共查询到20条相似文献,搜索用时 31 毫秒
1.
K.A. Bush 《Journal of statistical planning and inference》1979,3(4):387-394
By a family of designs we mean a set of designs whose parameters can be represented as functions of an auxiliary variable t where the design will exist for infinitely many values of t. The best known family is probably the family of finite projective planes with υ = b = t2 + t + 1, r = k = t + 1, and λ = 1. In some instances, notably coding theory, the existence of families is essential to provide the degree of precision required which can well vary from one coding problem to another. A natural vehicle for developing binary codes is the class of Hadamard matrices. Bush (1977) introduced the idea of constructing semi-regular designs using Hadamard matrices whereas the present study is concerned mostly with construction of regular designs using Hadamard matrices. While codes constructed from these designs are not optimal in the usual sense, it is possible that they may still have substantial value since, with different values of λ1 and λ2, there are different error correcting capabilities. 相似文献
2.
The generalized lambda distribution, GLD(λ1, λ2 λ3, λ4), is a four-parameter family that has been used for fitting distributions to a wide variety of data sets. The analysis of the λ3 and λ4 values that actually yield valid distributions has (until now) been incomplete. Moreover, because of computational problems and theoretical shortcomings, the moment space over which the GLD can be applied has been limited. This paper completes the analysis of the λ3 and λ4 values that are associated with valid distributions, improves previous computational methods to reduce errors associated with fitting data, expands the parameter space over which the GLD can be used, and uses a four-parameter generalized beta distribution to cover the portion of the parameter space where the GLD is not applicable. In short, the paper extends the GLD to an EGLD system that can be used for fitting distributions to data sets that that are cited in the literature as actually occurring in practice. Examples of use of the proposed system are included 相似文献
3.
In this article, a semi-Markovian random walk with delay and a discrete interference of chance (X(t)) is considered. It is assumed that the random variables ζ n , n = 1, 2,…, which describe the discrete interference of chance form an ergodic Markov chain with ergodic distribution which is a gamma distribution with parameters (α, λ). Under this assumption, the asymptotic expansions for the first four moments of the ergodic distribution of the process X(t) are derived, as λ → 0. Moreover, by using the Riemann zeta-function, the coefficients of these asymptotic expansions are expressed by means of numerical characteristics of the summands, when the process considered is a semi-Markovian Gaussian random walk with small drift β. 相似文献
4.
Michael D. Huffman 《统计学通讯:理论与方法》2013,42(12):3063-3074
Suppose two Poisson processes with rates γ1 and γ2 are observed for fixed times tl and t2. This paper considers hypothesis tests and confidence intervals for the parameter ρ = γ2/γ1. Uniformly most powerful unbiased tests and uniformly most accurate unbiased confidence intervals exist for ρ, but they require randomization and so are not used in practice. Several alternative procedures have been proposed. In the context of one-sided hypothesis tests these procedures are reviewed and compared on numerical grounds and by use of the conditionality and repeated sampling principles. It is argued that a conditional binomial test which rejects with conditional level closest to but not necessarily less than, the nominal a is the most reasonable. This test is different from the usual conditional binomial test which rejects with conditional level closeset to but less than or equal to the nominal α Numerical results indicate that an approximate procedure based on the Poisson variance stabilizing transformation has properties similar to the preferred conditional binomial test. Values for λ1 = t1λ1 required to achieve a specified power are considered. These results are also discussed in terms of test inversion to obtain confidence intervals. 相似文献
5.
Asatoshi Maeshiro 《统计学通讯:理论与方法》2013,42(4):1185-1204
This study reveals that contrary to the conventional wisdom among econometricians, the bias of the OLS estimator can be quite small when the estimator is applied to a geometrically distributed lag model, yt<ce:glyph name="dbnd6"/> α + βx t+ λy t-1. + ut, with autocorrelated disturbances, be they AR(1), MA(1), MA(2), AR(2), and ARMA(1,1). This happens when λ is large and xtis smoothly trended (e.g., a real GNP series). In fact, the bias of the OLS estimator becomes zero at one parameter combination, and the OLS estimator performs well over a wide range around this parameter combination. By decomposing the disturbance term into two parts, the paper also explains why OLS shows such an unexpected property. These findings have both pedagogical and practical significance. 相似文献
6.
