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1.
A one-sided testing problem based on an i.i.d. sample of observations is considered. The usual one-sided sequential probability ratio test would be based on a random walk derived from these observations. Here we propose a sequential test where the random walk is replaced by Lindleys random walk which starts anew at zero as soon as it becomes negative. We derive the asymptotics of the expected sample size and the error probabilities of this sequential test. We discuss the advantages of this test for certain nonsymmetric situations.Acknowledgement. The authors thank the referee for helpful comments and suggestions. Their research was supported by the German Research Foundation (DFG) and the Russian Foundation for Basic Research (RFBR).  相似文献   

2.
Consider N independent stochastic processes \((X_i(t), t\in [0,T])\), \(i=1,\ldots , N\), defined by a stochastic differential equation with random effects where the drift term depends linearly on a random vector \(\Phi _i\) and the diffusion coefficient depends on another linear random effect \(\Psi _i\). For these effects, we consider a joint parametric distribution. We propose and study two approximate likelihoods for estimating the parameters of this joint distribution based on discrete observations of the processes on a fixed time interval. Consistent and \(\sqrt{N}\)-asymptotically Gaussian estimators are obtained when both the number of individuals and the number of observations per individual tend to infinity. The estimation methods are investigated on simulated data and show good performances.  相似文献   

3.
Eugene F. Schuster 《Metrika》1993,40(1):325-332
We consider the sample survey type problem of estimating the proportionp of a finite population of sizeN having a given attribute by the proportion of successes in a random sample (with or without replacement) of sizer from the population. Our main result indicates that is always at least a 91.0% confidence interval (C.I.) for the parameterp. We show that is at least as large under the hypergeometric model of simple random sampling without replacement as it is under the corresponding binomial model of random sampling with replacement. The significance of our main result is that it is a good, easily stated accuracy rule, holding for allr, N, andp, which can easily be understood by the layman when assessing accuracy of the estimator and discussing the relationship between accuracy and sample size.  相似文献   

4.
In this work the ranked set sampling technique has been applied to estimate the scale parameter $\alpha $ of a log-logistic distribution under a situation where the units in a sample can be ordered by judgement method without any error. We have evaluated the Fisher information contained in the order statistics arising from this distribution and observed that median of a random sample contains the maximum information about the parameter $\alpha $ . Accordingly we have used median ranked set sampling to estimate $\alpha $ . We have further carried out the multistage median ranked set sampling to estimate $\alpha $ with improved precision. Suppose it is not possible to rank the units in a sample according to judgement method without error but the units can be ordered based on an auxiliary variable $Z$ such that $(X, Z)$ has a Morgenstern type bivariate log-logistic distribution (MTBLLD). In such a situation we have derived the Fisher information contained in the concomitant of rth order statistic of a random sample of size $n$ from MTBLLD and identified those concomitants among others which possess largest amount of Fisher information and defined an unbalanced ranked set sampling utilizing those units in the sample and thereby proposed an estimator of $\alpha $ using the measurements made on those units in this ranked set sample.  相似文献   

5.
This paper considers three ratio estimators of the population mean using known correlation coefficient between the study and auxiliary variables in simple random sample when some sample observations are missing. The suggested estimators are compared with the estimators of Singh and Horn (Metrika 51:267–276, 2000), Singh and Deo (Stat Pap 44:555–579, 2003) and Kadilar and Cingi (Commun Stat Theory Methods 37:2226–2236, 2008). They are compared with other imputation estimators based on the mean or a ratio. It is found that the suggested estimators are approximately unbiased for the population mean. Also, it turns out that the suggested estimators perform well when compared with the other estimators considered in this study.  相似文献   

6.
Cyrille Joutard 《Metrika》2017,80(6-8):663-683
We establish strong large deviation results for an arbitrary sequence of random vectors under some assumptions on the normalized cumulant generating function. In other words, we give asymptotic approximations for a multivariate tail probability of the same kind as the one obtained by Bahadur and Rao (Ann Math Stat 31:1015–1027, 1960) for the sample mean (in the one-dimensional case). The proof of our results follows the same lines as in Chaganty and Sethuraman (J Stat Plan Inference, 55:265–280, 1996). We also present three statistical applications to illustrate our results, the first one dealing with a vector of independent sample variances, the second one with a Gaussian multiple linear regression model and the third one with the multivariate Nadaraya–Watson estimator. Some numerical results are also presented for the first two applications.  相似文献   

