk equivariant (MMRE) estimator of the matrix parameter is
obtained in each case. Illustrative examples are provided in which MMRE estimators are obtained with respect to two matrix
loss functions. 相似文献
5.
Divakar Sharma 《统计学通讯:理论与方法》2013,42(5):611-623
Suppose an estimation problem is invariant under a group of transformations and one is interested in finding an optimal equivariant estimator. The usual proactice is to confine attention to non-randomized equivariant estimators based on a minimal sufficient statistic. A justification of this restriction to a smaller clas of estimators is given in this paper under certain conditions. 相似文献
6.
For a class of distributions which are invariant under a group of transformations, we propose an estimator ot an estimable parameter. The estimator, which we call the invariant U-statistic, is the uniformly minimum variance unbiased estimator of the corresponding estimable parameter for the class of all continuous distributions which are invariant under the group of transformations. 相似文献
7.
Annaliisa Kankainen Sara Taskinen Hannu Oja 《Statistical Methods and Applications》2007,16(3):357-379
Classical univariate measures of asymmetry such as Pearson’s (mean-median)/σ or (mean-mode)/σ often measure the standardized
distance between two separate location parameters and have been widely used in assessing univariate normality. Similarly,
measures of univariate kurtosis are often just ratios of two scale measures. The classical standardized fourth moment and
the ratio of the mean deviation to the standard deviation serve as examples. In this paper we consider tests of multinormality
which are based on the Mahalanobis distance between two multivariate location vector estimates or on the (matrix) distance
between two scatter matrix estimates, respectively. Asymptotic theory is developed to provide approximate null distributions
as well as to consider asymptotic efficiencies. Limiting Pitman efficiencies for contiguous sequences of contaminated normal
distributions are calculated and the efficiencies are compared to those of the classical tests by Mardia. Simulations are
used to compare finite sample efficiencies. The theory is also illustrated by an example. 相似文献
8.
Gauri Sankar Datta 《统计学通讯:理论与方法》2013,42(11):3713-3727
The present article considers the Pitman Closeness (PC) criterion of certain hierarchical Bayes (HB) predictors derived under a normal mixed linear models for known ratios of variance components using a uniform prior for the vector of fixed effects and some proper or improper prior on the error variance. For a generalized Euclidean error, simultaneous HB predictors of several linear combinations of vector of effects are shown to be the Pitman-closest in the frequentist sense in the class of equivariant predictors for location group of transformations. The normality assumption can be relaxed to show that these HB predictors are the Pitman-closest for location-scale group of transformations for a wider family of elliptically symmetric distributions. Also for this family, the HB predictors turn out to be Pitman-closest in the class of all linear unbiased predictors (LUPs). All these results are extended for the HB predictor of finite population mean vector in the context of finite population sampling. 相似文献
9.
10.
M. L. Targhetta 《Statistical Papers》1993,34(1):175-180
We consider a particular subclass of the two-parameter exponential family with natural parameters γ1, γ2 and characterize those distributions of the family having a ratio of the mean value and the variance that is a linear function
of γ1 by the form of the moment generating function. As special cases we find the normal and the gamma distributions. 相似文献
11.
For location, scale and location–scale models, which are common in practical applications, we derive optimum equivariant estimators and predictors using the Pitman closeness criterion. This approach is very robust with respect to the choice of the loss function as it only requires the loss function to be strictly monotone. We also prove that, in general, the Pitman closeness comparison of any two equivariant predictors depends on the unknown parameter only through a maximal invariant, and hence it is independent of the parameter when the parameter space is transitive. We present several examples illustrating applications of our theoretical results. 相似文献
12.
《Journal of statistical planning and inference》1999,75(2):353-362
The theorem of Kagan et al. (1967), (Sankhya Ser. A. 27, 405) on the characterization of the normal law is extended to the characterization of a broad class of distribution shapes, also in the linear regression model, and the stability of this characterization is considered. The results enable, among others, to construct an asymptotically efficient estimator from a subclass of equivariant asymptotically linear estimators of θ. 相似文献
13.
This paper is concerned with estimating the common hazard rate of two exponential distributions with unknown and ordered location parameters under a general class of bowl-shaped scale invariant loss functions. The inadmissibility of the best affine equivariant estimator is established by deriving an improved estimator. Another estimator is obtained which improves upon the best affine equivariant estimator. A class of improving estimators is derived using the integral expression of risk difference approach of Kubokawa [A unified approach to improving equivariant estimators. Ann Statist. 1994;22(1):290–299]. These results are applied to specific loss functions. It is further shown that these estimators can be derived for four important sampling schemes: (i) complete and i.i.d. sample, (ii) record values, (iii) type-II censoring, and (iv) progressive Type-II censoring. A simulation study is carried out for numerically comparing the risk performance of these proposed estimators. 相似文献
14.
