20 research outputs found
Nonlinear least squares estimators with differential rates of convergence
No full textAssume observations Y[subscript] t, defined on a complete probability space ([omega], F, P), are generated by the model Y[subscript]t=f[subscript]t([theta][superscript]0)+e[subscript]t, t=1,2,..., where [theta][superscript]0 is the true parameter vector lying in a subset [theta] of a Euclidean space, f[subscript] t is a known function of both [omega] and [theta], where [omega] is an element of [omega] and [theta] is an element of [theta], f[subscript] t([omega],·) is almost surely twice continuously differentiable with respect to [theta] in some open, convex neighborhood S of [theta][superscript]0, and the e[subscript] t are zero mean unobservable random variables. The e[subscript] t can be independent or martingale differences. The sums of squares of the first partial derivatives of f[subscript] t([theta]) with respect to different components of the parameter [theta] are permitted to increase at different rates. Also, f[subscript] t can be a function of an increasing number of lagged values of the dependent variable Y[subscript] t as the index t increases;Under some regularity conditions it is demonstrated that there is a solution of the least squares equations which is a strongly consistent estimator of [theta][superscript]0. Furthermore, the properly normalized estimator has an asymptotic distribution. The limiting distribution of some components of the least squares estimator can be nonnormal. With differential rates, as sample size n increases, different components of the least squares estimator require different normalizers;Our theory can be applied to the estimation of regression models with autoregressive errors and to nonlinear models with time trend or random walks among the explanatory variables. Another example of the application of our theory is the ordinary least squares estimation of the parameters of the autoregressive moving average model of order (1,1) with an autoregressive unit root. A small Monte Carlo study of the estimators for the autoregressive moving average model indicates that the large sample results provide a reasonable approximation for samples on the order of 100.</p
Availability of a periodically inspected system supported by a spare unit, under perfect repair or perfect upgrade
No full textAvailability of a periodically inspected system supported by a spare unit, under perfect repair or perfect upgrade
No full textThe exact availability and the limiting average availability of a periodically inspected system, supported by a spare and maintained with perfect repairs or upgrades, are obtained for arbitrary life-, repair- and upgrade-time distributions. Illustrative examples, graphs and table are presented.Gamma Limiting average availability New better than used in expectation Reliability Renewal Weibull
A note on testing for a unit root in an ARIMA(p,1,0) signal observed with MA(q) noise
No full textAn ARIMA(p,1,0) signal contaminated by MA(q) noise is a restricted ARIMA(p,1,p + q + 1) process. For this model restricted by nonlinear constraints, it is shown that the maximum likelihood estimator of the unit root is strongly consistent and its limiting distribution is the same as that of the least squares estimator of the unit root in an AR(1) process tabulated by Dickey and Fuller.Measurement error maximum likelihood estimation large sample properties unit root nonstationarity
Linking Diversity and Disparity Measures
No full textThe purpose of this paper is to examine links between the diversity measures (Patil and Taillie 1982) and the disparity measures (Lindsay 1994), quantities apparently developed for somewhat different purposes. We demonstrate that numerous diversity measures satisfying all the desirable criteria mentioned by Patil and Taillie can be defined by the generating functions of certain disparities and the associated residual adjustment functions. This provides the statistician and the ecologist a wide class of flexible indices for the statistical measurement of diversity
Minimum disparity estimation in the errors-in-variables model
No full textRobust estimators are determined using the minimum disparity estimation method (Lindsay, 1994; Basu and Lindsay, 1994) in the errors-in-variables model. These estimators are asymptotically fully efficient for the model considered and have strong robustness features. In a numerical example these estimators compare favorably with the orthogonal regression M-estimators of Zamar (1989).Hellinger distance Kernel density estimation Robustness Transparent kernel
