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1.
The estimation of the regression parameters for the ill-conditioned logistic regression model is considered in this paper. We proposed five ridge regression (RR) estimators, namely, unrestricted RR, restricted ridge regression, preliminary test RR, shrinkage ridge regression and positive rule RR estimators for estimating the parameters $(\beta )$ when it is suspected that the parameter $\beta $ may belong to a linear subspace defined by $H\beta =h$ . Asymptotic properties of the estimators are studied with respect to quadratic risks. The performances of the proposed estimators are compared based on the quadratic bias and risk functions under both null and alternative hypotheses, which specify certain restrictions on the regression parameters. The conditions of superiority of the proposed estimators for departure and ridge parameters are given. Some graphical representations and efficiency analysis have been presented which support the findings of the paper.  相似文献   

2.
The stress-strength reliability $R=P(Y<X)$ , where $X$ and $Y$ are independent continuous random variables, has obtained wide attention in many areas of application, such as in engineering statistics and biostatistics. Classical likelihood-based inference about $R$ has been widely examined under various assumptions on $X$ and $Y$ . However, it is well-known that first order inference can be inaccurate, in particular when the sample size is small or in presence of unknown parameters. The aim of this paper is to illustrate higher-order likelihood-based procedures for parametric inference in small samples, which provide accurate point estimators and confidence intervals for $R$ . The proposed procedures are illustrated under the assumptions of Gaussian and exponential models for $(X,Y)$ . Moreover, simulation studies are performed in order to study the accuracy of the proposed methodology, and an application to real data is discussed. An implementation of the proposed method in the R software is provided.  相似文献   

3.
In 2005, Chen et al. introduced a sequential importance sampling (SIS) procedure to analyze zero-one two-way tables with given fixed marginal sums (row and column sums) via the conditional Poisson (CP) distribution. They showed that compared with Monte Carlo Markov chain (MCMC)-based approaches, their importance sampling method is more efficient in terms of running time and also provides an easy and accurate estimate of the total number of contingency tables with fixed marginal sums. In this paper, we extend their result to zero-one multi-way ( $d$ -way, $d \ge 2$ ) contingency tables under the no $d$ -way interaction model, i.e., with fixed $d-1$ marginal sums. Also, we show by simulations that the SIS procedure with CP distribution to estimate the number of zero-one three-way tables under the no three-way interaction model given marginal sums works very well even with some rejections. We also applied our method to Samson’s monks data set.  相似文献   

4.
We address the problem of adaptive minimax density estimation on \(\mathbb{R }^d\) with \(\mathbb{L }_p\) -loss on the anisotropic Nikol’skii classes. We fully characterize behavior of the minimax risk for different relationships between regularity parameters and norm indexes in definitions of the functional class and of the risk. In particular, we show that there are four different regimes with respect to the behavior of the minimax risk. We develop a single estimator which is (nearly) optimal in order over the complete scale of the anisotropic Nikol’skii classes. Our estimation procedure is based on a data-driven selection of an estimator from a fixed family of kernel estimators.  相似文献   

5.
We consider estimating the bivariate survival function when both components are subject to random left truncation and right censoring. Using the idea of Sankran and Antony (Sankhyã 69:425–447, 2007) in the competing risks set up, we propose two types of estimators as generalizations of the Dabrowska (Ann Stat 18:1475–1489, 1988) and Campbell and Földes (Nonparametric statistical inference, North-Holland, Amsterdam 1982) estimators. The proposed estimators are easy to implement and do not require iteration. The consistency of the proposed estimators is established. Simulation results indicate that the proposed estimators can outperform the estimators of Shen and Yan (J Stat Plan Inference 138:4041–4054, 2008), which require complex iteration.  相似文献   

6.
This paper presents a truncated estimation method of ratio type functionals by dependent sample of finite size. This method makes it possible to obtain estimators with guaranteed accuracy in the sense of the $L_m$ -norm, $m\ge 2$ . As an illustration, the parametric and non-parametric estimation problems on a time interval of a fixed length are considered. In particular, parameters of linear (autoregressive) and non-linear discrete-time processes are estimated. Moreover, the parameter estimation problem of non-Gaussian Ornstein-Uhlenbeck process by discrete-time observations and the estimation problem of a multivariate logarithmic derivative of a noise density of an autoregressive process with guaranteed accuracy are solved. In addition to non-asymptotic properties, the limit behavior of presented estimators is investigated. It is shown that all the truncated estimators have asymptotic properties of basic estimators. In particular, the asymptotic efficiency in the mean square sense of the truncated estimator of the dynamic parameter of a stable autoregressive process is established.  相似文献   

7.
Sample functions of random processes are used to make inferences about the properties of estimators. In particular, it is proved that optimal equivariant sequential estimation designs with stopping timet such that Εt n 1, are better than optimal equivariant estimation of the location parameter for samples of sizen, with largen. It is assumed that the density has cusps of first or second kind.  相似文献   

8.
In this paper we estimate the parameters in the stochastic SIS epidemic model by using pseudo-maximum likelihood estimation (pseudo-MLE) and least squares estimation. We obtain the point estimators and $100 (1-\alpha )\%$ confidence intervals as well as $100 (1-\alpha )\%$ joint confidence regions by applying least squares techniques. The pseudo-MLEs have almost the same form as the least squares case. We also obtain the exact as well as the asymptotic $100 (1-\alpha )\%$ joint confidence regions for the pseudo-MLEs. Computer simulations are performed to illustrate our theory.  相似文献   

9.
Times between consecutive events are often of interest in medical studies. Usually the events represent different states of the disease process and are modeled using multi-state models. This paper introduces and studies a feasible estimation method for the transition probabilities in a progressive three-state model. We assume that the vector of gap times $(T_1,T_2)$ satisfies a nonparametric location-scale regression model $T_2=m(T_1)+\sigma (T_1)\epsilon $ , where the functions $m$ and $\sigma $ are ‘smooth’, and $\epsilon $ is independent of $T_1$ . Under this model, Van Keilegom et al. (J Stat Plan Inference 141:1118–1131, 2011) proposed estimators of the transition probabilities. However, the important issue of automatic bandwidth choice in this setting has not been examined, making the analysis of real datasets rather difficult. In this paper, we study the performance of their estimator in practice, we propose some modifications and study practical issues related to the implementation of the estimator, which involves the choice of an appropriate bandwidth. In an extensive simulation study the good performance of the method is shown. Simulations also demonstrate that the proposed estimator compares favorably with alternative estimators. Furthermore, the proposed methodology is illustrated with a real database on breast cancer.  相似文献   

10.
Motivated by the availability of continuous event sequences that trace the social behavior in a population e.g. email, we believe that mutually exciting Hawkes processes provide a realistic and informative model for these sequences. For complex mutually exciting processes, the numerical optimization used for univariate self exciting processes may not provide stable estimates. Furthermore, convergence can be exceedingly slow, making estimation computationally expensive and multiple random restarts doubly so. We derive an expectation maximization algorithm for maximum likelihood estimation mutually exciting processes that is faster, more robust, and less biased than estimation based on numerical optimization. For an exponentially decaying excitement function, each EM step can be computed in a single $O(N)$ pass through the data, for $N$ observations, without requiring the entire dataset to be in memory. More generally, exact inference is $\Theta (N^{2})$ , but we identify some simple $\Theta (N)$ approximation strategies that seem to provide good estimates while reducing the computational cost.  相似文献   

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