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1.
Consider the model where there are I independent multivariate normal treatment populations with p×1 mean vectors μi, i=1,…,I, and covariance matrix Σ. Independently the (I+1)st population corresponds to a control and it too is multivariate normal with mean vector μI+1 and covariance matrix Σ. Now consider the following two multiple testing problems. 相似文献
2.
We consider a linear regression model with regression parameter β=(β1,…,βp) and independent and identically N(0,σ2) distributed errors. Suppose that the parameter of interest is θ=aTβ where a is a specified vector. Define the parameter τ=cTβ-t where the vector c and the number t are specified and a and c are linearly independent. Also suppose that we have uncertain prior information that τ=0. We present a new frequentist 1-α confidence interval for θ that utilizes this prior information. We require this confidence interval to (a) have endpoints that are continuous functions of the data and (b) coincide with the standard 1-α confidence interval when the data strongly contradict this prior information. This interval is optimal in the sense that it has minimum weighted average expected length where the largest weight is given to this expected length when τ=0. This minimization leads to an interval that has the following desirable properties. This interval has expected length that (a) is relatively small when the prior information about τ is correct and (b) has a maximum value that is not too large. The following problem will be used to illustrate the application of this new confidence interval. Consider a 2×2 factorial experiment with 20 replicates. Suppose that the parameter of interest θ is a specified simple effect and that we have uncertain prior information that the two-factor interaction is zero. Our aim is to find a frequentist 0.95 confidence interval for θ that utilizes this prior information. 相似文献
3.
In this paper we study the class S 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), down steps D=(1,-1), and left steps 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 S. 相似文献
4.
E-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). For number of blocks b of the form b=3n+1, there are two distinct optimal designs depending on the value of ρ, with the best design being unequally replicated for large ρ. For other values of b, binary, equireplicate designs with specified within-block assignment patterns are best. In many cases, the stronger majorization optimality is established. 相似文献
5.
Linear and quadratic forms as well as other low degree polynomials play an important role in statistical inference. Asymptotic results and limit distributions are obtained for a class of statistics depending on μ+X, with X any random vector and μ non-random vector with ∥μ∥→+∞. This class contain the polynomials in μ+X. An application to the case of normal X is presented. This application includes a new central limit theorem which is connected with the increase of non-centrality for samples of fixed size. Moreover upper bounds for the suprema of the differences between exact and approximate distributions and their quantiles are obtained. 相似文献
6.
Alexander Kukush Andrii Malenko Hans Schneeweiss 《Journal of statistical planning and inference》2009
We consider a regression of y on x given by a pair of mean and variance functions with a parameter vector θ to be estimated that also appears in the distribution of the regressor variable x. The estimation of θ is based on an extended quasi-score (QS) function. We show that the QS estimator is optimal within a wide class of estimators based on linear-in-y unbiased estimating functions. Of special interest is the case where the distribution of x depends only on a subvector α of θ, which may be considered a nuisance parameter. In general, α must be estimated simultaneously together with the rest of θ, but there are cases where α can be pre-estimated. A major application of this model is the classical measurement error model, where the corrected score (CS) estimator is an alternative to the QS estimator. We derive conditions under which the QS estimator is strictly more efficient than the CS estimator. 相似文献
7.
We determine a credible set A that is the “best” with respect to the variation of the prior distribution in a neighborhood Γ of the starting prior π0(θ). Among the class of sets with credibility γ under π0, the “optimally robust” set will be the one which maximizes the minimum probability of including θ as the prior varies over Γ. This procedure is also Γ-minimax with respect to the risk function, probability of non-inclusion. We find the optimally robust credible set for three neighborhood classes Γ, the ε-contamination class, the density ratio class and the density bounded class. A consequence of this investigation is that the maximum likelihood set is seen to be an optimal credible set from a robustness perspective. 相似文献
8.
We consider Bayesian density estimation for compactly supported densities using Bernstein mixtures of beta-densities equipped with a Dirichlet prior on the distribution function. We derive the rate of convergence for α-smooth densities for 0<α?2 and show that a faster rate of convergence can be obtained by using fewer terms in the mixtures than proposed before. The Bayesian procedure adapts to the unknown value of α. The modified Bayesian procedure is rate-optimal if α is at most one. This result can be extended to two dimensions. 相似文献
9.
Consider the nonparametric location-scale regression model Y=m(X)+σ(X)ε, where the error ε is independent of the covariate X, and m and σ are smooth but unknown functions. The pair (X,Y) is allowed to be subject to selection bias. We construct tests for the hypothesis that 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
10.
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 x a stochastic process M(x;t), 0<t<r, is defined. Each mark process M(x;t) is compared with its expected value, say F(t;θ), to produce a discrepancy measure at x, where θ 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
11.
José Antonio Moler Fernando Plo Miguel San Miguel 《Journal of statistical planning and inference》2007
We study a randomized adaptive design to assign one of the L treatments to patients who arrive sequentially by means of an urn model. At each stage n, a reward is distributed between treatments. The treatment applied is rewarded according to its response, 0?Yn?1, and 1-Yn is distributed among the other treatments according to their performance until stage n-1. Patients can be classified in K+1 levels and we assume that the effect of this level in the response to the treatments is linear. We study the asymptotic behavior of the design when the ordinary least square estimators are used as a measure of performance until stage n-1. 相似文献
12.
