重权数在复杂调查的方差估计中的应用

 方差估计是抽样调查的重要组成部分,重抽样方法是常用的方差估计方法。重权数方法与重抽样方法类似,也是利用计算机的优势通过重复获得大量不同的子样本的重权数估计目标参数的估计量和方差估计量,是一种稳健、通用、有效的方差估计方法。本文主要介绍重权数在复杂抽样调查的方差计算中的理论和应用。     

Generation of random matrices with orthonormal columns and multivariate normal wariates with given sample mean and covariance

In this paper, an algorithm for generating random matrices with orthonormal columns is introduced. As pointed out by a referee, the algorithm is almost identical to Wedderburn's (1975) unpublished method. The method can also be considered as an extension of Stewart's (1980) method, which was designed to generate random orthogonal matrices. It is found outperforming a simple extension of the QR factorization method and that of Heiberger's (1978) method. This paper also demonstrates how the algorithm can be used in generating multivariate normal variates with given sample mean and sample covariance matrix.     

Rank reducible varying coefficient model

We propose in this article a novel dimension reduction method for varying coefficient models. The proposed method explores the rank reducible structure of those varying coefficients, hence, can do dimension reduction and semiparametric estimation, simultaneously. As a result, the new method not only improves estimation accuracy but also facilitates practical interpretation. To determine the structure dimension, a consistent BIC criterion is developed. Numerical experiments are also presented.     

Confounded row–column designs

Confounded row–column designs for factorial experiments are considered and a simple method of construction using the classical method of confounding is described. Partially confounded designs are also studied and a method for generating Rao's (1946) designs is presented.     

A METHOD FOR DETERMINING THE ASYMPTOTIC EFFICIENCY OF SOME SEQUENTIAL PROBABILITY RATIO TESTS

This paper gives a method for decomposing many sequential probability ratio tests into smaller independent components called “modules”. A function of some characteristics of modules can be used to determine the asymptotically most efficient of a set of statistical tests in which a, the probability of type I error equals β, the probability of type II error. The same test is seen also to give the asymptotically most efficient of the corresponding set of tests in which a is not equal to β. The “module” method is used to give an explanation for the super-efficiency of the play-the-winner and play-the-loser rules in two-sample binomial sampling. An example showing how complex cases can be analysed numerically using this method is also given.     

Response shrinkage estimation in multinomial logit models

A shrinkage estimation method for multinomial logit models is developed. The proposed method is based on shrinking the responses for each category towards the underlying probabilities. The estimator is also used in combination with Pregibon's resistant fitting. The resulting estimator can also be used to control the over-estimation of Pregibon's resistant estimator. The proposed method handles not only the problem of separation in multinomial logit models but estimates also exist when the number of covariates is large relative to the sample size. Estimates exist even when the MLE does not exist. Estimates can be easily computed with all commonly used statistical packages supporting the fitting procedures with weights. Estimates are compared with the usual MLE and Firth's bias reduction technique in a simulation study and an application.     

Partitioning with Respect to a Control: Unequal Sample Sizes Case

This article describes a method for partitioning with respect to a control for the situation in which the treatment sample sizes are unequal and also for the situation where the treatment sample sizes are equal except for a few missing values. Calculation of the critical values required for finding confidence limits is discussed and tables are presented for the “almost equal” sample size case. An application of this method to length of stay data for congestive heart failure patients is also provided.     

Numerical Comparison Between Different Empirical Prediction Intervals Under the Fay-Herriot Model

Recently, an empirical best linear unbiased predictor is widely used as a practical approach to small area inference. It is also of interest to construct empirical prediction intervals. However, we do not know which method should be used from among the several existing prediction intervals. In this article, we first obtain an empirical prediction interval by using the residual maximum likelihood method for estimating unknown model variance parameters. Then we compare the later with other intervals with the residual maximum likelihood method. Additionally, some different parametric bootstrap methods for constructing empirical prediction intervals are also compared in a simulation study.     

Identification of seasonal arima models using a filtering method

This paper proposes an identification method of ARIMA models for seasonal time series using an intermediary model and a filtering method. This method is found to be useful when conventional methods, such as using sample ACF and PACF, fail to reveal a clear-cut model. This filtering identification method is also found to be particularly effective when a seasonal time series is subjected to calendar variations, moving-holiday effects, and interventions.     

Prediction intervals for the random intercept linear model

Our main purpose is to give a method of constructing prediction intervals for the mean of us future observations in the random intercept linear model, A method is also indicated for constructing exact confidence intervals on the expected value of a future observation.     

Reliability computation under dynamic stress–strength modeling with cumulative stress and strength degradation

Reliability function is defined under suitable assumptions for dynamic stress–strength scenarios where strength degrades and stress accumulates over time. Methods for numerical evaluation of reliability are suggested under deterministic strength degradation and cumulative damage due to shocks arriving according to a point process, in particular a Poisson process, using simulation method and inversion theorem. These methods are specifically useful in the scenarios where damage distributions do not possess closure property under convolution. The method is also extended for non-identical, dependent damage distributions as well as for random strength degradation. Results from inversion method is compared with known approximate methods and also verified by simulation. As it turns out, the simulation method seems to have an edge in terms of computational burden and has much wider domain of applicability.     

