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This article presents discussions on the optimal and robust designs for trigonometric regression models under different optimality criteria. First, we investigate the classical Q-optimal designs for estimating the response function in a full trigonometric regression model with a given order. The equivalencies of Q-, A-, and G-optimal designs for trigonometric regression in general are also articulated...
Let $$(X_1,X_2,\ldots ,X_n)$$ ( X 1 , X 2 , … , X n ) be a Gaussian random vector with a common correlation coefficient $$\rho _n,\,0\le \rho _n<1$$ ρ n , 0 ≤ ρ n < 1 , and let $$M_n= \max (X_1,\ldots , X_n),\,n\ge 1$$ M n = max ( X 1 , … , X n ) , n ≥ 1 . For any given $$a>0$$ a > 0 , define $$T_n(a)= \left\{ j,\,1\le j\le...
In this article, we study sooner/later waiting time problems for simple patterns in a sequence of bivariate trials. The double generating functions of the sooner/later waiting times for the simple patterns are expressed in terms of the double generating functions of the numbers of occurrences of the simple patterns. Effective computational tools are developed for the evaluation of the waiting time...
In this paper, we propose an extension to the first-order branching process with immigration in the presence of fixed covariates and unobservable random effects. The extension permits the possibility that individuals from the second generation of the process may contribute to the total number of offsprings at time $$t$$ t by producing offsprings of their own. We will study the basic properties...
This paper analyzes weekly closing price data of the S&P 500 stock index and electrical insulation element lifetimes data based on generalized extreme value distribution. A new estimation method, modified maximum spacings (MSP) method, is proposed and obtained by using interior penalty function algorithm. The standard error of the proposed method is calculated through Bootstrap method. The asymptotic...
In this paper, we consider a family of bivariate distributions which is a generalization of the Morgenstern family of bivariate distributions. We have derived some properties of concomitants of record values which characterize this generalized class of distributions. The role of concomitants of record values in the unique determination of the parent bivariate distribution has been established. We...
High-dimensional data are becoming prevalent, and many new methodologies and accompanying theories for high-dimensional data analysis have emerged in response. Empirical likelihood, as a classical nonparametric method of statistical inference, has proved to possess many good features. In this paper, our focus is to investigate the asymptotic behavior of empirical likelihood for regression coefficients...
A stochastic marked point process model based on doubly stochastic Poisson process is considered in the problem of prediction for the total size of future marks in a given period, given the history of the process. The underlying marked point process $$(T_{i},Y_{i})_{i\ge 1}$$ ( T i , Y i ) i ≥ 1 , where $$T_{i}$$ T i is the time of occurrence of the $$i$$ i th...
The limiting behavior of the hazard rate of coherent systems based on sequential order statistics is examined. Related results for the survival function of the system lifetime are also considered. For deriving the results, properties of limits involving a relevation transform are studied in detail. Then, limits of characteristics in sequential $$k$$ k -out-of- $$n$$ n systems and general...
Existing model averaging methods are generally based on ordinary least squares (OLS) estimators. However, it is well known that the James–Stein (JS) estimator dominates the OLS estimator under quadratic loss, provided that the dimension of coefficient is larger than two. Thus, we focus on model averaging based on JS estimators instead of OLS estimators. We develop a weight choice method and prove...
We study here extremes of residuals of the bivariate lifetime and the residual of extremes of the two lifetimes. In the case of generalized Marshall–Olkin model and the total time transformed exponential model, we first present some sufficient conditions for the extremes of residuals to be stochastically larger than the residual of the corresponding extremes, and then investigate the stochastic order...
The non-parametric likelihood L(F) for censored data, including univariate or multivariate right-censored, doubly-censored, interval-censored, or masked competing risks data, is proposed by Peto (Appl Stat 22:86–91, 1973). It does not involve censoring distributions. In the literature, several noninformative conditions are proposed to justify L(F) so that the GMLE can be consistent (see, for examples,...
U-type designs and orthogonal Latin hypercube designs (OLHDs) have been used extensively for performing computer experiments. Both have good spaced filling properties in one-dimension. U-type designs may not have low correlations among the main effects, quadratic effects and two-factor interactions. On the other hand, OLHDs are hard to be found due to their large number of levels for each factor....
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