Conditional inference in finite population sampling under a calibration model

Several estimators, including the classical and the regression estimators of finite population mean, are compared, both theoretically and empirically, under a calibration model, where the dependent variable(y), and not the independent variable(x), can be observed for all units of the finite population. It is shown asymptotically that when conditioned on x, the bias of the classical estimator may be much smaller than that of the regression estimators; whereas when conditioned on y, the regression estimator may have much smaller conditional bias than the classical estimator. Since all the y's(not x's) can be observed, it seems appropriate to make comparison under the conditional distribution of each estimator with y fixed. In this case, the regression estimator has smaller variance, smaller conditional bias, and the conditional coverage probability closer to its nominal level     

The Identification of Multiple Outliers in ARIMA Models

Abstract

There are three main problems in the existing procedures for detecting outliers in ARIMA models. The first one is the biased estimation of the initial parameter values that may strongly affect the power to detect outliers. The second problem is the confusion between level shifts and innovative outliers when the series has a level shift. The third problem is masking. We propose a procedure that keeps the powerful features of previous methods but improves the initial parameter estimate, avoids the confusion between innovative outliers and level shifts and includes joint tests for sequences of additive outliers in order to solve the masking problem. A Monte Carlo study and one example of the performance of the proposed procedure are presented.     

Nonparametric Bayes and empirical Bayes estimation of the population median,with application in finite-population sampling

ABSTRACT

Nonparametric Bayes and empirical Bayes estimators of the population median are provided under Dirichlet process priors. The finite-population sampling is used to estimate the finite-population median under Dirichlet process priors. The asymptotic properties of the estimators are obtained from a frequentist perspective.     

Partitioned cross-validation

Partitioned cross-validation is proposed as a method for overcoming the large amounts of across sample variability to which ordinary cross-validation is subject. The price for cutting down on the sample noise is that a type of bias is intriduced. A theory is presented for optimal trade-off of this variance and bias. Comparison with other bandwidth selection methods is given.     

Estimation of tail parameters under type i censoring

This paper is a continuation of previous work concerning the estimation of tail-parameters under Type II censoring (Weissman 1978). The same estimation problem is considered here, this truip under Type I censoring. A sample of size n is censored below aE a given level x₀it is assumed that che underlying distriibution .function (df)belogs to the domain of attraction of a known extreme-value distribution and that K - K(x_o) , the number of observed values, remains finite as on - ∞ . We offer here estimators, which are asymptotically maximum likelihood estimators (MLE's), for quantiles associated with the tail of F such as location and scale parameters, quantiles and F(x) itself (for x in the tail). The results are applied to two illustrative examples.     

Further Results on Zellner's Minimum Expected Loss and Full Information Maximum Likelihood Estimators for Undersized Samples

The article presents a consistent set of conditions that a prior pdf for the reduced-form parameters must satisfy if Zellner's MELO estimators for the structural coefficients of a linear structural econometric model are to exist in all normal cases where the available sample is undersized. Also, the conditions under which the full information maximum likelihood estimators of structural coefficients exist are given. Finally, the article reports application of MELO estimation to Klein's Model I.     

A method for approximate fully bayesian analysis of parameters

Stochastic modeling of the geology in petroleum reservoirs has become an important tool in order to investigate flow properties in the reservoir. The stochastic models used contain parameters which must be estimated based on observations and geological knowledge. The amount of data available is however quite limited due to high drilling costs etc., and the lack of data prevents the use of many of the standard data driven approaches to the parameter estimation problem. Modern simulation based methods using Markov chain Monte Carlo simulation, can however be used to do fully Bayesian analysis with respect to parameters in the reservoir model, with the drawback of relatively high computational costs. In this paper, we propose a simple, relatively fast approximate method for fully Bayesian analysis of the parameters. We illustrate the method on both simulated and real data using a two-dimensional marked point model for reservoir characterization.     

Influence curve of the monotonic dependence function for binormal distributions

Explicit formulae are derived for the influence curve of the monotonic dependence function in the case of binormal distributions, and are compared with those for the correlation coefficient. The interpretation of the comparison is given.     

Maximum likelihood and optimum location of observation sites in geodetic and spatial surveying

In geodetic and spatial surveying, accurate statistical es-timates of the Cartesian coordinates of a stationary target depend, in general, on such factors as target position, number and type of instruments, their location, their accuracy, and their mix. Direct measurements are assumed to be made in elevation, azimuth, and range with errors independently and normally distributed. For a mix of instruments, theoretical arguments are established using maximum likelihood estimation to determine the optimal siting of the instruments which minimizes (GDOP)² or the square of the geo-metric dilution of precision = sum of the variances of the estimates in the three orthogonal directions.     

Some asymptotic properties of point estimation with n-dimensional fuzzy data

Some asymptotic properties of point estimation with n-dimensional fuzzy data with respect to a special L ₂-metric ρ are investigated in this article. It is shown that the collection of all n-dimensional fuzzy data endowed with the ρ-metric is a complete and separable space. Some criterions for point estimation in such fuzzy environments are proposed, and the sample mean, variance and covariance with n-dimensional fuzzy data under these criteria are further studied.