改革工业品价格统计——兼谈指数方法在工业统计中应用的可能

一、历史的回顾 长期以来,在我国工业统计的实践中,一直没有建立起直接的工业品价格统计制度,而是采取间接推导的方法,来大体反映工业品出厂价格的变动趋势。这种间接推导的方法,就是用工业总产值的动态指标,通过按拉氏物量指数公式计算的工业生产指数,推导出按巴氏价格指数公式计算的工业品出厂价格指数。其计算公式是,∑p_1q_1/∑p_0q_0=(∑p_0q_1/∑p_0q_0)×(∑p_1q_1/∑p_0q_1),移项后得:∑p_1q_1/∑p_0q_1=(∑p_1q_1/∑p_0q_0)÷(∑p_0q_1/∑p_0q_0) p_1和p_0分别为报告期和基期的工业品出厂价格;q_1和q_0分别为报告期和基期的工业品生产数量;∑p_1q_1和∑p_0q_0分别为报告期和基期按现行价格(即当年价格)计算的工业总产值。     

计算我国工业生产价格指数的公式问题

编制我国工业生产价格指数,国家统计局颁发的《工业产品价格统计试行方案》是采用下面的公式:工业生产价格指数((?))=∑各工业产品出厂价格指数×该产品的权数/∑各产品的权数=∑KW/∑W式中的各工业产品出厂价格指数K,是较均匀地分布在各部门、各行业的400种(包括700个规格)代表产品的出厂价格指数。某代表产品出厂价格指数K=报告期某代表产品的实际平均出厂价格/基期某代表产品的实际平均出厂价格=P_1/P_0。各代表产品实际平均出厂价格是用该产品各种价格(即国家定价、计划外超产加价、浮动价、市场     

平均指数中权数意义的新解释

大多数统计学教科书在论述“统计指数”这一章时,都将平均指数的权数作为个体商品具有的“重要程度”来阐述。“重要程度”所指为何?一般都将其解释为有关时期内各种商品的总值指标,如拉氏指数的权数对应于基期的价值指标p0iq0i,派氏指数的权数则对应为报告期的价值指标p1iq1i等。以某一时期的销售额或支出额的总值规模来反映个体商品的代表性程度,销售量越大,影响程度就越高,这符合通常将权数作为次数的理     

DIVISIA指数的理论与实践

一、Divisia指数的导出和扩充1924年,法国经济学家Divisia给出了一种全新的指数形式:P_(t/0)=EXP(∫(∑q_tdp_t)/(C_p∑q_tp_t)),Q_(t/0)=EXP(∫(∑p_tdq_t)/(C_p∑p_tq_t)),其中C_p、C_q代表{dp_t}、{dq_t}的积分路径。t代表现期,_0代表基期,q_t、p_t为现期某种商品的数量和单价。P_(t/0)衡量的是价格从基期到现期的变化情况,Q_(t/0)衡量的是商品数量     

上海市主要经济统计指标一览表(1995年1～2月)

i 萍 装 翔 蒜 群 封 辫 油 墨。≯邑;i i蓦:三 喜一 0母刮≮州卅擀爿r爿JC匕Ⅲ1剖池高I芎督兰0丁是口曼匕曼妒曲一舞面封差盈础拱扣I怫 麟 岸 盈 囊蓁 茎鐾耋 硼 唆篮再 三粤 霉耋耋 至警 爹多j 禹掣 暑置蕾 __景 §兰_= 吲__ =^= ;垂. 兰i; ! i目皿1吲到口{剐剐爿dⅫ爿。爿l爿l爿l己,吲Ⅲ1罚j0刮。1爿L爿。爿r皤口吲叠∑1b{爿l爿l爿【÷菩 P ; 饕譬譬#茹 ;j; l ; i茹j㈦㈨…¨…’I¨㈨^ —碌三 ,兰 露蚕兰;Z一’0苫油口∽相似文献   

符号检验在经济指数中运用的探讨

一、引言现行的经济指数检验理论作为评价各指数优劣的尺度,只是就各类指数自身而论看其能否满足、能否符合这些检验,但对特定的经济环境下,用什么尺度来检验各类指数的优劣则没有涉及。换言之,这些现有的指数检验理论未能建立样本指数与总体指数真实值的关系,从而无法评价各个样本指数反映经济现象变动的方向和程度。又由于同一代表品样本,运用不同的指数计算必然会得出不同的结果,因而必须探讨运用什么方法来识别它们逼近指数真值的程度[1]。经济指数是借助代表品样本来对社会商品物价指标和物量指标动态变化的一种度量,这种度量应该是能…     

常用统计软件关于岭回归计算原理的比较分析

一、引言 对于多元线性回归模型Y=Xβ+ε,其中Y为因变量的观测向量,维度为n×1,X是自变量的观测矩阵,其维度为n×(p+1),β是p+1维的系数向量,ε是n维随机向量且εi～ N(0,σ28).根据Gauss-Markov定理,参数β的最小二乘估计量β=(X'X)-1X'Y是最优线性无偏估计(BLUE).当自变量之间存在高度的共线性,则最小二乘估计的结果尽管在理论上有较好的性质,但在实际应用中,参数估计值可能会极不稳定,易导致参数估计值缺乏合理含义. 针对多重共线性对模型估计所带来的这些影响,Hoerl (1962)和Hoerl & Kennard(1970)分别提出和发展了一种改进普通最小二乘估计的方法,也就是现在大家所熟知的岭回归(Ridge Regression).     