7.
Probability theory in fuzzy sample spaces   总被引:2,自引:0,他引:2  
This paper tries to develop a neat and comprehensive probability theory for sample spaces where the events are fuzzy subsets of The investigations are focussed on the discussion how to equip those sample spaces with suitable -algebras and metrics. In the end we can point out a unified concept of random elements in the sample spaces under consideration which is linked with compatible metrics to express random errors. The result is supported by presenting a strong law of large numbers, a central limit theorem and a Glivenko-Cantelli theorem for these kinds of random elements, formulated simultaneously w.r.t. the selected metrics. As a by-product the line of reasoning, which is followed within the paper, enables us to generalize as well as to bring together already known results and concepts from literature.Acknowledgement. The author would like to thank the participants of the 23rd Linz Seminar on Fuzzy Set Theory for the intensive discussion of the paper. Especially he is indebted to Professors Diamond and Höhle whose remarks have helped to get deeper insights into the subject. Additionally, the author is grateful to one anonymous referee for careful reading and valuable proposals which have led to an improvement of the first draft.This paper was presented at the 23rd Linz Seminar on Fuzzy Set Theory, Linz, Austria, February 5–9, 2002.  相似文献   

8.
Majid Asadi 《Metrika》2017,80(6-8):649-661
We propose a new measure of association between two continuous random variables X and Y based on the covariance between X and the log-odds rate associated to Y. The proposed index of correlation lies in the range [\(-1\), 1]. We show that the extremes of the range, i.e., \(-1\) and 1, are attainable by the Fr\(\acute{\mathrm{e}}\)chet bivariate minimal and maximal distributions, respectively. It is also shown that if X and Y have bivariate normal distribution, the resulting measure of correlation equals the Pearson correlation coefficient \(\rho \). Some interpretations and relationships to other variability measures are presented. Among others, it is shown that for non-negative random variables the proposed association measure can be represented in terms of the mean residual and mean inactivity functions. Some illustrative examples are also provided.  相似文献   

9.
Given a random sample from a continuous and positive density ff, the logistic transformation is applied and a log density estimate is provided by using basis functions approach. The number of basis functions acts as the smoothing parameter and it is estimated by minimizing a penalized proxy of the Kullback–Leibler distance which includes as particular cases AIC and BIC criteria. We prove that this estimator is consistent.  相似文献   

10.
In this paper we study convolution residuals, that is, if $X_1,X_2,\ldots ,X_n$ are independent random variables, we study the distributions, and the properties, of the sums $\sum _{i=1}^lX_i-t$ given that $\sum _{i=1}^kX_i>t$ , where $t\in \mathbb R $ , and $1\le k\le l\le n$ . Various stochastic orders, among convolution residuals based on observations from either one or two samples, are derived. As a consequence computable bounds on the survival functions and on the expected values of convolution residuals are obtained. Some applications in reliability theory and queueing theory are described.  相似文献   

11.
In this paper, the authors evaluate the effectiveness of Statement of Cash Flows measures in the classification and prediction of bankruptcy. The problems of biased estimators and bankruptcy probabilities and of optimal cut-off rates are addressed by using a large random sample and conditional marginal probability density functions. It is found that cashflow variables provide statistically better classification and prediction rates when used with traditional accounting variables when bankruptcy is defined as a Chapter 11 filing.  相似文献   

12.
Xuejun Wang  Xin Deng  Shuhe Hu 《Metrika》2018,81(7):797-820
This paper is concerned with the semiparametric regression model \(y_i=x_i\beta +g(t_i)+\sigma _ie_i,~~i=1,2,\ldots ,n,\) where \(\sigma _i^2=f(u_i)\), \((x_i,t_i,u_i)\) are known fixed design points, \(\beta \) is an unknown parameter to be estimated, \(g(\cdot )\) and \(f(\cdot )\) are unknown functions, random errors \(e_i\) are widely orthant dependent random variables. The p-th (\(p>0\)) mean consistency and strong consistency for least squares estimators and weighted least squares estimators of \(\beta \) and g under some more mild conditions are investigated. A simulation study is also undertaken to assess the finite sample performance of the results that we established. The results obtained in the paper generalize and improve some corresponding ones of negatively associated random variables.  相似文献   

13.
Consider an i.i.d. sample \({X^*_{1},X^*_{2},\ldots,X^*_{n}}\) from a location-scale family, and assume that the only available observations consist of the partial maxima (or minima) sequence, \({X^*_{1:1},X^*_{2:2},\ldots,X^*_{n:n}}\), where \({X^*_{j:j}=\max\{ X^*_1, \ldots,X^*_j \}}\). This kind of truncation appears in several circumstances, including best performances in athletics events. In the case of partial maxima, the form of the BLUEs (best linear unbiased estimators) is quite similar to the form of the well-known Lloyd’s (in Biometrica 39:88–95, 1952) BLUEs, based on (the sufficient sample of) order statistics, but, in contrast to the classical case, their consistency is no longer obvious. The present paper is mainly concerned with the scale parameter, showing that the variance of the partial maxima BLUE is at most of order O(1/ log n), for a wide class of distributions.  相似文献   

