Unbiased statistical estimation functions for parameters in presence of nuisance parameters

We consider the problem of estimating a vector interesting parameter in the presence of nuisance parameters through vector unbiased statistical estimation functions (USEFs). An extension of the Cramer—Rao inequality relevant to the present problem is obtained. Three possible optimality criteria in the class of regular vector USEFs are those based on (i) the non-negative definiteness of the difference of dispersion matrices (ii) the trace of the dispersion matrix and (iii) the determinant of the dispersion matrix. We refer to these three criteria as M-optimality, T- optimality and D-optimality respectively. The equivalence of these three optimality criteria is established. By restricting the class of regular USEFs considered by Ferreira (1982), we study some interesting properties of the standardized USEFs and establish essential uniqueness of standardized M-optimal USEF in this restricted class. Finally some illustrative examples are included.     

Applications of social area analysis to program planning and evaluation

The development of social area analysis as a research technique is highlighted, and two illustrative applications are presented. The first example applies social area analysis to the study of an urban region's demography and the distribution of social problems found there. The second example illustrates how social area analysis can be integrated within a larger evaluation effort. Suggestions for undertaking social area analyses and related demographic studies are presented.     

The effects of conflict,quality, and time on small group information use and behavior in evaluative decision making situations

Graduate students simulated school board members making decisions about educational programs. Situation contexts within the program evaluation reports were varied by conflict (high, low), quality (high, low), and time (long, short). Analyses of Variance (ANOVA) of the qualitative measures m the 2 × 2 × 2 factorial design indicated significant results at the .01 level. The quality of decisions affect support for program continuation. Interactions of conflict and quality affected need for more information and more time in decision making. A conflict and time interaction affected preference to talk to other board members. Changes in situational contexts affected information need and use in small, decision making groups.     

Estimating the quantile function of a location-scale family of distributions based on few selected order statistics

Some general asymptotic methods of estimating the quantile function, Q(ξ), 0<ξ<1, of location-scale families of distributions based on a few selected order statistics are considered, with applications to some nonregular distributions. Specific results are discussed for the ABLUE of Q(ξ) for the location-scale exponential and double exponential distributions. As a further application of the exponential results, we discuss a nonlinear estimator of Q(ξ) for the scale-shape Pareto distribution.     

Minimax estimation of a lower-bounded scale parameter of a gamma distribution for scale-invariant squared-error loss

Let X have a gamma distribution with known shape parameter θr;aL and unknown scale parameter θ. Suppose it is known that θ ≥ a for some known a > 0. An admissible minimax estimator for scale-invariant squared-error loss is presented. This estimator is the pointwise limit of a sequence of Bayes estimators. Further, the class of truncated linear estimators C = {θ_ρ|θ_ρ(x) = max(a, ρ), ρ > 0} is studied. It is shown that each θ_ρ is inadmissible and that exactly one of them is minimax. Finally, it is shown that Katz's [Ann. Math. Statist., 32, 136–142 (1961)] estimator of θ is not minimax for our loss function. Some further properties of and comparisons among these estimators are also presented.     

An empirical Bayes approach to outliers

A formulation of the problem of detecting outliers as an empirical Bayes problem is studied. In so doing we encounter a non-standard empirical Bayes problem for which the notion of average risk asymptotic optimality (a.r.a.o.) of procedures is defined. Some general theorems giving sufficient conditions for a.r.a.o. procedures are developed. These general results are then used in various formulations of the outlier problem for underlying normal distributions to give a.r.a.o. empirical Bayes procedures. Rates of convergence results are also given using the methods of Johns and Van Ryzin (1971, 1972).     

中国共产党的先进性是具体的历史的

江泽民同志在“5·3 1”讲话、“十六大”报告中 ,强调指出党的先进性是具体的历史的 ,也就是与时俱进。这是马克思主义世界观的根本要求 ,是时代的根本要求。只有这样 ,才能始终做到“三个代表”。     

射孔对破裂压力及裂缝形态影响数值模拟研究

针对射孔对水力压裂过程中的破裂压力以及裂缝形态的问题，通过建立不同射孔方位和不同远场主应力条件下裂缝扩展模型，将位移不连续方法（DDM）应用于水力压裂过程中的力学分析研究，同时在裂缝扩展准则上运用修正了的G准则—F准则并进行裂缝扩展规律研究。根据不同射孔方位和不同远场主应力条件下裂缝扩展的模拟计算，在地应力大小和方位确定的情况下，破裂压力随着射孔方位的增大而升高，并且随着方位角的增大，裂缝形态会发生转向，而且裂缝壁面粗糙，会增大压裂液摩阻。对于实际的射孔参数优化设计和压裂施工具有参考意义     

Sequence-compound estimation in scale-exponential families and speed of convergence

This paper deals with a sequence-compound estimation. The component problem is the squared error loss estimation of θ?[a,b] based on an observation X whose p.d.f. is of the form $\text{u(x)c(θ)}\text{exp}\text{(?}\text{x}\text{θ}\text{)}$. For each $\text{0<t<}\text{1}\text{2}$ a class of sequence-compound estimators $\text{ψ}\text{?}\text{=}\text{ψ}\text{?}{}_1\text{,}\text{ψ}\text{?}{}_2\text{,…)}$ is exhibited whose compound risk (average of risks) up to stage n differs from the Bayes envelope (in the component problem) w.r.t. the empiric distribution G_n of the parameters involved up to stage n by a quantity of order O(n^?δt) for a δ>0. It is also shown that at any stage i the difference of the risk of ψ?_i and the risk of the Bayes response w.r.t. G_i?1 is O(i^?δt). Examples of the above type of families are given where δ is min{1,$\text{2a}\text{b}$} and t is arbitrarily close to $\text{1}\text{2}$. Here it may be worthwhile to mention that a rate $\text{O}\text{(n}{}^{\mathrm{<mtext>?</mtext><mtext>1</mtext><mtext>2</mtext>}}\text{)}$ or better has not yet been obtained even in a very special family of densities.