分层三阶段及以上抽样的自加权抽样设计

大型抽样调查总是采用分层多阶段抽样.分层多阶段抽样若采用自加权的抽样设计,则总体总量的估计量形式简单,易于计算.本文提出了分层三阶段及以上抽样的自加权抽样设计方法.     

Differential and ergodic transforms

In this paper we consider weighted differences of ergodic averages and averages associated with differentiation. These weighted differences are shown to converge a.e., as well as in . These results have consequences for unconditional convergence of the series of differences, and give some information about how the averages converge. Received: 6 March 2000 / Published online: 4 April 2002     

Certain weighted averages of generalized Ramanujan sums

We derive certain identities involving various known arithmetical functions and a generalized version of Ramanujan sum. L. Tóth constructed certain weighted averages of Ramanujan sums with various arithmetic functions as weights. We choose a generalization of Ramanujan sum given by E. Cohen and derive the weighted averages corresponding to the versions of the weighted averages established by Tóth.     

Weighted Hardy-Littlewood operators and commutators on p-adic functional spaces

In this paper we give necessary and sufficient conditions for the boundedness of the weighted Hardy-Littlewood averages and the weighted Cesàro averages on p-adic Triebel-Lizorkin spaces and p-adic Morrey-Herz spaces. Especially, the corresponding operator norms in each case are established. Furthermore, sufficient conditions of the boundedness of the commutators of weighted Hardy-Littlewood operators, and weighted Cesàro operators with symbols in the Lipschitz spaces on p-adic Morrey-Herz spaces are also given.     

An Estimate of the Odds Ratio That Always Exists

This article proposes an estimate of the odds ratio in a (2 × 2) table obtained from studies in which the row totals are fixed by design, such as a phase II clinical trial. Our estimate, based on the median unbiased estimate of the probabilities of success in the (2× 2) table, will always be in the interval (0, ∞). Another estimate of the odds ratio which has such properties is obtained when adding .5 to each cell of the table. Using simulations, we compared our proposed estimate to that obtained by adding .5 to every cell, and found that our estimate had smaller finite sample bias, and larger mean square error. We also propose the use of the bootstrap to form a confidence interval for the odds ratio based on our proposed estimate. Instead of a Monte Carlo bootstrap, one can easily calculate the “exact” bootstrap distribution of our estimate of the odds ratio, and use this distribution to calculate confidence intervals.     

Some properties of a simple moving average when applied to forecasting a time series

Simple (equally weighted) moving averages are frequently used to estimate the current level of a time series, with this value being projected as a forecast for future observations. A key measure of the effectiveness of the method is the sampling error of the estimator, which this paper defines in terms of characteristics of the data. This enables the optimal length of the average for any steady state model to be established and the lead time forecast error derived. A comparison of the performance of a simple moving average (SMA) with an exponentially weighted moving average (EWMA) is made. It is shown that, for a steady state model, the variance of the forecast error is typically less than 3% higher than the appropriate EWMA. This relatively small difference may explain the inconclusive results from the empirical studies about the relative predictive performance of the two methods.     

Connections in Proportional Reasoning: Levers,Arithmetic Means,Mixtures, Batting Averages,and Speeds

The lever is used to give an alternate physical representation of, and as a means to connect, situations that involve weighted averages and inverse proportionality, such as arithmetic means, mixtures, batting averages, and speeds. Geometric representations of the situations are also provided as another way to make connections.     

复杂设计下类均值复制与类加权均值复制的比较（英文）

复制数据是处理抽样调查中数据项目缺失的一种常用方法。在两种常见模型及复杂抽样设计下，本文对处理数据项目缺失的类均值复制和类加权均值复制方法进行了对比。     

Optimality and robustness of combinations of moving averages

A combination of moving averages has been shown previously to be more accurate than simple moving averages, under certain conditions, and to be more robust to non-optimal parameter specification. However, the use of the method depends on specification of three parameters: length of greater moving average, length of shorter moving average, and the weighting given to the former. In this paper, expressions are derived for the optimal values of the three parameters, under the conditions of a steady state model. These expressions reduce a three-parameter search to a single-parameter search. An expression is given for the variance of the sampling error of the optimal combination of moving averages and this is shown to be marginally greater than that for exponentially weighted moving averages (EWMA). Similar expressions for optimal parameters and the resultant variance are derived for equally weighted combinations. The sampling variance of the mean of such combinations is shown to be almost identical to the optimal general combination, thus simplifying the use of combinations further. It is demonstrated that equal weight combinations are more robust than EWMA to noise to signal ratios lower than expected, but less robust to noise to signal ratios higher than expected.     

