共查询到20条相似文献,搜索用时 343 毫秒
1.
Luc P. Devroye 《Revue canadienne de statistique》1978,6(2):179-191
If (X1,Y1), …, (Xn,Yn) is a sequence of independent identically distributed Rd × R-valued random vectors then Nadaraya (1964) and Watson (1964) proposed to estimate the regression function m(x) = ? {Y1|X1 = x{ by where K is a known density and {hn} is a sequence of positive numbers satisfying certain properties. In this paper a variety of conditions are given for the strong convergence to 0 of essXsup|mn (X)-m(X)| (here X is independent of the data and distributed as X1). The theorems are valid for all distributions of X1 and for all sequences {hn} satisfying hn → 0 and nh/log n→0. 相似文献
2.
Consider a given sequence {Tn} of estimators for a real-valued parameter θ. This paper studies asymptotic properties of restricted Bayes tests of the following form: reject H0:θ ≤ θ0 in favour of the alternative θ > θ0 if Tn ≤ Cn, where the critical point Cn is determined to minimize among all tests of this form the expected probability of error with respect to the prior distribution. Such tests may or may not be fully Bayes tests, and so are called Tn-Bayes. Under fairly broad conditions it is shown that and the Tn-Bayes risk where an is the order of the standard error of Tn, - is the prior density, and μ is the median of F, the limit distribution of (Tn – θ)/anb(θ). Several examples are given. 相似文献
3.
Lanh Tat Tran 《Revue canadienne de statistique》1991,19(4):371-387
Let X1 be a strictly stationary multiple time series with values in Rd and with a common density f. Let X1,.,.,Xn, be n consecutive observations of X1. Let k = kn, be a sequence of positive integers, and let Hni be the distance from Xi to its kth nearest neighbour among Xj, j i. The multivariate variable-kernel estimate fn, of f is defined by where K is a given density. The complete convergence of fn, to f on compact sets is established for time series satisfying a dependence condition (referred to as the strong mixing condition in the locally transitive sense) weaker than the strong mixing condition. Appropriate choices of k are explicitly given. The results apply to autoregressive processes and bilinear time-series models. 相似文献
4.
We consider n pairs of random variables (X11,X21),(X12,X22),… (X1n,X2n) having a bivariate elliptically contoured density of the form where θ1 θ2 are location parameters and Δ = ((λik)) is a 2 × 2 symmetric positive definite matrix of scale parameters. The exact distribution of the Pearson product-moment correlation coefficient between X1 and X2 is obtained. The usual case when a sample of size n is drawn from a bivariate normal population is a special case of the abovementioned model. 相似文献
5.
Bernard Clement 《Revue canadienne de statistique》1975,3(2):203-222
The problem of estimating the effects in a balanced two-way classification with interaction \documentclass{article}\pagestyle{empty}\begin{document}$i = 1, \ldots ,I;j = 1, \ldots ,J;k = 1, \ldots ,K$\end{document} using a random effect model is considered from a Bayesian view point. Posterior distributions of ri, cj and tij are obtained under the assumptions that ri, cj, tij and eijk are all independently drawn from normal distributions with zero meansand variances \documentclass{article}\pagestyle{empty}\begin{document}$\sigma _r^2 ,\sigma _c^2 ,\sigma _t^2 ,\sigma _e^2$\end{document} respectively. A non informative reference prior is adopted for \documentclass{article}\pagestyle{empty}\begin{document}$\mu ,\sigma _r^2 ,\sigma _c^2 ,\sigma _t^2 ,\sigma _e^2$\end{document}. Various features of thisposterior distribution are obtained. The same features of the psoterior distribution for a fixed effect model are also obtained. A numerical example is given. 相似文献
6.
Alain Boulanger 《Revue canadienne de statistique》1983,11(4):265-269
For X1, …, XN a random sample from a distribution F, let the process SδN(t) be defined as where K2N = σNi=1(ci ? c?)2 and R xi, + Δd, is the rank of Xi + Δdi, among X1 + Δd1, …, XN + ΔdN. The purpose of this note is to prove that, under certain regularity conditions on F and on the constants ci and di, SΔN (t) is asymptotically approximately a linear function of Δ, uniformly in t and in Δ, |Δ| ≤ C. The special case of two samples is considered. 相似文献
7.
What is the interpretation of a confidence interval following estimation of a Box-Cox transformation parameter λ? Several authors have argued that confidence intervals for linear model parameters ψ can be constructed as if λ. were known in advance, rather than estimated, provided the estimand is interpreted conditionally given $\hat \lambda$. If the estimand is defined as $\psi \left( {\hat \lambda } \right)$, a function of the estimated transformation, can the nominal confidence level be regarded as a conditional coverage probability given $\hat \lambda$, where the interval is random and the estimand is fixed? Or should it be regarded as an unconditional probability, where both the interval and the estimand are random? This article investigates these questions via large-n approximations, small- σ approximations, and simulations. It is shown that, when model assumptions are satisfied and n is large, the nominal confidence level closely approximates the conditional coverage probability. When n is small, this conditional approximation is still good for regression models with small error variance. The conditional approximation can be poor for regression models with moderate error variance and single-factor ANOVA models with small to moderate error variance. In these situations the nominal confidence level still provides a good approximation for the unconditional coverage probability. This suggests that, while the estimand may be interpreted conditionally, the confidence level should sometimes be interpreted unconditionally. 相似文献
8.
