A minimum average risk approach to shrinkage estimators of the normal mean

For the problem of estimating the normal mean based on a random sample X ₁,...,X _n when a prior value ₀ is available, a class of shrinkage estimators % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-qqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xHapdbiqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaubeaeqaje% aWbaGaamOBaaWcbeqdbaGafqiVd0MbaKaaaaGccaqGGaGaaiikaiaa% dUgacaGGPaGaeyypa0Jaam4AaiaacIcadaqfqaqabKqaahaacaqGUb% aaleqaneaacaqGubaaaOGaaiykaiaabccadaqfqaqabKqaahaacaWG% UbaaleqaneaaceqGybGbaebaaaGccaqGGaGaey4kaSIaaeiiaiaacI% cacaaIXaGaaeiiaiabgkHiTiaabccacaWGRbGaaiikamaavababeqc% baCaaiaab6gaaSqab0qaaiaabsfaaaGccaGGPaGaaiykamaavababe% qcbaCaaiaad6gaaSqab0qaaiabeY7aTbaaaaa!5615!\[\mathop {\hat \mu }\nolimits_n {\rm{ }}(k) = k(\mathop {\rm{T}}\nolimits_{\rm{n}} ){\rm{ }}\mathop {{\rm{\bar X}}}\nolimits_n {\rm{ }} + {\rm{ }}(1{\rm{ }} - {\rm{ }}k(\mathop {\rm{T}}\nolimits_{\rm{n}} ))\mathop \mu \nolimits_n \] is considered, where % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-qqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xHapdbiqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaubeaeqaje% aWbaGaamOBaaWcbeqcdawaaiaadsfaaaGccaqGGaGaaeypaiaabcca% caWGUbWaaWbaaSqabeaacaaIXaGaai4laiaaikdaaaGccaGGOaWaa0% aaaeaacaWGybaaamaaBaaajeaWbaGaamOBaaWcbeaakiaabccacqGH% sislcaqGGaWaaubeaeqajeaWbaGaaGimaaWcbeqdbaGaaeiVdaaaki% aacMcacaqGGaGaae4laiabeccaGiabeo8aZbaa!4C33!\[\mathop T\nolimits_n {\rm{ = }}n^{1/2} (\overline X _n {\rm{ }} - {\rm{ }}\mathop {\rm{\mu }}\nolimits_0 ){\rm{ /}} \sigma \] and k is a weight function. For certain choices of k, % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-qqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xHapdbiqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaubeaeqaje% aWbaGaamOBaaWcbeqdbaGafqiVd0MbaKaaaaGccaqGGaGaaiikaiaa% dUgacaGGPaaaaa!3CEE!\[\mathop {\hat \mu }\nolimits_n {\rm{ }}(k)\] coincides with previously studied preliminary test and shrinkage estimators. We consider choosing k from a natural non-parametric family of weight functions so as to minimize average risk relative to a specified prior p. We study how, by varying p, the MSE efficiency (relative to \-X) properties of % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-qqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xHapdbiqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaubeaeqaje% aWbaGaamOBaaWcbeqdbaGafqiVd0MbaKaaaaGccaqGGaGaaiikaiaa% dUgacaGGPaaaaa!3CEE!\[\mathop {\hat \mu }\nolimits_n {\rm{ }}(k)\] can be controlled. In the process, a certain robustness property of the usual family of posterior mean estimators, corresponding to the conjugate normal priors, is observed.     

