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1.
We consider the estimation of smooth regression functions in a class of conditionally parametric co-variate-response models. Independent and identically distributed observations are available from the distribution of (Z,X)(Z,X), where Z is a real-valued co-variate with some unknown distribution, and the response X conditional on Z   is distributed according to the density p(·,ψ(Z))p(·,ψ(Z)), where p(·,θ)p(·,θ) is a one-parameter exponential family. The function ψψ is a smooth monotone function. Under this formulation, the regression function E(X|Z)E(X|Z) is monotone in the co-variate Z   (and can be expressed as a one–one function of ψψ); hence the term “monotone response model”. Using a penalized least squares approach that incorporates both monotonicity and smoothness, we develop a scheme for producing smooth monotone estimates of the regression function and also the function ψψ across this entire class of models. Point-wise asymptotic normality of this estimator is established, with the rate of convergence depending on the smoothing parameter. This enables construction of Wald-type (point-wise) as well as pivotal confidence sets for ψψ and also the regression function. The methodology is extended to the general heteroscedastic model, and its asymptotic properties are discussed.  相似文献   

2.
Consider the nonparametric location-scale regression model Y=m(X)+σ(X)εY=m(X)+σ(X)ε, where the error εε is independent of the covariate XX, and mm and σσ are smooth but unknown functions. The pair (X,Y)(X,Y) is allowed to be subject to selection bias. We construct tests for the hypothesis that m(·)m(·) belongs to some parametric family of regression functions. The proposed tests compare the nonparametric maximum likelihood estimator (NPMLE) based on the residuals obtained under the assumed parametric model, with the NPMLE based on the residuals obtained without using the parametric model assumption. The asymptotic distribution of the test statistics is obtained. A bootstrap procedure is proposed to approximate the critical values of the tests. Finally, the finite sample performance of the proposed tests is studied in a simulation study, and the developed tests are applied on environmental data.  相似文献   

3.
This paper discusses a new perspective in fitting spatial point process models. Specifically the spatial point process of interest is treated as a marked point process where at each observed event xx a stochastic process M(x;t)M(x;t), 0<t<r0<t<r, is defined. Each mark process M(x;t)M(x;t) is compared with its expected value, say F(t;θ)F(t;θ), to produce a discrepancy measure at xx, where θθ is a set of unknown parameters. All individual discrepancy measures are combined to define an overall measure which will then be minimized to estimate the unknown parameters. The proposed approach can be easily applied to data with sample size commonly encountered in practice. Simulations and an application to a real data example demonstrate the efficacy of the proposed approach.  相似文献   

4.
In Hedayat and Pesotan [1992, Two-level factorial designs for main effects and selected two-factor interactions. Statist. Sinica 2, 453–464.] the concepts of a g(n,e)g(n,e)-design and a g(n,e)g(n,e)-matrix are introduced to study designs of nn factor two-level experiments which can unbiasedly estimate the mean, the nn main effects and ee specified two-factor interactions appearing in an orthogonal polynomial model and it is observed that the construction of a g-design is equivalent to the construction of a g  -matrix. This paper deals with the construction of D-optimal g(n,1)g(n,1)-matrices. A standard form for a g(n,1)g(n,1)-matrix is introduced and some lower and upper bounds on the absolute determinant value of a D-optimal g(n,1)g(n,1)-matrix in the class of all g(n,1)g(n,1)-matrices are obtained and an approach to construct D-optimal g(n,1)g(n,1)-matrices is given for 2?n?82?n?8. For two specific subclasses, namely a certain class of g(n,1)g(n,1)-matrices within the class of g(n,1)g(n,1)-matrices of index one and the class C(H)C(H) of g(8t+2,1)g(8t+2,1)-matrices constructed from a normalized Hadamard matrix H   of order 8t+4(t?1)8t+4(t?1) two techniques for the construction of the restricted D-optimal matrices are given.  相似文献   

5.
In the context of Bayesian statistical analysis, elicitation is the process of formulating a prior density f(·)f(·) about one or more uncertain quantities to represent a person's knowledge and beliefs. Several different methods of eliciting prior distributions for one unknown parameter have been proposed. However, there are relatively few methods for specifying a multivariate prior distribution and most are just applicable to specific classes of problems and/or based on restrictive conditions, such as independence of variables. Besides, many of these procedures require the elicitation of variances and correlations, and sometimes elicitation of hyperparameters which are difficult for experts to specify in practice. Garthwaite et al. (2005) discuss the different methods proposed in the literature and the difficulties of eliciting multivariate prior distributions. We describe a flexible method of eliciting multivariate prior distributions applicable to a wide class of practical problems. Our approach does not assume a parametric form for the unknown prior density f(·)f(·), instead we use nonparametric Bayesian inference, modelling f(·)f(·) by a Gaussian process prior distribution. The expert is then asked to specify certain summaries of his/her distribution, such as the mean, mode, marginal quantiles and a small number of joint probabilities. The analyst receives that information, treating it as a data set D   with which to update his/her prior beliefs to obtain the posterior distribution for f(·)f(·). Theoretical properties of joint and marginal priors are derived and numerical illustrations to demonstrate our approach are given.  相似文献   