Günter M. T. Weiss 《Revue canadienne de statistique》1985,13(4):317-324
We consider the estimation of a location parameter θ in a one-sample problem. A measure of the asymptotic performance of an estimator sequence {Tn} = T is given by the exponential rate of convergence to zero of the tail probability, which for consistent estimator sequences is bounded by a constant, B (θ, ?), called the Bahadur bound. We consider two consistent estimators: the maximum-likelihood estimator (mle) and a consistent estimator based on a likelihood-ratio statistic, which we call the probability-ratio estimator (pre). In order to compare the local behaviour of these estimators, we obtain Taylor series expansions in ? for B (θ, ?) and the exponential rates of the mle and pre. Finally, some numerical work is presented in which we consider a variety of underlying distributions. 相似文献
9.
R. Ponnapalli 《Revue canadienne de statistique》1976,4(1):33-50
Suppose the multinomial parameters pr (θ) are functions of a real valued parameter 0, r = 1,2, …, k. A minimum discrepancy (m.d.) estimator θ of θ is defined as one which minimises the discrepancy function D = Σ nrf(pr/nr), for a suitable function f where nr is the relative frequency in r-th cell, r = 1,2, …, k. All the usual estimators like maximum likelihood (m. l), minimum chi-square (m. c. s.)., etc. are m.d. estimators. All m.d. estimators have the same asymptotic (first order) efficiency. They are compared on the basis of their deficiencies, a concept recently introduced by Hodges and Lehmann [2]. The expression for least deficiency at any θ is derived. It is shown that in general uniformly least deficient estimators do not exist. Necessary and sufficient conditions on pr (0) for m. t. and m. c. s. estimators to be uniformly least deficient are obtained. 相似文献
10.
The problem of nonparametric estimation of a probability density function when the sample observations are contaminated with random noise is studied. A particular estimator f?n(x) is proposed which uses kernel-density and deconvolution techniques. The estimator f?n(x) is shown to be uniformly consistent, and its appearance and properties are affected by constants Mn and hn which the user may choose. The optimal choices of Mn and hn depend on the sample size n, the noise distribution, and the true distribution which is being estimated. Particular selections for Mn and hn which minimize upper-bound functions of the mean squared error for f?n(x) are recommended. 相似文献
11.
Chandrakant M. Deo 《Revue canadienne de statistique》1978,6(1):91-94
Let (Sn) be partial sums of a non-degenerate sequence of Identically and independently distributed random variables taking values in a separable Hilbert space. Then for 0 ≤ β ≤ 3/2, the series converges almost nowhere. For β > 3/2 this may not be true. 相似文献
12.
M. Ahsanullah 《Statistical Papers》1988,29(1):151-157
Suppose X1, X2, ..., Xm is a random sample of size m from a population with probability density function f(x), x>0 and let X1,m<...m,m be the corresponding order statistics. We assume m as an integer valued random variable with P(m=k)=p(1?p)k?1, k=1, 2, ... and 0 and n X1,n for fixed n characterizes the exponential distribution. In this paper we prove that under the assumption of monotone hazard rate the identical distribution of and (n?r+1) (Xr,n?Xr?1,n) for some fixed r and n with 1≤r≤n, n≥2, X0,n=0, characterizes the exponential distribution. Under the assumption of monotone hazard rate the conjecture of Kakosyan, Klebanov and Melamed follows from the above result with r=1. 相似文献
13.
N. Balakrishnan 《统计学通讯:理论与方法》2013,42(5):880-906
In this article, we establish several recurrence relations for the single and product moments of progressively Type-II right censored order statistics from a log-logistic distribution. The use of these relations in a systematic recursive manner would enable the computation of all the means, variances and covariances of progressively Type-II right censored order statistics from the log-logistic distribution for all sample sizes n, effective sample sizes m, and all progressive censoring schemes (R 1,…, R m ). The results established here generalize the corresponding results for the usual order statistics due to Balakrishnan and Malik (1987) and Balakrishnan et al. (1987). The moments so determined are then utilized to derive best linear unbiased estimators for the scale- and location-scale log-logistic distributions. A comparison of these estimates with the maximum likelihood estimates is made through Monte Carlo simulation. The best linear unbiased predictors of progressively censored failure times is then discussed briefly. Finally, a numerical example is presented to illustrate all the methods of inference developed here. 相似文献
14.
Ronald Pyke 《Revue canadienne de statistique》1984,12(4):241-264
Two processes of importance in statistics and probability are the empirical and partial-sum processes. Based on d-dimensional data X1, … Xa the empirical measure is defined for any A ⊂ Rd by the sample proportion of observations in A. When normalized, Fn yields the empirical process Wn: = n1/2 (Fn - F), where F denotes the “true” probability measure. To define partial-sum processes, one needs data that are assigned to specified locations (in contrast to the above, where specified unit masses are assigned to random locations). A suitable context for many applications is that of data attached to points of a lattice, say {Xj:j ϵ Jd} where J = {1, 2,…}, for which the partial sums are defined for any A ⊂ Rd by Thus S(A) is the sum of the data contained in A. When normalized, S yields the partial-sum process. This paper provides an overview of asymptotic results for empirical and partial-sum processes, including strong laws and central limit theorems, together with some indications of their inferential implications. 相似文献
15.