Non-rejective implementations of the Sampford sampling design

Sampford sampling is a method for unequal probability sampling. There exist several implementations of the Sampford sampling design which all are rejective methods, i.e. the sample is not always accepted. Thus the existing methods can be time consuming or even infeasible in some situations. In this paper, a fast and non-rejective list-sequential method, which works in all situations, is presented. The method is a modification of a previously existing rejective list-sequential method. Another list-sequential implementation of Sampford sampling is also presented.     

Bootstrap method in ranking and slippage problems

In this paper, the bootstrap method of Efron (1979) is given for a ranking and a slippage problem, where the ranking (or slippage) is with respect to the mean of the distributions. The method is also applied to obtain a confidence interval for the largest mean.     

A novel weighted likelihood estimation with empirical Bayes flavor

We propose a novel approach to estimation, where a set of estimators of a parameter is combined into a weighted average to produce the final estimator. The weights are chosen to be proportional to the likelihood evaluated at the estimators. We investigate the method for a set of estimators obtained by using the maximum likelihood principle applied to each individual observation. The method can be viewed as a Bayesian approach with a data-driven prior distribution. We provide several examples illustrating the new method and argue for its consistency, asymptotic normality, and efficiency. We also conduct simulation studies to assess the performance of the estimators. This straightforward methodology produces consistent estimators comparable with those obtained by the maximum likelihood method. The method also approximates the distribution of the estimator through the “posterior” distribution.     

Change detection in the mean of a white Gaussian process by the backward standardized sum

A statistical method for detection of a change in the mean of a white Gaussian noise process is developed in this paper. The decision function of the method searches for the maximum of the backward standardized sum in a moving window to detect the change. Statistical properties of the decision function are derived to set the detection threshold. The derivation of the mean delay function and the optimal size of the moving window is also presented. The performance of the proposed method is compared, in terms of the mean delay for the detection, with that of the exponentially weighted moving average (EWMA). The mean delays of the cumulative sum control charts are also compared for benchmarking. The performance comparison is carried out by evaluating the average run length functions and by simulations. The results conclude that the mean detection delay of the proposed method is shorter than that of the standard EWMA for the same Type I error probability.     

Large-sample quantile estimation in pareto laws

A large-sample method of estimation for the parameters of Pareto laws is investigatedo The estimates are derived by using a small subset of k sample quantiles out of the original observations. The optimum spacing of the k quantiles is also examined. A Monte Carlo study compares this method with the method of moments and that of maximum likelihood for a selected set of parameter values and sample sizes.     

A Two-Stage Estimation Method for Random Coefficient Differential Equation Models with Application to Longitudinal HIV Dynamic Data

We propose a two-stage estimation method for random coefficient ordinary differential equation (ODE) models. A maximum pseudo-likelihood estimator (MPLE) is derived based on a mixed-effects modeling approach and its asymptotic properties for population parameters are established. The proposed method does not require repeatedly solving ODEs, and is computationally efficient although it does pay a price with the loss of some estimation efficiency. However, the method does offer an alternative approach when the exact likelihood approach fails due to model complexity and high-dimensional parameter space, and it can also serve as a method to obtain the starting estimates for more accurate estimation methods. In addition, the proposed method does not need to specify the initial values of state variables and preserves all the advantages of the mixed-effects modeling approach. The finite sample properties of the proposed estimator are studied via Monte Carlo simulations and the methodology is also illustrated with application to an AIDS clinical data set.     

A Consistent Method of Estimation For The Three-Parameter Gamma Distribution

For the three-parameter gamma distribution, it is known that the method of moments as well as the maximum likelihood method have difficulties such as non-existence in some range of the parameters, convergence problems, and large variability. For this reason, in this article, we propose a method of estimation based on a transformation involving order statistics from the sample. In this method, the estimates always exist uniquely over the entire parameter space, and the estimators also have consistency over the entire parameter space. The bias and mean squared error of the estimators are also examined by means of a Monte Carlo simulation study, and the empirical results show the small-sample superiority in addition to the desirable large sample properties.     

A theorem on the density of the density ordinate and an alternative interpretation of the bqx-muller method

This paper obtains a theorem about the density of the density ordinate when the latter is regarded as a random variable in its own right. The theorem is used to provide an alternative interpretation of the BOX-MULLER simulation method which extends also to an alternative method for simulating from the LAPLACE density     

Multiresolution anomaly detection method for fractional Gaussian noise

Driven by network intrusion detection, we propose a MultiResolution Anomaly Detection (MRAD) method, which effectively utilizes the multiscale properties of Internet features and network anomalies. In this paper, several theoretical properties of the MRAD method are explored. A major new result is the mathematical formulation of the notion that a two-scaled MRAD method has larger power than the average power of the detection method based on the given two scales. Test threshold is also developed. Comparisons between MRAD method and other classical outlier detectors in time series are reported as well.