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1.
This paper presents a method for estimating the model Λ(Y)=min(β′X+U, C), where Y is a scalar, Λ is an unknown increasing function, X is a vector of explanatory variables, β is a vector of unknown parameters, U has unknown cumulative distribution function F, and C is a censoring threshold. It is not assumed that Λ and F belong to known parametric families; they are estimated nonparametrically. This model includes many widely used models as special cases, including the proportional hazards model with unobserved heterogeneity. The paper develops n1/2-consistent, asymptotically normal estimators of Λ and F. Estimators of β that are n1/2-consistent and asymptotically normal already exist. The results of Monte Carlo experiments illustrate the finite-sample behavior of the estimators.  相似文献   

2.
Let (T,τ,μ) be a finite measure space, X be a Banach space, P be a metric space and let L1(μ,X) denote the space of equivalence classes of X-valued Bochner integrable functions on (T,τ,μ). We show that if φ:T×P→2X is a set-valued function such that for each fixed pεP, φ(·,p) has a measurable graph and for each fixed tεT, φ(t,·) is either upper or lower semicontinuous then the Aumann integral of φ, i.e.,∫Tφ(t,p)dμ(t)= {∫Tx(t)dμ(t):xεSφ(p)}, where Sφ(p)= {yεL1(μ,X):y(t)εφ(t,p)μ−a.e.}, is either upper or lower semicontinuous in the variable p as well. Our results generalize those of Aumann (1965, 1976) who has considered the above problem for X=Rn, and they have useful applications in general equilibrium and game theory.  相似文献   

3.
LetX 1,…,X m andY 1,…,Y n be two independent samples from continuous distributionsF andG respectively. Using a Hoeffding (1951) type theorem, we obtain the distributions of the vector S=(S (1),…,S (n)), whereS (j)=# (X i ’s≤Y (j)) andY (j) is thej-th order statistic ofY sample, under three truncation models: (a)G is a left truncation ofF orG is a right truncation ofF, (b)F is a right truncation ofH andG is a left truncation ofH, whereH is some continuous distribution function, (c)G is a two tail truncation ofF. Exploiting the relation between S and the vectorR of the ranks of the order statistics of theY-sample in the pooled sample, we can obtain exact distributions of many rank tests. We use these to compare powers of the Hajek test (Hajek 1967), the Sidak Vondracek test (1957) and the Mann-Whitney-Wilcoxon test. We derive some order relations between the values of the probagility-functions under each model. Hence find that the tests based onS (1) andS (n) are the UMP rank tests for the alternative (a). We also find LMP rank tests under the alternatives (b) and (c).  相似文献   

4.
Given X,, where X is a topologically connected space and is an asymmetric binary relation, necessary and sufficient conditions are presented for the existence of a continuous representation of the form, u, δ; that is, for x,yX, xy if and only if u(x)>u(y)+δ where u:X→ is continuous and δ is a strictly positive real number. The results are related to existing results for numerical representations of interval orders and semiorders.  相似文献   

5.
In this paper we study the relationship between regression analysis and a multivariate dependency measure. If the general regression model Y=f() holds for some function f, where 1i1< i2<···im k, and X1,...,Xk is a set of possible explanatory random variables for Y. Then there exists a dependency relation between the random variable Y and the random vector (). Using the dependency statistic defined below, we can detect such dependency even if the function f is not linear. We present several examples with real and simulated data to illustrate this assertion. We also present a way to select the appropriate subset among the random variables X1,X2,...,Xk, which better explain Y.  相似文献   

6.
For random elements X and Y (e.g. vectors) a complete characterization of their association is given in terms of an odds ratio function. The main result establishes for any odds ratio function and any pre-specified marginals the unique existence of a corresponding joint distribution (the joint density is obtained as a limit of an iterative procedure of marginal fittings). Restricting only the odds ratio function but not the marginals leads to semi-parmetric association models for which statistical inference is available for samples drawn conditionally on either X or Y. Log-bilinear association models for random vectors X and Y are introduced which generalize standard (regression) models by removing restrictions on the marginals. In particular, the logistic regression model is recognized as a log-bilinear association model. And the joint distribution of X and Y is shown to be multivariate normal if and only if both marginals are normal and the association is log-bilinear.Acknowledgements The author thanks both referees for their helpful comments which improved the first draft of the paper.  相似文献   