Graphical designs and gale duality

Mathematical Programming - A graphical design is a subset of graph vertices such that the weighted averages of certain graph eigenvectors over the design agree with their global averages. We use...     

Weak and universal consistency of moving weighted averages

The properties of weighted averages as linear estimators of a regression function and its derivatives are investigated for the fixed design case. Results on weak consistency and on universal consistency are derived, using a modification of the definition of Stone [10]. As examples we consider kernel estimates and weighted local regression estimators and show that the general results apply.     

An improved Afriat–Diewert–Parkan nonparametric production function estimator

Recent developments in the production frontier literature include nonparametric estimators with shape constraints. A few of these estimators rely on the Afriat inequalities to provide piecewise linear approximations to the production function/frontier. We show in this paper that these Afriat–Diewert–Parkan (ADP) estimators have deficiencies in the presence of moderate statistical noise including overfitting and a relatively high estimator variance. We propose new estimators with lower variance and a relatively low bias. We consider such alternative estimators based on (weighted) averages of random hinge functions with parameter restrictions. Small sample properties of the estimators are presented that show our new estimators outperform the existing ADP estimators when moderate to large amounts of noise are present.     

Multiplicative decision rules for multiobjective decision problems

Properties of consistency of general decision rules for multiobjective decision problems are discussed. Decision rules based on the family of weighted geometric averages are introduced, their properties are analysed and possible implementations are discussed.     

Second order asymptotic comparison of estimators of a common parameter in the double exponential case

Summary The problem to estimate a common parameter for the pooled sample from the double exponential distributions is discussed in the presence of nuisance parameters. The maximum likelihood estimator, a weighted median, a weighted mean and others are asymptotically compared up to the second order, i.e. the ordern ^−1/2 with the asymptotic expansions of their distributions. University of Electro-communications     

The mean as the balance point: thought experiments with measuring sticks

This article presents activities to help students establish a connection between the mean and the balance point of a lever. The lever and its law are discussed briefly. Thought experiments with a meterstick are presented to emphasize different properties of the mean and weighted averages.     

A robust forecasting system,based on the combination of two simple moving averages

For series with negligible growth and seasonality, simple moving averages are frequently used to estimate the current level of a process, and the resultant value projected as a forecast for future observations. This paper shows that a linear combination of two simple moving averages (SMA) can provide an improved estimate of the underlying level of the process. The proposition is demonstrated by simulation, and good combinations are listed. The theory underlying the improvement is developed. The general rules are then illustrated through an application in an inventory situation.     

Convergence of weighted averages of random variables revisited

We show that for a large class of positive weights including the ones that are eventually monotone decreasing and those that are eventually monotone increasing but vary regularly, if the averages of random variables converge in some sense, then their corresponding weighted averages also converge in the same sense. We will also replace the sufficient conditions in the fundamental result of Jamison, Pruitt, and Orey for i.i.d. random variables that make their work more transparent.

     

Discount Weighted Moving Averages

An estimator to replace exponentially weighted moving averages is described and examples of its use are given. It has similar limiting properties but includes the on-line estimation of the forecast error variance as an integral part. The procedures for starting off and intervention are given.     

Subdivision Schemes of Sets and the Approximation of Set-Valued Functions in the Symmetric Difference Metric

In this work we construct subdivision schemes refining general subsets of ? ⁿ and study their applications to the approximation of set-valued functions. Differently from previous works on set-valued approximation, our methods are developed and analyzed in the metric space of Lebesgue measurable sets endowed with the symmetric difference metric. The construction of the set-valued subdivision schemes is based on a new weighted average of two sets, which is defined for positive weights (corresponding to interpolation) and also when one weight is negative (corresponding to extrapolation). Using the new average with positive weights, we adapt to sets spline subdivision schemes computed by the Lane–Riesenfeld algorithm, which requires only averages of pairs of numbers. The averages of numbers are then replaced by the new averages of pairs of sets. Among other features of the resulting set-valued subdivision schemes, we prove their monotonicity preservation property. Using the new weighted average of sets with both positive and negative weights, we adapt to sets the 4-point interpolatory subdivision scheme. Finally, we discuss the extension of the results obtained in metric spaces of sets, to general metric spaces endowed with an averaging operation satisfying certain properties.     

非齐次树上马氏链的若干强偏差定理

通过构造适当的非负鞅,将Doob鞅收敛定理应用于几乎处处收敛的研究,给出了一类非齐次树上马氏链场加权和滑动平均的若干强偏差定理.