【正文】 167。 167。 在一般的實(shí)際問(wèn)題中， 設(shè)概率權(quán)函數(shù) 。 在國(guó)內(nèi)， 洪圣巖對(duì)如何在核估計(jì)中選取最佳窗寬做了研究；薛留根對(duì)密度函數(shù)核估計(jì)進(jìn)行了相關(guān)問(wèn)題的研究； 趙林城（ 1984）將核估計(jì)同近鄰估計(jì)進(jìn)行了對(duì)比，并且通過(guò) ? 的自適應(yīng)估計(jì)最終可以得到最優(yōu)收斂速度； 秦更生對(duì)隨機(jī)刪失場(chǎng)合中的部分線性模型的核光滑方法進(jìn)行了研究；王啟華對(duì)隨機(jī)刪失情況下概率密度核估計(jì)中的光滑 Bootstrap 逼近進(jìn)行了分析； 朱仲義、李朝暉對(duì)最小二乘估計(jì)與半?yún)?shù)函數(shù)模型的核進(jìn)行了研究 。為了彌補(bǔ)參數(shù)和非參數(shù)模型的各自不足，測(cè)繪學(xué)界又將統(tǒng)計(jì)領(lǐng)域中的偏線性回歸模型引入到測(cè)量數(shù)據(jù)處理中，這就是現(xiàn)在的半?yún)?shù)平差模型，并取得了顯著的研究成果。我國(guó)對(duì)于半?yún)?shù)回歸的研究，主要在統(tǒng)計(jì)領(lǐng)域內(nèi)，其中主要研究?jī)?nèi)容包括： 洪圣巖 [13]對(duì)于半?yún)?shù)回歸模型中的一系列估計(jì)理論做了研究 ；柴根象和孫平 [14]對(duì)于大樣本估計(jì)的性質(zhì)和半?yún)?shù)中估計(jì)量的性質(zhì)做了研究；朱仲義（ 1999） [15]用統(tǒng)計(jì)的方法對(duì)于半?yún)?shù)非線性模型做了系統(tǒng)的研究；曾林蕊（ 20xx） [18]對(duì)廣義的半?yún)?shù)模型中的統(tǒng)計(jì)診斷方法做了研究；其中，柴根象、洪圣巖（ 1995） [17]的著作 《半?yún)?shù)回歸模型》對(duì)于半?yún)?shù)中的理論與方法做了系統(tǒng)的介紹和研究。 半?yún)?shù)核估計(jì)理論 ........................................................................................... 6 167。 第二章主 要研究半?yún)?shù)核估計(jì)的理論，包括核權(quán)函數(shù)和核函數(shù)的選取問(wèn)題；介紹了核估計(jì)的兩種方法，即最小二乘核估計(jì)和偏核光滑估計(jì)，分析了這兩種方法的各自特點(diǎn)，并解算了其參數(shù)和非參數(shù)分量；同時(shí)討論了窗寬參數(shù) h 在核估計(jì)中的重要作用，在小樣本估計(jì)中，樣本的大小，核函數(shù)的選取以及窗寬參數(shù)共同決定了核估計(jì)性能的好壞。本文主要 研究半?yún)?shù)的最小二乘核估計(jì)和偏核光滑估計(jì)，通過(guò)解算其參數(shù)分量和非參數(shù)分量及推導(dǎo)其期望、偏差、方差及均方誤差等統(tǒng)計(jì)性質(zhì)，研究窗寬參數(shù)的選取，并通過(guò)模擬算例證 明和對(duì)比最小二乘核估計(jì)和偏核光滑估計(jì)各自在參數(shù)和非參數(shù)分量估計(jì)以及估計(jì)系統(tǒng)誤差等方面的有效性和可行性 ,并將半?yún)?shù)核估計(jì)應(yīng)用到平面坐標(biāo)轉(zhuǎn)換中。 highlights the semiparametric estimation theoretical aspects of kernel research at home and abroad ,and the contents of this paper are: semiparametric kernel estimation including migraine kernel smooth estimation, partial residuals estimated neighbor kernel estimation, least squares estimation and NW kernel estimation, this paper mainly studies migraine kernel smooth estimation and least squares estimation. The second chapter studies the theory of semiparametric kernel kernel weight functions and kernel function selection two kernel estimation method, namely migraine kernel smooth estimation and least squares estimation,analysis of the characteristics of each of these two methods,and extract fet their parametric and nonparametric a small sample estimates, the sample size, the selection of kernel function and window width parameters together determine the kernel estimation performance , numerical examples demonstrates that the ponent parameters of two methods is correct and we pare the result. The third chapter is to derive a semiparametric kernel estimation (parametric and nonparametric ponent ponent) of the statistical properties, according to which We can infer the scope of application of the properties includes its estimated expectation, variance, bias, mean square error. It also discusses the problem of the window width parameter selection, window width is an important parameter smoothing parameter, It Plays a balancing role on the degree of curve fitting and smoothness,in fact, it is to play a role as a smoothing factor,that it is good or not influences the properties of the estimation,.The smaller Window width is, the smaller the kernel estimation bias is, but the greater estimates of the variance is. In the window width parameter selection, we discuss minimum mean square error method and classic GCV method and so window width changes, it is impossible