7.
Summary LetX andY be two random vectors with values in ℝ k and ℝ∝, respectively. IfZ=(X T,Y T) T is multivariate normal thenX givenY=y andY givenX=x are (multivariate) normal; the converse is wrong. In this paper simple additional conditions are stated such that the converse is true, too. Furthermore, the case is treated that the random vectorZ=(X 1 T , …,X t T ) T is splitted intot≥3 partsX 1, …,X t.  相似文献   

8.
Prof. Dr. W. Stute 《Metrika》1992,39(1):257-267
LetX 1, ...,X n be an i.i.d. sample from some parametric family {θ :θ (Θ} of densities. In the random censorship model one observesZ i =min (X i ,Y i ) andδ i =1{ x i Y i}, whereY i is a censoring variable being independent ofX i . In this paper we investigate the strong consistency ofθ n maximizing the modified likelihood function based on (Z i ,δ i , 1≤in. The main result constitutes an extension of Wald’s theorem for complete data to censored data. Work partially supported by the “Deutsche Forschungsgemeinschaft”.  相似文献   

9.
In questo lavoro si studia il problema di ricerca della distribuzione di probabilità comune da assegnare a due numeri aleatori discreti che assumano i primin valori interi naturali in modo che la loro somma abbia moda di minima probabilità.Il problema è affrontato sia dal punto di vista teorico tramite gli strumenti della programmazione matematica, sia dal punto di vista numerico.
LetX andY be two random numbers with the same distribution function; in this paper we consider the problem of finding a random numberX+Y having mode with minimal probability. In particular we have considered only the case ofX andY assuming the firstn integer values, so thatp (dimensionn) is the common distribution andq (dimension 2n–1) is the distribution ofX+Y; then the problem is to minimizem=maxq 1.In the known literature it appears that theoretical results and numerical experience have brought to various conjectures not confermed. In this paper the problem is considered from the mathematical programming point of view. Several theoretical results are obtained even if the full solution of the problem is not reached. Anyway, such results, limiting the search range of a solution, suggested extended numerical testing, also for rather large values ofn, so that non trivial conclusions can be derived.


Pervenuto il 22-1-82  相似文献   

10.
11.
We introduce an iterative procedure for estimating the unknown density of a random variable X from n independent copies of Y=X+ɛ, where ɛ is normally distributed measurement error independent of X. Mean integrated squared error convergence rates are studied over function classes arising from Fourier conditions. Minimax rates are derived for these classes. It is found that the sequence of estimators defined by the iterative procedure attains the optimal rates. In addition, it is shown that the sequence of estimators converges exponentially fast to an estimator within the class of deconvoluting kernel density estimators. The iterative scheme shows how, in practice, density estimation from indirect observations may be performed by simply correcting an appropriate ordinary density estimator. This allows to assess the effect that the perturbation due to contamination by ɛ has on the density to be estimated. We also suggest a method to select the smoothing parameter required by the iterative approach and, utilizing this method, perform a simulation study.  相似文献   

12.
Summary Let X1,.,., Xm, and Y1, Yn, be two independent samples from the same distribution and let X and Y be the means of these samples. What is the maximal value of P(X < Y)?  相似文献   

13.
14.
An enterprise is owned jointly by m agents, the ith agent's share being θi > 0 where ∑iθi=1. The enterprise is able to produce some non-negative n-vector x of goods where x lies in some convex production set X. An operation consists of choosing a vector from X and distributing it among the agents. The problem is to find an operations such that the value of the ith agent's bundle measured in a given price system is proportional to θi and such that the operation is (Pareto) optimal with respect to the agent's preferences. It is shown under standard assumptions that operations which are both optimal and proportional always exist. It is also shown that these operations are unique if (a) X is given by a separable production function, and (b) when X represents production of a single good over n time periods.  相似文献   