Consider two independent random samples of size f + 1 , one from an N (μ1, σ21) distribution and the other from an N (μ2, σ22) distribution, where σ21/σ22∈ (0, ∞) . The Welch ‘approximate degrees of freedom’ (‘approximate t‐solution’) confidence interval for μ1?μ2 is commonly used when it cannot be guaranteed that σ21/σ22= 1 . Kabaila (2005, Comm. Statist. Theory and Methods 34 , 291–302) multiplied the half‐width of this interval by a positive constant so that the resulting interval, denoted by J0, has minimum coverage probability 1 ?α. Now suppose that we have uncertain prior information that σ21/σ22= 1. We consider a broad class of confidence intervals for μ1?μ2 with minimum coverage probability 1 ?α. This class includes the interval J0, which we use as the standard against which other members of will be judged. A confidence interval utilizes the prior information substantially better than J0 if (expected length of J)/(expected length of J0) is (a) substantially less than 1 (less than 0.96, say) for σ21/σ22= 1 , and (b) not too much larger than 1 for all other values of σ21/σ22 . For a given f, does there exist a confidence interval that satisfies these conditions? We focus on the question of whether condition (a) can be satisfied. For each given f, we compute a lower bound to the minimum over of (expected length of J)/(expected length of J0) when σ21/σ22= 1 . For 1 ?α= 0.95 , this lower bound is not substantially less than 1. Thus, there does not exist any confidence interval belonging to that utilizes the prior information substantially better than J0. 相似文献
16.
If {Xn} is an irreducible aperiodic Markov chain on a state apace denote the mean one step change of position, or “drift”, of {Xn} at j. The main result of this note is to show that, when |µ(j)| is bounded, {Xn} admits a stationary distribution {πj}if and only if for some N > 0 and some state i, lim inf ∑when this holds, the limit infimum is in fact . Many of the known sufficient or necessary criteria for the existence of a stationary distribution can then be derived easily from this and related results. 相似文献
17.
Javier Roio 《统计学通讯:理论与方法》2013,42(12):3745-3748
Let X1, …,Xn be a random sample from a normal distribution with mean θ and variance σ2 The problem is to estimate θ with loss function L(θ,e) = v(e-θ) where v(x) = b(exp(ax)-ax-l) and where a, b are constants with b>0, a¦0. Zellner (1986), showed that [Xbar] ? σ2a/2n dominates [Xbar] and hence [Xbar] is inadmissible. The question of what values of c and d render c[Xbar]+ d admissible is studied here. 相似文献
18.
The authors derive the null and non-null distributions of the test statistic v=ymin/ymax (where ymin= min xij, ymax= max xij, J=1,2, …, k) connected with testing the equality of scale parameters θ1, θ2, …θk in certain, class of density functions given by 相似文献
19.
We introduce a modified version ?nof the piecewiss linear hisiugrimi uf Beirlant et al. (1998) which is a true probability density, i.e., ?n[d] 0 and [d]?n=1. We prove that ?nestimates the underlying densitv ? strongly consistently in the L1mmn, derive large deviation inequalities for the t\ error \?n- f\ and prove that £||/"-/|| tends to zero with the rate n -1\3, We also show that the derivative lf'n estimates consistently in ine expected Lx error the derivative/ of sufficiently smooth density and evaluate the rate of convergence n-i/5 for Epf'n -f'% The estimator/" thus enables to approximate/in the Besov space with a guaranteed rate of convergence. Optimization of the smoothing parameter is also studied. The theoretical or experimentally approximated values of the expected errors E\\?n- f\\ and E||2?'n-?' are compared with tiie errors aCiiieveu u-y t"e histogram of Beirlant et ah, and other nonparametric methods. 相似文献
20.
Antonio Cuevas Wenceslao González-Manteiga Alberto Rodríguez-Casal 《Australian & New Zealand Journal of Statistics》2006,48(1):7-19
Given an unknown function (e.g. a probability density, a regression function, …) f and a constant c, the problem of estimating the level set L(c) ={f≥c} is considered. This problem is tackled in a very general framework, which allows f to be defined on a metric space different from . Such a degree of generality is motivated by practical considerations and, in fact, an example with astronomical data is analyzed where the domain of f is the unit sphere. A plug‐in approach is followed; that is, L(c) is estimated by Ln(c) ={fn≥c} , where fn is an estimator of f. Two results are obtained concerning consistency and convergence rates, with respect to the Hausdorff metric, of the boundaries ?Ln(c) towards ?L(c) . Also, the consistency of Ln(c) to L(c) is shown, under mild conditions, with respect to the L1 distance. Special attention is paid to the particular case of spherical data. 相似文献