14.
This paper concerns a longitudinal study, of a random sample of nascent entrepreneurs in Canada (based on an initial screening sample of 49,763 households). We study gender differences, including number and type of gestational activities, the characteristics of the business created, and the status of the start-up effort after the 4th year of data collection. Logistic regression is used to predict the creation of an operating business from gender and other variables. Four of nine gender difference hypotheses were supported. Findings show that women who are members of a start-up team are six times more likely to achieve an operating business.
Susan ElgieEmail:
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15.
Summary SupposeX is a non-negative random variable with an absolutely continuous (with respect to Lebesgue measure) distribution functionF (x) and the corresponding probability density functionf(x). LetX 1,X 2,...,X n be a random sample of sizen fromF andX i,n is thei-th smallest order statistics. We define thej-th order gapg i,j(n) asg i,j(n)=X i+j,n–Xi,n 1i<n, 1nn–i. In this paper a characterization of the exponential distribution is given by considering a distribution property ofg i,j(n).  相似文献   

16.
A normality assumption is usually made for the discrimination between two stationary time series processes. A nonparametric approach is desirable whenever there is doubt concerning the validity of this normality assumption. In this paper a nonparametric approach is suggested based on kernel density estimation firstly on (p+1) sample autocorrelations and secondly on (p+1) consecutive observations. A numerical comparison is made between Fishers linear discrimination based on sample autocorrelations and kernel density discrimination for AR and MA processes with and without Gaussian noise. The methods are applied to some seismological data.  相似文献   

17.
Joachim Kunert 《Metrika》1994,41(1):71-81
We consider the simple block model with random block effects, the block effects having variance b 2 =2;, with 2 the variance of the errors. It is assumed that the experimenter can vary the sizes of the blocks. The universal optimality of certain designs for all over all designs with the same number of blocks and the same number of observations is shown. It is of interest to note that if Balanced Incomplete Block Designs compete, then they perform equally well for =0 and for =, i.e. in the one way classification model and in the simple block model with fixed block effects, but they perform worse for every (0, ).The result is, however, theoretical in nature. It treats a situation which is not very likely to happen in practice. The interest lies in the fact that it provides a counterexample to a conjecture on optimality of designs in mixed models.  相似文献   

18.
The paper derives a general Central Limit Theorem (CLT) and asymptotic distributions for sample moments related to panel data models with large nn. The results allow for the data to be cross sectionally dependent, while at the same time allowing the regressors to be only sequentially rather than strictly exogenous. The setup is sufficiently general to accommodate situations where cross sectional dependence stems from spatial interactions and/or from the presence of common factors. The latter leads to the need for random norming. The limit theorem for sample moments is derived by showing that the moment conditions can be recast such that a martingale difference array central limit theorem can be applied. We prove such a central limit theorem by first extending results for stable convergence in Hall and Heyde (1980) to non-nested martingale arrays relevant for our applications. We illustrate our result by establishing a generalized estimation theory for GMM estimators of a fixed effect panel model without imposing i.i.d. or strict exogeneity conditions. We also discuss a class of Maximum Likelihood (ML) estimators that can be analyzed using our CLT.  相似文献   

19.
In this paper, we discuss asymptotic infimum coverage probability (ICP) of eight widely used confidence intervals for proportions, including the Agresti–Coull (A–C) interval (Am Stat 52:119–126, 1998) and the Clopper–Pearson (C–P) interval (Biometrika 26:404–413, 1934). For the A–C interval, a sharp upper bound for its asymptotic ICP is derived. It is less than nominal for the commonly applied nominal values of 0.99, 0.95 and 0.9 and is equal to zero when the nominal level is below 0.4802. The \(1-\alpha \) C–P interval is known to be conservative. However, we show through a brief numerical study that the C–P interval with a given average coverage probability \(1-\gamma \) typically has a similar or larger ICP and a smaller average expected length than the corresponding A–C interval, and its ICP approaches to \(1-\gamma \) when the sample size goes large. All mathematical proofs and R-codes for computation in the paper are given in Supplementary Materials.  相似文献   

20.
In this paper we study the relationship between regression analysis and a multivariate dependency measure. If the general regression model Y=f() holds for some function f, where 1i1< i2<···im k, and X1,...,Xk is a set of possible explanatory random variables for Y. Then there exists a dependency relation between the random variable Y and the random vector (). Using the dependency statistic defined below, we can detect such dependency even if the function f is not linear. We present several examples with real and simulated data to illustrate this assertion. We also present a way to select the appropriate subset among the random variables X1,X2,...,Xk, which better explain Y.  相似文献   

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