15.
Pareto optimality (sometimes known as Pareto efficiency) is an important notion in social sciences and related areas, see e.g. Klaus (2006), Chun (2005), Hild (2004), Kibris (2003), Nandeibam (2003), Papai (2001), Peris and Sanchez (2001), Brams and Fishburn (2000), Denicolo (1999), Klaus et al. (1998), Peremans et al. (1997), and Vohra (1992). This notion invariably involves the comparison of the utility of one outcome versus another, i.e. the ratio of two utilities or in general the ratio of two random variables. In this note, we derive the exact distribution of the ratio X/(XY) when X and Y are Pareto random variables, Pareto distribution being the first and the most popular distribution used in social sciences and related areas.  相似文献   

16.
In the paper we study regressional versions of Lukacs' characterization of the gamma law. We consider constancy of regression instead of Lukacs' independence condition in three new schemes. Up to now the constancy of regressions of U=X/(X + Y) given V=X + Y for independent X and Y has been considered in the literature. Here we are concerned with constancy of regressions for X and Y while independence of U and V is assumed instead.  相似文献   

17.
Dr. N. Henze 《Metrika》1984,31(1):259-273
Summary For independents-variate samplesX 1, ...,X m i.i.d.f. (.),Y 1, ...,Y n i.i.d. g. (.), where the densitiesf (.),g (.) are assumed to be continuous on their respective sets of positivity, consider the numberT m,n of pointsZ of the pooled sample (which are either of typeX or of typeY) such that the nearest neighbor ofZ is of the same type asZ. We show that, as , independently of (.). An omnibus test for the two sample problem f(.)g(.) orf(.)g(.)? may be obtained by rejecting the hypothesisf(.)g(.) for large values ofT m,n.  相似文献   

18.
Estimation with longitudinal Y having nonignorable dropout is considered when the joint distribution of Y and covariate X is nonparametric and the dropout propensity conditional on (Y,X) is parametric. We apply the generalised method of moments to estimate the parameters in the nonignorable dropout propensity based on estimating equations constructed using an instrument Z, which is part of X related to Y but unrelated to the dropout propensity conditioned on Y and other covariates. Population means and other parameters in the nonparametric distribution of Y can be estimated based on inverse propensity weighting with estimated propensity. To improve efficiency, we derive a model‐assisted regression estimator making use of information provided by the covariates and previously observed Y‐values in the longitudinal setting. The model‐assisted regression estimator is protected from model misspecification and is asymptotically normal and more efficient when the working models are correct and some other conditions are satisfied. The finite‐sample performance of the estimators is studied through simulation, and an application to the HIV‐CD4 data set is also presented as illustration.  相似文献   

19.
D. A. Ioannides 《Metrika》1999,50(1):19-35
Let {(X i, Y i,)}, i≥1, be a strictly stationary process from noisy observations. We examine the effect of the noise in the response Y and the covariates X on the nonparametric estimation of the conditional mode function. To estimate this function we are using deconvoluting kernel estimators. The asymptotic behavior of these estimators depends on the smoothness of the noise distribution, which is classified as either ordinary smooth or super smooth. Uniform convergence with almost sure convergence rates is established for strongly mixing stochastic processes, when the noise distribution is ordinary smooth. Received: April 1998  相似文献   

20.
It is shown that if (X 1, X 2, . . . , X n ) is a random vector with a logconcave (logconvex) joint reliability function, then X P = min iP X i has increasing (decreasing) hazard rate. Analogously, it is shown that if (X 1, X 2, . . . , X n ) has a logconcave (logconvex) joint distribution function, then X P  = max iP X i has decreasing (increasing) reversed hazard rate. If the random vector is absolutely continuous with a logconcave density function, then it has a logconcave reliability and distribution functions and hence we obtain a result given by Hu and Li (Metrika 65:325–330, 2007). It is also shown that if (X 1, X 2, . . . , X n ) has an exchangeable logconcave density function then both X P and X P have increasing likelihood ratio.  相似文献   

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