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1.

We consider the regression model yi = ?(xi ) + ε in which the function ? or its pth derivative ?(p) may have a discontinuity at some unknown point τ. By fitting local polynomials from the left and right, we test the null that ?(p) is continuous against the alternative that ?(p)(τ?) ≠ ?(p)(τ+). We obtain Darling-Erdös type limit theorems for the test statistics under the null hypothesis of no change, as well as their limits in probability under the alternative. Consistency of the related change-point estimators is also established.  相似文献   

2.
We describe some simple methods for improving the performance of stationarity tests (i.e., tests that have a stationary null and a unit-root alternative). Specifically, we increase the rate of convergence of the test under the unit-root alternative from O p(T) to O p (T 2), then suggest an optimal method of selecting the order of the autoregressive component in the fitted autoregressive integrated moving average model on which the test is based. Simulation evidence suggests that these modifications work well. We apply the modified procedure to U.S. monthly macroeconomic data and uncover new evidence of a unit root in unemployment.  相似文献   

3.
We study the problem of approximating a stochastic process Y = {Y(t: tT} with known and continuous covariance function R on the basis of finitely many observations Y(t 1,), …, Y(t n ). Dependent on the knowledge about the mean function, we use different approximations ? and measure their performance by the corresponding maximum mean squared error sub t∈T E(Y(t) ? ?(t))2. For a compact T ? ? p we prove sufficient conditions for the existence of optimal designs. For the class of covariance functions on T 2 = [0, 1]2 which satisfy generalized Sacks/Ylvisaker regularity conditions of order zero or are of product type, we construct sequences of designs for which the proposed approximations perform asymptotically optimal.  相似文献   

4.
We provide general conditions to ensure the valid Laplace approximations to the marginal likelihoods under model misspecification, and derive the Bayesian information criteria including all terms of order Op(1). Under conditions in theorem 1 of Lv and Liu [J. R. Statist. Soc. B, 76, (2014), 141–167] and a continuity condition for prior densities, asymptotic expansions with error terms of order op(1) are derived for the log-marginal likelihoods of possibly misspecified generalized linear models. We present some numerical examples to illustrate the finite sample performance of the proposed information criteria in misspecified models.  相似文献   

5.
In this paper, by considering a (3n+1) -dimensional random vector (X0, XT, YT, ZT)T having a multivariate elliptical distribution, we derive the exact joint distribution of (X0, aTX(n), bTY[n], cTZ[n])T, where a, b, c∈?n, X(n)=(X(1), …, X(n))T, X(1)<···<X(n), is the vector of order statistics arising from X, and Y[n]=(Y[1], …, Y[n])T and Z[n]=(Z[1], …, Z[n])T denote the vectors of concomitants corresponding to X(n) ((Y[r], Z[r])T, for r=1, …, n, is the vector of bivariate concomitants corresponding to X(r)). We then present an alternate approach for the derivation of the exact joint distribution of (X0, X(r), Y[r], Z[r])T, for r=1, …, n. We show that these joint distributions can be expressed as mixtures of four-variate unified skew-elliptical distributions and these mixture forms facilitate the prediction of X(r), say, based on the concomitants Y[r] and Z[r]. Finally, we illustrate the usefulness of our results by a real data.  相似文献   

6.
We consider the specific transformation of a Wiener process {X(t), t ≥ 0} in the presence of an absorbing barrier a that results when this process is “time-locked” with respect to its first passage time T a through a criterion level a, and the evolution of X(t) is considered backwards (retrospectively) from T a . Formally, we study the random variables defined by Y(t) ≡ X(T a  ? t) and derive explicit results for their density and mean, and also for their asymptotic forms. We discuss how our results can aid interpretations of time series “response-locked” to their times of crossing a criterion level.  相似文献   

7.
Abstract

We introduce here the truncated version of the unified skew-normal (SUN) distributions. By considering a special truncations for both univariate and multivariate cases, we derive the joint distribution of consecutive order statistics X(r, ..., r + k) = (X(r), ..., X(r + K))T from an exchangeable n-dimensional normal random vector X. Further we show that the conditional distributions of X(r + j, ..., r + k) given X(r, ..., r + j ? 1), X(r, ..., r + k) given (X(r) > t)?and X(r, ..., r + k) given (X(r + k) < t) are special types of singular SUN distributions. We use these results to determine some measures in the reliability theory such as the mean past life (MPL) function and mean residual life (MRL) function.  相似文献   