6.
The problem of classifying all isomorphism classes of OA(N,k,s,t)OA(N,k,s,t)'s is shown to be equivalent to finding all isomorphism classes of non-negative integer solutions to a system of linear equations under the symmetry group of the system of equations. A branch-and-cut algorithm developed by Margot [2002. Pruning by isomorphism in branch-and-cut. Math. Programming Ser. A 94, 71–90; 2003a. Exploiting orbits in symmetric ILP. Math. Programming Ser. B 98, 3–21; 2003b. Small covering designs by branch-and-cut. Math. Programming Ser. B 94, 207–220; 2007. Symmetric ILP: coloring and small integers. Discrete Optim., 4, 40–62] for solving integer programming problems with large symmetry groups is used to find all non-isomorphic OA(24,7,2,2)OA(24,7,2,2)'s, OA(24,k,2,3)OA(24,k,2,3)'s for 6?k?116?k?11, OA(32,k,2,3)OA(32,k,2,3)'s for 6?k?116?k?11, OA(40,k,2,3)OA(40,k,2,3)'s for 6?k?106?k?10, OA(48,k,2,3)OA(48,k,2,3)'s for 6?k?86?k?8, OA(56,k,2,3)OA(56,k,2,3)'s, OA(80,k,2,4)OA(80,k,2,4)'s, OA(112,k,2,4)OA(112,k,2,4)'s, for k=6,7k=6,7, OA(64,k,2,4)OA(64,k,2,4)'s, OA(96,k,2,4)OA(96,k,2,4)'s for k=7,8k=7,8, and OA(144,k,2,4)OA(144,k,2,4)'s for k=8,9k=8,9. Further applications to classifying covering arrays with the minimum number of runs and packing arrays with the maximum number of runs are presented.  相似文献   

7.
In reliability and survival analysis, comparison of two or more populations is an important problem. For example, while comparing a treatment group with a control group, one may be interested in determining whether the observations in the treatment group have a longer lifetime than those from the control group, that is, whether the treatment is effective or not. In such a study, it would be extremely valuable to make a decision based on early failures. In this paper, we consider independent progressively Type-II censored random samples from two populations with cumulative distribution function's (cdf) F(·)F(·) and G(·)G(·) respectively, and discuss a precedence test for testing the equality of the two distributions based on placements. For this purpose, we derive the joint distribution of the first l   placement statistics from the progressively censored sample from F(·)F(·). We then derive the exact null distribution of the precedence test statistic which is simply the sum of the placements. We provide the rejection regions for fixed levels of significance and various sample sizes and different progressive censoring schemes.  相似文献   

8.
A ridge function with shape function g   in the horizontal direction is a function of the form g(x)h(y,0)g(x)h(y,0). Along each horizontal line it has the shape g(x)g(x), multiplied by a function h(y,0)h(y,0) which depends on the y-value of the horizontal line. Similarly a ridge function with shape function g   in the vertical direction has the form g(y)h(x,π/2)g(y)h(x,π/2). For a given shape function g it may or may not be possible to represent an arbitrary   function f(x,y)f(x,y) as a superposition over all angles of a ridge function with shape g   in each direction, where h=hf=hf,gh=hf=hf,g depends on the functions f and g   and also on the direction, θ:h=hf,g(·,θ)θ:h=hf,g(·,θ). We show that if g   is Gaussian centered at zero then this is always possible and we give the function hf,ghf,g for a given f(x,y)f(x,y). For highpass or for odd shapes g  , we show it is impossible to represent an arbitrary f(x,y)f(x,y), i.e. in general there is no hf,ghf,g. Note that our problem is similar to tomography, where the problem is to invert the Radon transform, except that the use of the word inversion is here somewhat “inverted”: in tomography f(x,y)f(x,y) is unknown and we find it by inverting the projections of f  ; here, f(x,y)f(x,y) is known, g(z)g(z) is known, and hf(·,θ)=hf,g(·,θ)hf(·,θ)=hf,g(·,θ) is the unknown.  相似文献   

9.
10.
In this paper, we study a random field U?(t,x)U?(t,x) governed by some type of stochastic partial differential equations with an unknown parameter θθ and a small noise ??. We construct an estimator of θθ based on the continuous observation of N   Fourier coefficients of U?(t,x)U?(t,x), and prove the strong convergence and asymptotic normality of the estimator when the noise ?? tends to zero.  相似文献   

11.
Consider the model where there are II independent multivariate normal treatment populations with p×1p×1 mean vectors μiμi, i=1,…,Ii=1,,I, and covariance matrix ΣΣ. Independently the (I+1)(I+1)st population corresponds to a control and it too is multivariate normal with mean vector μI+1μI+1 and covariance matrix ΣΣ. Now consider the following two multiple testing problems.  相似文献   

