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1.
Various criteria have been proposed for determining the reliability of noncompartmental pharmacokinetic estimates of the terminal disposition phase half‐life (t1/2) and the extrapolated area under the curve (AUCextrap). This simulation study assessed the performance of two frequently used reportability rules: the terminal disposition phase regression adjusted‐r2 classification rule and the regression data point time span classification rule. Using simulated data, these rules were assessed in relation to the magnitude of the variability in the terminal disposition phase slope, the length of the terminal disposition phase captured in the concentration‐time profile (data span), the number of data points present in the terminal disposition phase, and the type and level of variability in concentration measurement. The accuracy of estimating t1/2 was satisfactory for data spans of 1.5 and longer, given low measurement variability; and for spans of 2.5 and longer, given high measurement variability. Satisfactory accuracy in estimating AUCextrap was only achieved with low measurement variability and spans of 2.5 and longer. Neither of the classification rules improved the identification of accurate t1/2 and AUCextrap estimates. Based on the findings of this study, a strategy is proposed for determining the reportability of estimates of t1/2 and area under the curve extrapolated to infinity.  相似文献   

2.
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, tT, 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   

3.
As the sample size increases, the coefficient of skewness of the Fisher's transformation z= tanh-1r, of the correlation coefficient decreases much more rapidly than the excess of its kurtosis. Hence, the distribution of standardized z can be approximated more accurately in terms of the t distribution with matching kurtosis than by the unit normal distribution. This t distribution can, in turn be subjected to Wallace's approximation resulting in a new normal approximation for the Fisher's z transform. This approximation, which can be used to estimate the probabilities, as well as the percentiles, compares favorably in both accuracy and simplicity, with the two best earlier approximations, namely, those due to Ruben (1966) and Kraemer (1974). Fisher (1921) suggested approximating distribution of the variance stabilizing transform z=(1/2) log ((1 +r)/(1r)) of the correlation coefficient r by the normal distribution with mean = (1/2) log ((1 + p)/(lp)) and variance =l/(n3). This approximation is generally recognized as being remarkably accurate when ||Gr| is moderate but not so accurate when ||Gr| is large, even when n is not small (David (1938)). Among various alternatives to Fisher's approximation, the normalizing transformation due to Ruben (1966) and a t approximation due to Kraemer (1973), are interesting on the grounds of novelty, accuracy and/or aesthetics. If r?= r/√ (1r2) and r?|Gr = |Gr/√(1|Gr2), then Ruben (1966) showed that (1) gn (r,|Gr) ={(2n5)/2}1/2r?r{(2n3)/2}1/2r?|GR, {1 + (1/2)(r?r2+r?|Gr2)}1/2 is approximately unit normal. Kraemer (1973) suggests approximating (2) tn (r, |Gr) = (r|GR1) √ (n2), √(11r2) √(1|Gr2) by a Student's t variable with (n2) degrees of freedom, where after considering various valid choices for |Gr1 she recommends taking |Gr1= |Gr*, the median of r given n and |Gr.  相似文献   

4.
Several adjustments of the profile likelihood have the common effect of reducing the bias of the associated score function. Hence expansions for the adjusted score functions differ by a term, Dξ, that has small asymptotic order (n ). The effect of Dξ on other quantities of interest is studied. In particular, we find the bias and variance of the adjusted maximum-likelihood estimate to be relatively unaffected, while differences in the Bartlett correction depend on Dξ in a simple way.  相似文献   

5.
Abstract

This paper considers a partially non linear model E(Y|X, z, t) = f(X, β) + zTg(t) and gives its T-type estimate, which is a weighted quasi-likelihood estimate using sieve method and can be obtained by EM algorithm. The influence functions and asymptotic properties of T-type estimate (consistency and asymptotic normality) are discussed, and convergence rate of both parametric and non parametric components are obtained. Simulation results show the shape of influence functions and prove that the T-type estimate performs quite well. The proposed estimate is also applied to a data set and compared with the least square estimate and least absolute deviation estimate.  相似文献   

6.
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   

7.
Let Z 1, Z 2, . . . be a sequence of independent Bernoulli trials with constant success and failure probabilities p = Pr(Z t  = 1) and q = Pr(Z t  = 0) = 1 − p, respectively, t = 1, 2, . . . . For any given integer k ≥ 2 we consider the patterns E1{\mathcal{E}_{1}}: two successes are separated by at most k−2 failures, E2{\mathcal{E}_{2}}: two successes are separated by exactly k −2 failures, and E3{\mathcal{E}_{3}} : two successes are separated by at least k − 2 failures. Denote by Nn,k(i){ N_{n,k}^{(i)}} (respectively Mn,k(i){M_{n,k}^{(i)}}) the number of occurrences of the pattern Ei{\mathcal{E}_{i}} , i = 1, 2, 3, in Z 1, Z 2, . . . , Z n when the non-overlapping (respectively overlapping) counting scheme for runs and patterns is employed. Also, let Tr,k(i){T_{r,k}^{(i)}} (resp. Wr,k(i)){W_{r,k}^{(i)})} be the waiting time for the rth occurrence of the pattern Ei{\mathcal{E}_{i}}, i = 1, 2, 3, in Z 1, Z 2, . . . according to the non-overlapping (resp. overlapping) counting scheme. In this article we conduct a systematic study of Nn,k(i){N_{n,k}^{(i)}}, Mn,k(i){M_{n,k}^{(i)}}, Tr,k(i){T_{r,k}^{(i)}} and Wr,k(i){W_{r,k}^{(i)}} (i = 1, 2, 3) obtaining exact formulae, explicit or recursive, for their probability generating functions, probability mass functions and moments. An application is given.  相似文献   