8.
《随机性模型》2013,29(2):157-190
In this paper, we establish an explicit form of matrix decompositions for the queue length distributions of the MAP/G/1 queues under multiple and single vacations with N-policy. We show that the vector generating function Y (z) of the queue length at an arbitrary time and X (z) at departures are decomposed into Y (z) = p idle (z Y (z) and X (z) = p idle (z X (z) where p idle (z) is the vector generating function of the queue length at an arbitrary epoch at which the server is not in service, and ζ Y (z) and ζ X (z) are unidentified matrix generating functions.  相似文献   

9.
Yo Sheena † 《Statistics》2013,47(5):371-379
We consider the estimation of Σ of the p-dimensional normal distribution Np (0, Σ) when Σ?=?θ0 Ip ?+?θ1 aa′, where a is an unknown p-dimensional normalized vector and θ0?>?0, θ1?≥?0 are also unknown. First, we derive the restricted maximum likelihood (REML) estimator. Second, we propose a new estimator, which dominates the REML estimator with respect to Stein's loss function. Finally, we carry out Monte Carlo simulation to investigate the magnitude of the new estimator's superiority.  相似文献   

10.
11.
Consider an inhomogeneous Poisson process X on [0, T] whose unk-nown intensity function “switches” from a lower function g* to an upper function h* at some unknown point ?* that has to be identified. We consider two known continuous functions g and h such that g*(t) ? g(t) < h(t) ? h*(t) for 0 ? t ? T. We describe the behavior of the generalized likelihood ratio and Wald’s tests constructed on the basis of a misspecified model in the asymptotics of large samples. The power functions are studied under local alternatives and compared numerically with help of simulations. We also show the following robustness result: the Type I error rate is preserved even though a misspecified model is used to construct tests.  相似文献   

12.
13.
The Fisher exact test has been unjustly dismissed by some as ‘only conditional,’ whereas it is unconditionally the uniform most powerful test among all unbiased tests, tests of size α and with power greater than its nominal level of significance α. The problem with this truly optimal test is that it requires randomization at the critical value(s) to be of size α. Obviously, in practice, one does not want to conclude that ‘with probability x the we have a statistical significant result.’ Usually, the hypothesis is rejected only if the test statistic's outcome is more extreme than the critical value, reducing the actual size considerably.

The randomized unconditional Fisher exact is constructed (using Neyman–structure arguments) by deriving a conditional randomized test randomizing at critical values c(t) by probabilities γ(t), that both depend on the total number of successes T (the complete-sufficient statistic for the nuisance parameter—the common success probability) conditioned upon.

In this paper, the Fisher exact is approximated by deriving nonrandomized conditional tests with critical region including the critical value only if γ (t) > γ0, for a fixed threshold value γ0, such that the size of the unconditional modified test is for all value of the nuisance parameter—the common success probability—smaller, but as close as possible to α. It will be seen that this greatly improves the size of the test as compared with the conservative nonrandomized Fisher exact test.

Size, power, and p value comparison with the (virtual) randomized Fisher exact test, and the conservative nonrandomized Fisher exact, Pearson's chi-square test, with the more competitive mid-p value, the McDonald's modification, and Boschloo's modifications are performed under the assumption of two binomial samples.  相似文献   

14.
Inthis paper we build on previous work for estimation of the bivariatedistribution of the time variables T 1 and T 2when they are observable only on the condition that one of thetime variables, say T 1, is greater than (left-truncation)or less than (right truncation) some observed time variable C 1.In this paper, we introduce several results based on the InfluenceCurve (which we derive in this paper) of the NPMLE of the distributionF of (T 1,T 2) developed by van derLaan (van der Laan, 1996). Specifically we will: prove that theNPMLE is asymptotically equivalent to an estimator developedby Gürler (Gürler, 1997), derive the asymptotic distributionof the NPMLE based on its Influence Curve, present tests to determinethe amount of dependence between T 1 and T 2,present the results of simulation studies that compare the NPMLEand Gürler's estimator and evaluate the performance of boththe above mentioned tests and confidence intervals of Fbased on the asymptotic distribution of the NPMLE, and finallywe will apply the methods in a data analysis in which we alsopoint out practical issues that arise in the implementation ofthe estimator.  相似文献   