12.
We consider the problem of estimating the mean θθ of an Np(θ,Ip)Np(θ,Ip) distribution with squared error loss ∥δ−θ∥2δθ2 and under the constraint ∥θ∥≤mθm, for some constant m>0m>0. Using Stein's identity to obtain unbiased estimates of risk, Karlin's sign change arguments, and conditional risk analysis, we compare the risk performance of truncated linear estimators with that of the maximum likelihood estimator δmleδmle. We obtain for fixed (m,p)(m,p) sufficient conditions for dominance. An asymptotic framework is developed, where we demonstrate that the truncated linear minimax estimator dominates δmleδmle, and where we obtain simple and accurate measures of relative improvement in risk. Numerical evaluations illustrate the effectiveness of the asymptotic framework for approximating the risks for moderate or large values of p.  相似文献   

13.
This article develops test statistics for the homogeneity of the means of several treatment groups of count data in the presence of over-dispersion or under-dispersion when there is no likelihood available. The C(α)C(α) or score type tests based on the models that are specified by only the first two moments of the counts are obtained using quasi-likelihood, extended quasi-likelihood, and double extended quasi-likelihood. Monte Carlo simulations are then used to study the comparative behavior of these C(α)C(α) statistics compared to the C(α)C(α) statistic based on a parametric model, namely, the negative binomial model, in terms of the following: size; power; robustness for departures from the data distribution as well as dispersion homogeneity. These simulations demonstrate that the C(α)C(α) statistic based on the double extended quasi-likelihood holds the nominal size at the 5% level well in all data situations, and it shows some edge in power over the other statistics, and, in particular, it performs much better than the commonly used statistic based on the quasi-likelihood. This C(α)C(α) statistic also shows robustness for moderate heterogeneity due to dispersion. Finally, applications to ecological, toxicological and biological data are given.  相似文献   

14.
EE-optimal designs for comparing three treatments in blocks of size three are identified, where intrablock observations are correlated according to a first order autoregressive error process with parameter ρ∈(0,1)ρ(0,1). For number of blocks b   of the form b=3n+1b=3n+1, there are two distinct optimal designs depending on the value of ρρ, with the best design being unequally replicated for large ρρ. For other values of bb, binary, equireplicate designs with specified within-block assignment patterns are best. In many cases, the stronger majorization optimality is established.  相似文献   

15.
Skew Dyck paths     
In this paper we study the class SS of skew Dyck paths, i.e. of those lattice paths that are in the first quadrant, begin at the origin, end on the x-axis, consist of up steps  U=(1,1)U=(1,1), down steps  D=(1,-1)D=(1,-1), and left steps  L=(−1,-1)L=(1,-1), and such that up steps never overlap with left steps. In particular, we show that these paths are equinumerous with several other combinatorial objects, we describe some involutions on this class, and finally we consider several statistics on SS.  相似文献   

16.
17.
Super-simple cyclic designs are useful on constructing codes and designs such as superimposed codes, perfect hash families and optical orthogonal codes with index two. In this paper, we show that there exists a super-simple cyclic (v,4,λ)(v,4,λ) for 7?v?417?v?41 and all admissible λλ with two definite exceptions of (v,λ)=(9,3),(13,5)(v,λ)=(9,3),(13,5) and one possible exception of (v,λ)=(39,18)(v,λ)=(39,18). Some useful algorithms are explained for computer search and new designs are displayed.  相似文献   

18.
We consider m×mm×m covariance matrices, Σ1Σ1 and Σ2Σ2, which satisfy Σ2-Σ1Σ2-Σ1=Δ, where ΔΔ has a specified rank. Maximum likelihood estimators of Σ1Σ1 and Σ2Σ2 are obtained when sample covariance matrices having Wishart distributions are available and rank(Δ)rank(Δ) is known. The likelihood ratio statistic for a test about the value of rank(Δ)rank(Δ) is also given and some properties of its null distribution are obtained. The methods developed in this paper are illustrated through an example.  相似文献   

19.
We consider paths in the plane with (1,01,0), (0,10,1), and (a,ba,b)-steps that start at the origin, end at height nn, and stay strictly to the left of a given non-decreasing right boundary. We show that if the boundary is periodic and has slope at most b/ab/a, then the ordinary generating function for the number of such paths ending at height n   is algebraic. Our argument is in two parts. We use a simple combinatorial decomposition to obtain an Appell relation or “umbral” generating function, in which the power znzn is replaced by a power series of the form znφn(z),znφn(z), where φn(0)=1.φn(0)=1. Then we convert (in an explicit way) the umbral generating function to an ordinary generating function by solving a system of linear equations and a polynomial equation. This conversion implies that the ordinary generating function is algebraic. We give several concrete examples, including an alternative way to solve the tennis ball problem.  相似文献   

20.
The enumeration of binary cyclic self-orthogonal codes of length 63 is used to prove that any cyclic quasi-symmetric 2-(63,15,35)2-(63,15,35) design with block intersection numbers x=3x=3 and y=7y=7 is isomorphic to the geometric design having as blocks the three-dimensional subspaces in PG(5,2)PG(5,2).  相似文献   

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