to make kernel estimation bias and variance simultaneously smaller. Therefore, the optimal window width selection criteria must be balanced in the kernel tradeoff between bias and variance. This chapter provides an overview of the measurement error and introduces the related characteristics of systematic errors . Through simulation examples and examples of measurements, it Proves that semiparametric kernel estimation is feasible in removing outliers and separating system the semiparametric kernel estimation theory to the gravity measurements,through the practical examples given in this chapter, we prove that kernel estimation is effective in Coordinate transformation. KeyWords: Semiparametric model, Kernel estimation,Statistical properties,Systematic errors, Coordinate transformation 目錄 第一章 緒論 .................................................................................................................. 1 167。rdle,Mammenamp。綜上所述，對(duì)不同的平差模型進(jìn)行深入研究，更加精確地解算觀測(cè)量的最佳估值是現(xiàn)代測(cè)量數(shù)據(jù)處理中的基本首要內(nèi)容。由以上內(nèi)容分析可知，半?yún)?shù)平差模型的兩個(gè)特例是參數(shù)平差模型與非參數(shù)平差模型，當(dāng) 0B? 時(shí)為非參數(shù)平差模型，將 S 歸入誤差項(xiàng)則為參數(shù)平差模型 。模型為（ 19），則 )(its 的權(quán)函數(shù)估計(jì) )(iWtS 可表示為： )(iWtS =ikni i LtW )(? 其中 )(ki tW 為權(quán)函數(shù)，設(shè) ),。單從定義式來(lái)看，核估計(jì)在每一個(gè)觀察點(diǎn)iX 都會(huì)一個(gè)“碰撞”。在第二章中，不管是通過(guò)理論推導(dǎo)還是算例，都證明窗寬參數(shù)的選取的恰當(dāng)與否直接影響了估計(jì)結(jié)果的準(zhǔn)確度和精確度，因此，在半?yún)?shù)核估計(jì)中，窗寬參數(shù)的選取很重要。 由 所計(jì)算的半?yún)?shù)的兩種核估計(jì)的期望可知，這兩種核估計(jì)的非參數(shù)分量和參數(shù)分量的結(jié)果都是有偏的。 167。1( : ,... ) 0hn i nW t t t ?， 。 半?yún)?shù)核估計(jì)理論 目前，研究半?yún)?shù)平差模型的主要方法有偏樣條估計(jì)、最小二乘估計(jì)、分塊多項(xiàng)式估計(jì)、二階段估計(jì)、多項(xiàng)式估計(jì)、三角級(jí)數(shù)估計(jì)、小波估計(jì)等，但是目前只有張松林 [26]、丁士俊 [25]等對(duì)于半?yún)?shù)平差模型中的核估計(jì)進(jìn)行了研究。 當(dāng)今統(tǒng)計(jì)界對(duì)半?yún)?shù)模型的估計(jì)方法研究得較多的主要有樣條估計(jì)，最小二乘核估計(jì)，三角級(jí)數(shù)估計(jì)和分塊多項(xiàng)式估計(jì)，而且參數(shù)部分的模型只適用于線性函數(shù)模型，對(duì)于非線性模型研究得較少。 近些年來(lái)學(xué)者將半?yún)?shù)模型應(yīng)用到在測(cè)繪領(lǐng)域，利用半?yún)?shù)回歸模型來(lái)解決實(shí)際測(cè)量數(shù)據(jù)中含有系統(tǒng)信號(hào)的問(wèn)題，與參數(shù)平差模 型、非參數(shù)平差模型相比，半?yún)?shù)平差模型能利用其參數(shù)信號(hào)和非參數(shù)信號(hào)解決參數(shù)平差模型、非參數(shù)平差模型等單一解決方法不能解決的實(shí)際問(wèn)題，并且所得的估計(jì)量效果要好一些。 最小二乘核估計(jì)估計(jì)量的性質(zhì) ....................................................................... 12 167。窗寬 h 越小，則核估計(jì)的偏差越小，但估計(jì)的方差卻越大。大量的研究表明半?yún)?shù)模型在處理觀測(cè)量與待估參數(shù)之間的復(fù)雜關(guān)系時(shí)有很明顯的優(yōu)點(diǎn)，因此在很多領(lǐng)域得到了研究與應(yīng)用。 關(guān)鍵詞：半?yún)?shù)模型，核估計(jì)，統(tǒng)計(jì)性質(zhì)，系統(tǒng)誤差，坐標(biāo)轉(zhuǎn)換 Abstract The rapid development of modern science and technology not only provides a good opportunity for the development of surveying and mapping science, but also a higher requirement on Surveying and Mapping .First, as the development of modern measuring instruments and the plexity of observational data ,the precision of the measurement data processing bees increasingly demanding, but the entire survey adjustment system is determined by numerous factors, some of which affect the observation function not plex observational data lead classical least squares criterion to failure, resulting in some systematic error can not be eliminated and so on. Semiparametric model contains a parameter ponent and a nonparametric ponent, for a function with the observed values of the parameters of the known part of the presquares estimation taken a similar approach, some parameters about which fully parameterized。目前，一些學(xué)者對(duì)半?yún)?shù)模型