产业升级的测定及制约因素分析

一、产业升级测定产业升级通常表现为一定时期内产业结构的变动和产业结构效益的提高。产业升级的动态测定有多种方法,这里采用More值[1]和产业结构年均变动值[2]测定产业升级的速率,采用产业结构超前系数测定产业升级的方向。(一)产业升级进程的测定More值测定法是运用空间向量的原理,以向量空间中夹角为基础,将产业分为N个部门,构成一组n维向量,把两组向量在两个时期间的夹角,作为象征产业结构变化程度的指标,该指标值即为More结构变化值,简称More值。计算公式为:Mt =∑ni=1wi,t·wi,t 1∑ni=1w2i,t 1·∑ni=1w2i,t 11/2其中,Mt 表示M…     

费雪理想指数的分解分析

一、引言指数分析是许多人所熟悉且常用的经济分析方法。除了指数提供综合信息之外,如今人们对指数的分解也越来越感兴趣,通过分解,可以揭示综合价格指数或物量指数变化的根源,即通过分解可以了解综合指数中各构成分量对综合指数变化的贡献。例如,著名拉氏物价指数:Lp=!p1q0!p0     

不同标准差估计方法下过程能力指数估计量的比较研究

估计量是统计推断的基础,通常无偏性是对一个好的估计量的基本要求。通过严格的数学推导,证明人们现在提出的过程能力指数（Cp）的估计量都是有偏的,且都有高估Cp的倾向;之后构造了Cp的两个无偏估计量;探讨了这两个无偏估计量的估计效率;最后通过试算和比较,认为当样本容量n较大,同时估计精度又不要求太高时,可直接使用p作为Cp的估计量;但在样本容量较小,或者对估计精度要求很高的场合,则必须选择p（D）作为Cp的估计量。     

Simultaneous estimation of the multivariate normal mean under balanced loss function

This paper considers simultaneous estimation of multivariate normal mean vector using Zellner's(1994) balanced loss function which is defined as follows:

where 0 < w < 1 and for i = 1,…,p and j = 1,…,n, X_ij is distributed as normal with mean θi and variance 1. It is shown that the sample mean, X, is admissible when p <3. For p ≥3, we obtain that James-Stein type estimator which has uniformly smaller risk than that of sample mean X.     

Local asymptotic normality of intermediate and central order statistics

Consider n independent random variables Z_i,…, Z_n on R with common distribution function F, whose upper tail belongs to a parametric family F(t) = F_θ(t),t ≥ x₀, where θ ∈ ? ? R ^d. A necessary and sufficient condition for the family F_θ, θ ∈ ?, is established such that the k-th largest order statistic Z_n?k+1:n alone constitutes the central sequence yielding local asymptotic normality ( LAN ) of the loglikelihood ratio of the vector (Z_n?i+1:n)¹ _i=kof the k largest order statistics. This is achieved for k = k(n)→_n→∞∞ with k/n→_n→∞ 0.

In the case of vectors of central order statistics ( Z_r:n, Z_r+1:n,…, Z_s:n ), with r/n and s/n both converging to q ∈ ( 0,1 ), it turns out that under fairly general conditions any order statistic Z_m:n with r ≤ m ≤s builds the central sequence in a pertaining LAN expansion.These results lead to asymptotically optimal tests and estimators of the underlying parameter, which depend on single order statistics only     

Linear. empirical bayes estimation in the case of the wishart distribution

We consider independent pairs (X₁,∑₁), (X₂,∑₂),…,(X_n∑_n), where each Si is distributed according to some unknown density function g(∑) and, given ∑_i = ∑, X has a conditional density function g(x|∑) of the Wishart type. In each pair, the first component is observable but the second is not. After the (n + l)-th observation X_n+i is obtained, the objective is to estimate ∑ _n+i corresponding to X_n+i. This estimator is called an empirical Bayes (EB) estimator of ∑. We construct a linear EB estimator of ∑ and examine its precision.     