Na2SnO3系催化剂在甲烷氧化偶联反应中的催化性能及表面碱性的探讨

1982年Keller和Bhasin以金属氧化物为催化剂从甲烷制得少量乙烯和乙烷的工作引起了各国研究工作者的重视,此后报道了许多有研究价值的催化剂,其中添加碱金属对提高催化性能所起的作用引起了普遍的关注.Lunsford等首先用添加Li~+的MgO作催化剂,发现催化剂表面碱性增强的同时,生成C_2烃类产物的选择性明显增加.随后Iwamatu等在MgO中添加Na~+及Rb~+盐,Jones等在Mn~(4+)/SiO_2中添加Na~+,Otsuka等在Sm_2O_3中添加LiCl作为甲烷氧化偶联催化剂进行了研究,这些结果均表明,因添加碱金属使催化剂呈现     

紫外光度法间接测定脱脂乳中的芽孢数量

为了有效控制乳制品生产过程、保证质量,克服芽孢杆菌传统计数方法周期长的缺点,本实验通过分光光度法检测芽孢中特异性物质2,6-吡啶二羧酸(DPA)。根据DPA浓度与芽孢数量的关系,建立了快速检测脱脂乳中芽孢数量的方法。本研究对脱脂乳及其芽孢处理、DPA释放及采用紫外分光光度法检测做了研究。通过准确度和加标回收率检验,建立DPA含量与芽孢数的线性关系,回归方程为y=0.2084x-0.9363,r=0.6998,经验证可有效估测脱脂乳中芽孢数量(P<0.05)。     

四苯基卟啉及其衍生物的表面光电压谱

酞菁和卟啉染料是一类典型的分子半导体材料,由于其在生命过程、癌的治疗等生物学上的探索及其化学传感、光电特性在固体电子学器件研究中占有很重要的地位。尤以这类染料的光电性质深受人们的重视,这与太阳能光电池、光MOS晶体管等的应用前景是分     

多功能沸点仪的研究

本文提出了两种新型沸点仪——CP-Ⅰ型和CP-Ⅱ型沸点仪, 阐述了仪器各部分结构的设计思想和原理, 并对仪器的性能和各部分功能进行了较为完整的实验考核, 获得了预期的效果。     

Kinetics of uranium(VI) extraction by bis(octylsulfinyl)methane

The kinetics and mechanism of uranium(VI) extraction from nitric acid solution by bis(octylsulfinyl)methane (BOSM) are studied with the method of stationary interface cell. The effects of temperature, extractant and nitric acid concentrations are discussed. The results showed that the extraction process is controlled by the following reaction: UO₂(NO₃)₂ + BOSM_(i)⇄_k1 ^k-1UO₂(NO₃)₂BOSM_(i). The variation of enthalpy associated with the extraction is -22.1±2.1 kJ/mol. This revised version was published online in July 2006 with corrections to the Cover Date.     

反应条件对钌基氨合成催化剂性能的影响

用氨合成催化剂性能评价装置,研究了反应温度、压力、空速和氢氮比对以活性炭为载体的钌基氨合成催化剂活性的影响。研究表明,低于400℃时,随着反应温度降低,催化剂的活性急剧降低。随着压力升高,催化剂活性增大。但钌催化剂具有较高的低压活性,适宜低压合成氨。随着空速的降低,催化剂的活性明显提高。在空速和压力一定的条件下,最佳氢氮比随反应温度而异,并且当空速较高或反应温度较低时,氢氮比的变化对催化剂活性的影响更加明显。     

Preparation of Tin Oxide-Based Metal Oxide Particles

Tin oxide-doped hybrid particles were prepared by a wet chemical process with organic-inorganic (phenyl/silica) hybrid particles in an alcoholic solution. The phenyl/silica hybrid particles, with a diameter of ca. 790 nm were used as a new support material for tin oxide (SnO₂) particles from tin(IV) chloride. The surface of the particles was modified via nitration of aromatic groups in the particles, to promote formation of the tin oxide coating on the particles. The thickness and surface morphology of the tin oxide layer coated on the nitrated-phenyl/silica hybrid particles could be controlled by varying the tin(IV) chloride concentration and reaction time. The size and morphology of the resultant particles were investigated with field emission scanning electron microscopy (FE-SEM) and transmission electron microscopy (TEM). The particles obtained were also characterised by infrared (FTIR) and solid-state ¹³C magic angle spinning nuclear magnetic resonance (¹³C-CP/MAS NMR) spectroscopy. The effect of processing parameters on the crystallinity and structure of the doped hybrids were confirmed by X-ray diffraction (XRD) patterns.