Jonathan El Methni Laurent Gardes Stéphane Girard Armelle Guillou 《Journal of statistical planning and inference》2012
In Gardes et al. (2011), a new family of distributions is introduced, depending on two parameters τ and θ, which encompasses Pareto-type distributions as well as Weibull tail-distributions. Estimators for θ and extreme quantiles are also proposed, but they both depend on the unknown parameter τ, making them useless in practical situations. In this paper, we propose an estimator of τ which is independent of θ. Plugging our estimator of τ in the two previous ones allows us to estimate extreme quantiles from Pareto-type and Weibull tail-distributions in an unified way. The asymptotic distributions of our three new estimators are established and their efficiency is illustrated on a small simulation study and on a real data set. 相似文献
13.
In this paper, we study a random field U?(t,x) governed by some type of stochastic partial differential equations with an unknown parameter θ and a small noise ?. We construct an estimator of θ based on the continuous observation of N Fourier coefficients of U?(t,x), and prove the strong convergence and asymptotic normality of the estimator when the noise ? tends to zero. 相似文献
14.
Improving the estimators of the parameters of a probit regression model: A ridge regression approach
This paper considered the estimation of the regression parameters of a general probit regression model. Accordingly, we proposed five ridge regression (RR) estimators for the probit regression models for estimating the parameters (β) when the weighted design matrix is ill-conditioned and it is suspected that the parameter β may belong to a linear subspace defined by Hβ=h. Asymptotic properties of the estimators are studied with respect to quadratic biases, MSE matrices and quadratic risks. The regions of optimality of the proposed estimators are determined based on the quadratic risks. Some relative efficiency tables and risk graphs are provided to illustrate the numerical comparison of the estimators. We conclude that when q≥3, one would uses PRRRE; otherwise one uses PTRRE with some optimum size α. We also discuss the performance of the proposed estimators compare to the alternative ridge regression method due to Liu (1993). 相似文献
15.
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)-design and a g(n,e)-matrix are introduced to study designs of n factor two-level experiments which can unbiasedly estimate the mean, the n main effects and e 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)-matrices. A standard form for a g(n,1)-matrix is introduced and some lower and upper bounds on the absolute determinant value of a D-optimal g(n,1)-matrix in the class of all g(n,1)-matrices are obtained and an approach to construct D-optimal g(n,1)-matrices is given for 2?n?8. For two specific subclasses, namely a certain class of g(n,1)-matrices within the class of g(n,1)-matrices of index one and the class C(H) of g(8t+2,1)-matrices constructed from a normalized Hadamard matrix H of order 8t+4(t?1) two techniques for the construction of the restricted D-optimal matrices are given. 相似文献
16.
Suppose all events occurring in an unknown number (ν) of iid renewal processes, with a common renewal distribution F , are observed for a fixed time τ, where both ν and F are unknown. The individual processes are not known a priori, but for each event, the process that generated it is identified. For example, in software reliability application, the errors (or bugs) in a piece of software are not known a priori, but whenever the software fails, the error causing the failure is identified. We present a nonparametric method for estimating ν and investigate its properties. Our results show that the proposed estimator performs well in terms of bias and asymptotic normality, while the MLE of ν derived assuming that the common renewal distribution is exponential may be seriously biased if that assumption does not hold. 相似文献
17.
Joseph P.S. Kung Anna de Mier Xinyu Sun Catherine Yan 《Journal of statistical planning and inference》2009
We consider paths in the plane with (1,0), (0,1), and (a,b)-steps that start at the origin, end at height n, 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/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 zn is replaced by a power series of the form znφn(z), where 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
18.
In this paper, a k -step-stress accelerated life-testing is considered with an equal step duration τ. For small to moderate sample sizes, a practical modification is made to the model previously considered by Gouno et al. [2004. Optimal step-stress test under progressive Type-I censoring. IEEE Trans. Reliability 53, 383–393] in order to guarantee a feasible k -step-stress test under progressive Type-I censoring, and the optimal τ is determined under this model. Next, we discuss the determination of optimal τ under the condition that the step-stress test proceeds to the k -th stress level, and the efficiency of this conditional inference is compared to that of the previous case. In all cases considered, censoring is allowed at each point of stress change (viz., iτ, i=1,2,…,k). The determination of optimal τ is discussed under C-optimality, D-optimality, and A-optimality criteria. We investigate in detail the case of progressively Type-I right censored data from an exponential distribution with a single stress variable. 相似文献
19.
We consider m×m covariance matrices, Σ1 and Σ2, which satisfy Σ2-Σ1=Δ, where Δ has a specified rank. Maximum likelihood estimators of Σ1 and Σ2 are obtained when sample covariance matrices having Wishart distributions are available and rank(Δ) is known. The likelihood ratio statistic for a test about the value of 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
20.
Two fractional factorial designs are isomorphic if one can be obtained from the other by reordering the treatment combinations, relabelling the factor levels and relabelling the factors. By defining a word-pattern matrix, we are able to create a new isomorphism check which is much faster than existing checks for certain situations. We combine this with a new, extremely fast, sufficient condition for non-isomorphism to avoid checking certain cases. We then create a faster search algorithm by combining the Bingham and Sitter [1999. Minimum aberration fractional factorial split-plot designs. Technometrics 41, 62–70] search algorithm, the isomorphism check algorithm of Clark and Dean [2001. Equivalence of fractional factorial designs. Statist. Sinica 11, 537–547] with our proposed isomorphism check. The algorithm is used to extend the known set of existing non-isomorphic 128-run two-level regular designs with resolution ?4 to situations with 12, 13, 14, 15 and 16 factors, 256- and 512-run designs with resolution ?5 and ?17 factors and 1024-run even designs with resolution ?6 and ?18 factors. 相似文献