Goodness-of-Fit of the Distribution of Time-to-First-Occurrence in Recurrent Event Models 总被引:1,自引:1,他引:0
Imperfect repair models are a class of stochastic models that deal with recurrent phenomena. This article focuses on the Block, Borges, and Savits (1985) age-dependent minimal repair model (the BBS model) in which a system that fails at time t undergoes one of two types of repair: with probability p(t), a perfect repair is performed, or with probability 1-p(t), a minimal repair is performed. The goodness-of-fit problem of interest concerns the initial distribution of the failure ages. In particular, interest is on testing the null hypothesis that the hazard rate function of the time-to-first-event-occurrence, λ(·), is equal to a prespecified hazard rate function λ0(·). This paper extends the class of hazard-based smooth goodness-of-fit tests introduced in Peña (1998a) to the case where data accrual is from a BBS model. The goodness-of-fit tests are score tests derived by reformulating Neyman's idea of smooth tests in terms of hazard functions. Omnibus as well as directional tests are developed and simulation results are presented to illustrate the sensitivities of the proposed tests for certain types of alternatives. 相似文献
7.
John P. Mandeli F.-C.Helen Lee Walter T. Federer 《Journal of statistical planning and inference》1981,5(3):267-272
Complete sets of orthogonal F-squares of order n = sp, where g is a prime or prime power and p is a positive integer have been constructed by Hedayat, Raghavarao, and Seiden (1975). Federer (1977) has constructed complete sets of orthogonal F-squares of order n = 4t, where t is a positive integer. We give a general procedure for constructing orthogonal F-squares of order n from an orthogonal array (n, k, s, 2) and an OL(s, t) set, where n is not necessarily a prime or prime power. In particular, we show how to construct sets of orthogonal F-squares of order n = 2sp, where s is a prime or prime power and p is a positive integer. These sets are shown to be near complete and approach complete sets as s and/or p become large. We have also shown how to construct orthogonal arrays by these methods. In addition, the best upper bound on the number t of orthogonal F(n, λ1), F(n, λ2), …, F(n, λ1) squares is given. 相似文献
8.
Shiue and Bain proposed an approximate F statistic for testing equality of two gamma distribution scale parameters in presence of a common and unknown shape parameter. By generalizing Shiue and Bain's statistic we develop a new statistic for testing equality of L >= 2 gamma distribution scale parameters. We derive the distribution of the new statistic ESP for L = 2 and equal sample size situation. For other situations distribution of ESP is not known and test based on the ESP statistic has to be performed by using simulated critical values. We also derive a C(α) statistic CML and develop a likelihood ratio statistic, LR, two modified likelihood ratio statistics M and MLB and a quadratic statistic Q. The distribution of each of the statistics CML, LR, M, MLB and Q is asymptotically chi-square with L - 1 degrees of freedom. We then conducted a monte-carlo simulation study to compare the perfor- mance of the statistics ESP, LR, M, MLB, CML and Q in terms of size and power. The statistics LR, M, MLB and Q are in general liberal and do not show power advantage over other statistics. The statistic CML, based on its asymptotic chi-square distribution, in general, holds nominal level well. It is most powerful or nearly most powerful in most situations and is simple to use. Hence, we recommend the statistic CML for use in general. For better power the statistic ESP, based on its empirical distribution, is recommended for the special situation for which there is evidence in the data that λ1 < … < λL and n1 < … < nL, where λ1 …, λL are the scale parameters and n1,…, nL are the sample sizes. 相似文献
9.
Nonparametric regression techniques such as spline smoothing and local fitting depend implicitly on a parametric model. For instance, the cubic smoothing spline estimate of a regression function ∫ μ based on observations ti, Yi is the minimizer of Σ{Yi ‐ μ(ti)}2 + λ∫(μ′′)2. Since ∫(μ″)2 is zero when μ is a line, the cubic smoothing spline estimate favors the parametric model μ(t) = αo + α1t. Here the authors consider replacing ∫(μ″)2 with the more general expression ∫(Lμ)2 where L is a linear differential operator with possibly nonconstant coefficients. The resulting estimate of μ performs well, particularly if Lμ is small. They present an O(n) algorithm for the computation of μ. This algorithm is applicable to a wide class of L's. They also suggest a method for the estimation of L. They study their estimates via simulation and apply them to several data sets. 相似文献
10.