8.
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   

9.
10.
We study the r-content Δ of the r -simplex generated by r+ 1 independent random points in R”. Each random point Zj is isotropic and distributed according to λ||Zj||2 ~ beta-type-2(n/2, v), λ, v > 0. We provide an asymptotic normality result which is analogous to the conjecture made by Miles (1971). A method is introduced to work out the exact density of W = (rλ)r(r!Δ)2/(r + |)r+l and hence that of Δ. The distribution of W is also related to some hypothesis-testing problems in multivariate analysis. Furthermore, by using this method, the distribution of W or Δ can easily be simulated.  相似文献   

11.
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   

12.
In this paper, by assuming that (X, Y 1, Y 2)T has a trivariate elliptical distribution, we derive the exact joint distribution of X and a linear combination of order statistics from (Y 1, Y 2)T and show that it is a mixture of unified bivariate skew-elliptical distributions. We then derive the corresponding marginal and conditional distributions for the special case of t kernel. We also present these results for an exchangeable case with t kernel and illustrate the established results with an air-pollution data.  相似文献   

13.
This paper considers the general linear regression model yc = X1β+ut under the heteroscedastic structure E(ut) = 0, E(u2) =σ2- (Xtβ)2, E(ut us) = 0, tæs, t, s= 1, T. It is shown that any estimated GLS estimator for β is asymptotically equivalent to the GLS estimator under some regularity conditions. A three-step GLS estimator, which calls upon the assumption E(ut2) =s?2(X,β)2 for the estimation of the disturbance covariance matrix, is considered.  相似文献   

14.
This article investigates parallel systems with n independent but not identically distributed (INID) components. Under the condition that, at time t 1 (t 1 > 0) the total number of failures of the components is r (r < n), and at time t 2 (t 2 ≥ t 1) the sys-tem is still working or it has failed, the mean residual life (MRL) function of the parallel system and the mean past lifetime (MPL) function of the components are conducted. Some representations and corresponding properties of the MRL function and the MPL function under several specific conditions are obtained.  相似文献   

15.
Suppose that the length of time in years for which a business operates until failure has a Pareto distribution. Let t 1?t 2?t r denote the survival lifetimes of the first r of a random sample of n businesses. Bayesian predictions are to be made on the ordered failure times of the remaining (n???r) businesses, using the conditional probability function. Numerical examples are given to illustrate our results.  相似文献   

16.
In order to reach the inference about a linear combination of two independent binomial proportions, various procedures exist (Wald's classic method, the exact, approximate, or maximized score methods, and the Newcombe-Zou method). This article defines and evaluates 25 different methods of inference, and selects the ones with the best behavior. In general terms, the optimal method is the classic Wald method applied to the data to which z 2 α/2/4 successes and z 2 α/2/4 failures are added (≈1 if α = 5%) if no sample proportion has a value of 0 or 1 (otherwise the added increase may be different).

Supplemental materials are available for this article. Go to the publisher's online edition of Communications in Statistics - Simulation and Computation to view the free supplemental file.  相似文献   

17.
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   

18.
The linear hypothesis test procedure is considered in the restricted linear modelsM r = {y, Xβ |Rβ = 0, σ 2V} andM r * = {y, Xβ |ARβ = 0, σ 2V}. Necessary and sufficient conditions are derived under which the statistic providing anF-test for the linear hypothesisH 0:Kβ=0 in the modelM r * (Mr) continues to be valid in the modelM r (M r * ); the results obtained cover the case whereM r * is replaced by the general Gauss-Markov modelM = {y, Xβ, σ 2V}.  相似文献   

19.
Let (θ1,x1),…,(θn,xn) be independent and identically distributed random vectors with E(xθ) = θ and Var(x|θ) = a + bθ + cθ2. Let ti be the linear Bayes estimator of θi and θ~i be the linear empirical Bayes estimator of θi as proposed in Robbins (1983). When Ex and Var x are unknown to the statistician. The regret of using θ~i instead of ti because of ignorance of the mean and the variance is ri = E(θi ? θi)2 ?E(tii)2. Under appropriate conditions cumulative regret Rn = r1+…rn is shown to have a finite limit even when n tends to infinity. The limit can be explicitly computed in terms of a,b,c and the first four moments of x.  相似文献   

20.
Let Wt be a one-dimensional Brownian motion on the probability space (Ω,F,P), and let dxt = a(xt)dt + b(xt)dwt, b2(x) > 0, be a one-dimensional Ito stochastic differential equation. For a(x) = a0 + a1x + … + anxn on a bounded interval we obtain a lower bound for p(t,x,y), the transition density function of the homogeneous Markov process xt, depending directly on the coefficients a0,a1, …, an, and b(x).  相似文献   

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