Previously proposed linear signed rank tests for multivariate location are not invariant under linear transformations of the observations, The asymptotic relative efficiencies of the tests 2 with respect to Hotelling's T2test depend on the direction of shift and the covariance matrix of the alternative distributions. For distributions with highly correlated components, the efficiencies of some of these tests can be arbitrarily low; they approach zero for certain multivariate normal alternatives, This article proposes a transformation of the data to be performed prior to standard linear signed rank tests, The resulting procedures have attractive power and efficiency properties compared to the original tests, In particular, for elliptically symmetric contiguous alternafives, the efficiencies of the new tests equal those of corresponding univariate linear signed rank tests with respect to the t test. 相似文献
15.
Summary This expository paper provides a framework for analysing de Finetti's representation theorem for exchangeable finitely additive
probabilities. Such an analysis is justified by reasoning of statistical nature, since it is shown that the abandonment of
the axiom of σ-additivity has some noteworthy consequences on the common interpretation of the Bayesian paradigm. The usual
(strong) fromulation of de Finetti's theorem is deduced from the finitely additive (weak) formulation, and it is used to solve
the problem of stating the existence of a stochastic process, with given finite-dimensional probability distributions, whose
sample paths are probability distributions. It is of importance, in particular, to specify prior distributions for nonparametric
inferential problems in a Bayesian setting.
Research partially supported by MPI (40% 1990, Gruppo Nazionale ?Modelli Probabilistici e Statistica Matematica?). 相似文献
16.
《Journal of Statistical Computation and Simulation》2012,82(3):261-274
Ranked set sampling (RSS) is a sampling procedure that can be used to improve the cost efficiency of selecting sample units of an experiment or a study. In this paper, RSS is considered for estimating the location and scale parameters a and b>0, as well as the population mean from the family F((x?a)/b). Modified best linear unbiased estimators (BLUEs) and best linear invariant estimators (BLIEs) are considered. Numerical computations with different location-scale distributions and different sample sizes are conducted to assess the efficiency of the suggested estimators. It is found that the modified BLIEs are uniformly higher than that of BLUEs for all distributions considered in this study. The modified BLUE and BLIE are more efficient when the underlying distribution is symmetric. 相似文献
17.
In this paper, we discuss a general class of skew two-piece skew-normal distributions, denoted by GSTPSN(λ1, λ2, ρ). We derive its moment generating function and discuss some simple and interesting properties of this distribution. We then
discuss the modes of these distributions and present a useful representation theorem as well. Next, we focus on a different
generalization of the two-piece skew-normal distribution which is a symmetric family of distributions and discuss some of
its properties. Finally, three well-known examples are used to illustrate the practical usefulness of this family of distributions. 相似文献
18.
We characterize the Pearson family of distributions by finding a relationship between the failure rate and the higher order
moments of residual life. We also present a characterization theorem of IFR(DFR) class of distributions in the Pearson family. 相似文献
19.
Equivariant functions can be useful for constructing of maximal invariant statistic. In this article, we discuss construction of maximal invariants based on a given weakly equivariant function under some additional conditions. The theory easily extends to the case of two or more weakly equivariant functions. Also, we derive a maximal invariant statistic when the group contains a sharply transitive and a characteristic subgroup. Finally, we consider the independence of invariant and weakly equivariant functions under some special conditions. 相似文献
20.
Two families of distributions are introduced and studied within the framework of parametric survival analysis. The families are derived from a general linear form by specifying a function of the survival function with certain restrictions. Distributions within each family are generated by transformations of the survival time variable subject to certain restrictions. Two specific transformations were selected and, thus, four distributions are identified for further study. The distributions have one scale and two shape parameters and include as special cases the exponential, Weibull, log-logistic and Gompertz distributions. One of the new distributions, the modified Weibull, is studied in some detail. The distributions are developed with an emphasis on those features that data analysts find especially useful for survivorship studies, A wide variety of hazard shapes are available. The survival, density and hazard functions may be written in simple algebraic forms. Parameter estimation is demonstrated using the least squares and maximum likelihood methods. Graphical techniques to assess goodness of fit are demonstrated. The models may be extended to include concmitant information. 相似文献