15.
A new statistic, (p), is developed for variable selection in a system-of-equations model. The standardized total mean square error in the (p)statistic is weighted by the covariance matrix of dependent variables instead of the error covariance matrix of the true model as in the original definition. The new statistic can be also used for model selection in the non-nested models. The estimate of (p), SC(p), is derived and shown to become SCε(p) in the similar form of Cp in a single-equation model when the covariance matrix of sampled dependent variables is replaced by the error covariance matrix under the full model.  相似文献   

16.
ABSTRACT

Let T1: n ? T2: n ? ??? ? Tn: n be ordered lifetimes of components of a parallel system. In this article, the α-quantile past lifetime from the failure of the component with lifetime Tr: n provided that the system has failed at or before time t has been introduced. Then, some properties of this measure have been studied.  相似文献   

17.
In analyzing the lifetime properties of a coherent system, the concept of “signature” is a useful tool. Let T be the lifetime of a coherent system having n iid components. The signature of the system is a probability vector s=(s1, s2, …, sn), such that si=P(T=Xi:n), where, Xi:n, i=1, 2, …, n denote the ordered lifetimes of the components. In this note, we assume that the system is working at time t>0. We consider the conditional signature of the system as a vector in which the ith element is defined as pi(t)=P(T=Xi:n|T>t) and investigate its properties as a function of time.  相似文献   

18.
In this article, we study the joint distribution of X and two linear combinations of order statistics, a T Y (2) and b T Y (2), where a = (a 1, a 2) T and b = (b 1, b 2) T are arbitrary vectors in R 2 and Y (2) = (Y (1), Y (2)) T is a vector of ordered statistics obtained from (Y 1, Y 2) T when (X, Y 1, Y 2) T follows a trivariate normal distribution with a positive definite covariance matrix. We show that this distribution belongs to the skew-normal family and hence our work is a generalization of Olkin and Viana (J Am Stat Assoc 90:1373–1379, 1995) and Loperfido (Test 17:370–380, 2008).  相似文献   

19.
ABSTRACT

In this article, we consider a (k + 1)n-dimensional elliptically contoured random vector (XT1, X2T, …, XTk, ZT)T = (X11, …, X1n, …, Xk1, …, Xkn, Z1, …, Zn)T and derive the distribution of concomitant of multivariate order statistics arising from X1, X2, …, Xk. Specially, we derive a mixture representation for concomitant of bivariate order statistics. The joint distribution of the concomitant of bivariate order statistics is also obtained. Finally, the usefulness of our result is illustrated by a real-life data.  相似文献   

20.
Following the paper by Genton and Loperfido [Generalized skew-elliptical distributions and their quadratic forms, Ann. Inst. Statist. Math. 57 (2005), pp. 389–401], we say that Z has a generalized skew-normal distribution, if its probability density function (p.d.f.) is given by f(z)=2φ p (z; ξ, Ω)π (z?ξ), z∈? p , where φ p (·; ξ, Ω) is the p-dimensional normal p.d.f. with location vector ξ and scale matrix Ω, ξ∈? p , Ω>0, and π is a skewing function from ? p to ?, that is 0≤π (z)≤1 and π (?z)=1?π (z), ? z∈? p . First the distribution of linear transformations of Z are studied, and some moments of Z and its quadratic forms are derived. Next we obtain the joint moment-generating functions (m.g.f.’s) of linear and quadratic forms of Z and then investigate conditions for their independence. Finally explicit forms for the above distributions, m.g.f.’s and moments are derived when π (z)=κ (αz), where α∈? p and κ is the normal, Laplace, logistic or uniform distribution function.  相似文献   

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