We propose a robust Kalman filter (RKF) to estimate the true but hidden return when microstructure noise is present. Following Zhou's definition, we assume the observed return Yt is the result of adding microstructure noise to the true but hidden return Xt. Microstructure noise is assumed to be independent and identically distributed (i.i.d.); it is also independent of Xt. When Xt is sampled from a geometric Brownian motion process to yield Yt, the Kalman filter can produce optimal estimates of Xt from Yt. However, the covariance matrix of microstructure noise and that of Xt must be known for this claim to hold. In practice, neither covariance matrix is known so they must be estimated. Our RKF, in contrast, does not need the covariance matrices as input. Simulation results show that the RKF gives essentially identical estimates to the Kalman filter, which has access to the covariance matrices. As applications, estimated Xt can be used to estimate the volatility of Xt. 相似文献
11.
Ram C. Dahiya 《统计学通讯:理论与方法》2013,42(2):113-120
Moment estimators for parameters in a truncated bivariate Poisson distribution are derived in Hamdan (1972) for the special case of λ1 = λ2, Where λ1, λ2 are the marginal means. Here we derive the maximum likelihood estimators for this special case. The information matrix is also obtained which provides asymptotic covariance matrix of the maximum likelihood estimators. The asymptotic covariance matrix of moment estimators is also derived. The asymptotic efficiency of moment estimators is computed and found to be very low. 相似文献
12.
Sequential estimation of parameters In a continuous time Markov branching process with Immigration with split rate λ1 Immigration rate λ2, offspring distribution {p1j≥O) and Immigration distribution {p2j≥l} is considered. A sequential version of the Cramér-Rao type information inequality is derived which gives a lower bound on the variances of unbiased estimators for any function of these parameters. Attaining the lower bounds depends on whether the sampling plan or stopping rule S, the estimator f, and the parametric function g = E(f) are efficient. All efficient triples (S,f,g) are characterized; It Is shown that for i = 1,2, only linear combinations of λipij j's or their ratios are efficiently estimable. Applications to a Yule process, a linear birth and death process with immigration and an M/M/∞ queue are also considered 相似文献
13.
Two statistical applications for estimation and prediction of flows in traffic networks are presented. In the first, the number of route users are assumed to be independent α-shifted gamma Γ(θ, λ0) random variables denoted H(α, θ, λ0), with common λ0. As a consequence, the link, OD (origin-destination) and node flows are also H(α, θ, λ0) variables. We assume that the main source of information is plate scanning, which permits us to identify, totally or partially, the vehicle route, OD and link flows by scanning their corresponding plate numbers at an adequately selected subset of links. A Bayesian approach using conjugate families is proposed that allows us to estimate different traffic flows. In the second application, a stochastic demand dynamic traffic model to predict some traffic variables and their time evolution in real networks is presented. The Bayesian network model considers that the variables are generalized Beta variables such that when marginally transformed to standard normal become multivariate normal. The model is able to provide a point estimate, a confidence interval or the density of the variable being predicted. Finally, the models are illustrated by their application to the Nguyen Dupuis network and the Vermont-State example. The resulting traffic predictions seem to be promising for real traffic networks and can be done in real time. 相似文献
14.
