PARAMETER ESTIMATION OF EXPONENTIAL DISTRIBUTION

Because of the importance of grouped data, many scholars have been devoted to the study of this kind of data. But, few documents have been concerned with the thresh-old parameter. In this paper, we assume that the threshold parameter is smaller than the first observing point. Then, on the basis of the two-parameter exponential distribution, the maximum likelihood estimations of both parameters are given, the sufficient and necessary conditions for their existence and uniqueness are argued, and the asymptotic properties of the estimations are also presented, according to which approximate confidence intervals of the parameters are derived. At the same time, the estimation of the parameters is generalized, and some methods are introduced to get explicit expressions of these generalized estimations. Also, a special case where the first failure time of the units is observed is considered.     

ASYMPTOTIC NORMALITY OF M-ESTIMATES IN THE EV MODEL

1.Introductionaamconsidert.heerrors--ill--vanal)les(EV)modelasfollowsfwhereXandxareobservableandUnobservableran(lolllvectorsoilCPrespectively,doisitp--dimensionalunknowllparametervector,(e,II")"isap Iudilnensiollalsphericalerrorvector,whichmeansthat(E,U")…     

ASYMPTOTICS OF MEAN TRANSFORMATION ESTIMATORS WITH ERRORS IN VARIABLES MODEL

This paper addresses estimation and its asymptotics of mean transformation θ = E[h（X）] of a random variable X based on n lid. observations from errors-in-variables model Y = X＋ v, where v is a measurement error with a known distribution and h（.） is a known smooth function. The asymptotics of deconvolution kernel estimator for ordinary smooth error distribution and expectation extrapolation estimator are given for normal error distribution respectively. Under some mild regularity conditions, the consistency and asymptotically normality are obtained for both type of estimators. Simulations show they have good performance.     

ASYMPTOTIC PROPERTIES OF L_1-NORM KERNEL ESTIMATOR OF THE CONDITIONAL MEDIAN

Let(X,Y) be a pair of R~d×R~1-valued random variables.In thispaper we investigate the asymptotic properties of the L_1-norm kernel estimator ofthe conditional median function of Y on X.Under appropriate regularity condi-tions,asymptotic normality and the optimal rates of convergence n~((-1)/(2+d))and(n~(-1)log n)~(1/(2+d)) in the L~q(1(?)q<∞)-and L~∞-norms restricted to a compactset,respectively,are obtained.Our study shows that this estimator and the well-known Nadaraya-Watson's kernel estimator of the conditional mean function of Yon X have the same asymptotic properties.     

ON ASYMPTOTIC NORMALITY OF PARAMETERS IN MULTIPLE LINEAR ERRORS－IN－VARIABLES MODEL

This paper studies the parameter estimation of multiple dimensional linear errors-in-variables (EV) models in the case where replicated observations are available in some experimental points. Asymptotic normality is established under mild conditions, and the parameters entering the asymptotic variance are consistently estimated to render the result useable in the construction of large-sample confidence regions.     

ASYMPTOTIC NORMALITY OF SOME ESTIMATORS IN A FIXED-DESIGN SEMIPARAMETRIC REGRESSION MODEL WITH LINEAR TIME SERIES ERRORS

Consider a semiparametric regression model with linear time series errors Yk = x'kβ g(tk) εk, 1 < k < n, where Yk's are responses, xk = (xk1,xk2,..... ,xkp)' and tk ∈T ∪R are fixed design points, β= (β1, β2, ....., βp)' is an unknown parameter vector, g(.) is an unknown bounded real-valued function defined on a compact subset T of the real line R, and εk is a linear process given by εk = ∑j=0∞j(?)ek-j,(?)= 1, where , are i.i.d. random variables. In this paper we establish the asymptotic normality of the least squares estimator of β, a smooth estimator of g(.), and estimators of the autocovariance and autocorrelation functions of the linear process εk.