Estimation of the mean of the selected gamma population

Let л₁ and л₂ denote two independent gamma populations G(α₁, p) and G(α₂, p) respectively. Assume α(i=1,2)are unknown and the common shape parameter p is a known positive integer. Let Y_i denote the sample mean based on a random sample of size n from the i-th population. For selecting the population with the larger mean, we consider, the natural rule according to which the population corresponding to the larger Y_i is selected. We consider? in this paper, the estimation of M, the mean of the selected population. It is shown that the natural estimator is positively biased. We obtain the uniformly minimum variance unbiased estimator(UMVE) of M. We also consider certain subclasses of estikmators of the form c₁x₍₁₎ +c₁x₍₂₎ and derive admissible estimators in these classes. The minimazity of certain estimators of interest is investigated. Itis shown that p(p+1)^-1x₍₁₎ is minimax and dominates the UMVUE. Also UMVUE is not minimax.     

OPTIMAL SEMIPARAMETRIC INFERENCE FOR THE TAIL INDEX BASED ON RATIOS OF THE LARGEST EXTREMES

The k largest order statistics in a random sample from a common heavy‐tailed parent distribution with a regularly varying tail can be characterized as Fréchet extremes. This paper establishes that consecutive ratios of such Fréchet extremes are mutually independent and distributed as functions of beta random variables. The maximum likelihood estimator of the tail index based on these ratios is derived, and the exact distribution of the maximum likelihood estimator is determined for fixed k, and the asymptotic distribution as k →∞ . Inferential procedures based upon the maximum likelihood estimator are shown to be optimal. The Fréchet extremes are not directly observable, but a feasible version of the maximum likelihood estimator is equivalent to Hill's statistic. A simple diagnostic is presented that can be used to decide on the largest value of k for which an assumption of Fréchet extremes is sustainable. The results are illustrated using data on commercial insurance claims arising from fires and explosions, and from hurricanes.     

Improved estimation of the mean vector for student-t model

Improved James-Stein type estimation of the mean vector μ of a multovaroate Student-t population of dimension p with ν degrees of freedom is considered. In addition to the sample data, uncertain prior information on the value of the mean vector, in the form of a null hypothesis, is used for the estiamtion. The usual maximum liklihood estimator((mle) of μ is obtained and a test statistic for testing H₀:μ=μ₀ is derived. Based on the mle of μ and the tes statistic the preliminary test estimator (PTE), Stein-type shrinkage estimator (SE) and positive-rule shrinkage esiimator (PRSE) are defined. The bias and the quadratic risk of the estimators are evaiuated. The relative performances of the estimators are mvestigated by analyzing the risks under different condltlons It is observed that the FRSE dommates over he other three estimators, regardless of the vaiidity of the null hypothesis and the value ν.     

Root-n-consistent Estimation in Partial Linear Models with Long-memory Errors

We consider estimation of β in the semiparametric regression model y ( i ) - x ^T( i )β + f ( i / n ) + ε( i ) where x ( i ) = g ( i )/ n ) + e ( i , f and g are unknown smooth functions and the processes ε( i ) and e ( i ) are stationary with short- or long-range dependence. For the case of i.i.d. errors, Speckman (1988) proposed a √ n –consistent estimator of β. In this paper it is shown that, under suitable regularity conditions, this estimator is asymptotically unbiased and √ n –consistent even if the errors exhibit long-range dependence. The orders of the finite sample bias and of the required bandwidth depend on the long-memory parameters. Simulations and a data example illustrate the method     

Estimation of an Ergodic Diffusion from Discrete Observations

We consider a one-dimensional diffusion process X , with ergodic property, with drift b ( x , θ) and diffusion coefficient a ( x , σ) depending on unknown parameters θ and σ. We are interested in the joint estimation of (θ, σ). For that purpose, we dispose of a discretized trajectory, observed at n equidistant times tⁿ_i = ih_n , 1 ≤ i ≤ n . We assume that h_n ← 0 and nh_n ←∞. Under the condition nh_n^p ← 0 for an arbitrary integer p , we exhibit a contrast dependent on p which provides us with an asymptotically normal and efficient estimator of (θ, σ).     

Large Sample Approximation of the Distribution for Convex-Hull Estimators of Boundaries

Abstract.  Given n independent and identically distributed observations in a set G  = {( x ,  y ) ∈ [0, 1] ^p  ×  R  : 0 ≤  y  ≤  g ( x )} with an unknown function g , called a boundary or frontier, it is desired to estimate g from the observations. The problem has several important applications including classification and cluster analysis, and is closely related to edge estimation in image reconstruction. The convex-hull estimator of a boundary or frontier is also very popular in econometrics, where it is a cornerstone of a method known as 'data envelope analysis'. In this paper, we give a large sample approximation of the distribution of the convex-hull estimator in the general case where p  ≥ 1. We discuss ways of using the large sample approximation to correct the bias of the convex-hull and the DEA estimators and to construct confidence intervals for the true function.