R.M. Hollander, D.H. Park and F. Proschan [A class of life distributions for aging, J. Amer. Statist. Assoc. 81 (1986) 91–95] introduced the concept of the larger class of life distributions called new better than used of specified age. In practice, one might be interested in the new better than used behaviour at an unknown but estimable age t0. Here, we investigate the testing of new better than used of specified age t0 (NBU-t0) alternatives. A class of test statistics for testing NBU-t0 (t0 is known) based on a U-statistic whose kernel depends on sub-sample minima is proposed. A member of the class of tests proposed by N. Ebrahimi and M. Habbibullah [Testing whether the survival distribution is new better than used of specified age, Biometrika 77 (1990) 212–215] for this problem belongs to the class of tests proposed here. The distributional properties of the class of test statistics are studied. The performances of a few members of the proposed class of tests are studied in terms of Pitman asymptotic relative efficiency. The Pitman ARE values show that the members of the class perform well in comparison with the N. Ebrahimi and M. Habbibullah [Testing whether the survival distribution is new better than used of specified age, Biometrika 77 (1990) 212–215] tests. The proposed class of tests is shown to be consistent for NBU-t0 alternatives. 相似文献
15.
Results of an exhaustive study of the bias of the least square estimator (LSE) of an first order autoregression coefficient α in a contaminated Gaussian model are presented. The model describes the following situation. The process is defined as Xt = α Xt-1 + Yt . Until a specified time T, Yt are iid normal N(0, 1). At the moment T we start our observations and since then the distribution of Yt, t≥T, is a Tukey mixture T(εσ) = (1 – ε)N(0,1) + εN(0, σ2). Bias of LSE as a function of α and ε, and σ2 is considered. A rather unexpected fact is revealed: given α and ε, the bias does not change montonically with σ (“the magnitude of the contaminant”), and similarly, given α and σ, the bias is not growing with ε (“the amount of contaminants”). 相似文献
16.
MAUD DELATTRE VALENTINE GENON‐CATALOT ADELINE SAMSON 《Scandinavian Journal of Statistics》2013,40(2):322-343
Abstract. We consider N independent stochastic processes (X i (t), t ∈ [0,T i ]), i=1,…, N, defined by a stochastic differential equation with drift term depending on a random variable φ i . The distribution of the random effect φ i depends on unknown parameters which are to be estimated from the continuous observation of the processes Xi. We give the expression of the exact likelihood. When the drift term depends linearly on the random effect φ i and φ i has Gaussian distribution, an explicit formula for the likelihood is obtained. We prove that the maximum likelihood estimator is consistent and asymptotically Gaussian, when T i =T for all i and N tends to infinity. We discuss the case of discrete observations. Estimators are computed on simulated data for several models and show good performances even when the length time interval of observations is not very large. 相似文献
17.
The failure rate r(t) is assumed to have the shape of the"first"part of the"bathtub"model, i.e.r(t) is non-increasing for t<r and is constant for t> r. Asymptotic distribution of one of the estimates proposed earlier has been investigated in this paper. This leads to a test for the hypothesis HQ r<r 0 vs H :r>r (where TQ > 0). Asymptotic expression for the power of this test under Pitman alternatives is derived. Some simulations are reported. 相似文献
18.
In this note we consider the problems of optimal linear prediction (o.l.p.) and the minimum mean squared error prediction (m.m.s.e.p.) of a sequence Xt, which fits to a stationary and invertible ARMA model through the filter (1 - Bs)d Xt= Yt. It is shown that these two predictors are not identical in general from the theoretical point of view. Permitting the degree of differencing d to take any real value, a set of conditions for these commonly applied prediction formulas to be identical is given. 相似文献
19.
M. A. Hamdan 《Revue canadienne de statistique》1977,5(2):235-240
Stuart's (1953) measure of association in contingency tables, tC, based on Kendall's (1962) t, is compared with Goodman and Kruskal's (1954, 1959, 1963, 1972) measure G. First, it is proved that |G| ≥ |tC|; and then it is shown that the upper bound for the asymptotic variance of G is not necessarily always smaller than the upper bound for the asymptotic variance of tC. It is proved, however, that the upper bound for the coefficient of variation of G cannot be larger in absolute value than the upper bound for the coefficient of variation of tC. The asymptotic variance of tC is also derived and hence we obtain an upper bound for this asymptotic variance which is sharper than Stuart's (1953) upper bound. 相似文献
20.
Ryszard Zielinski 《Statistics》2013,47(2):223-227
Given λ∈(0-,l), let xλ(F) denote the unique λ-quantile of the distribution F. A distribution-free median-unbiased estimator of xλ(F) is explicitly constructed 相似文献