【摘要】：線性模型是重要的統(tǒng)計模型,廣泛應用于醫(yī)學、工業(yè)、經(jīng)濟、管理、生物等眾多領域.本文主要研究了帶隨機約束條件的線性模型的參數(shù)估計問題.由于約束最小二乘估計在設計陣存在復共線性時不再是“好的”估計,因此學者們提出了許多有偏估計來代替約束最小二乘估計.本文提出了三種新的有偏估計,并討論了它們的相關性質.首先,在兩參數(shù)估計的基礎上,結合加權混合估計,提出了一種新的加權混合兩參數(shù)估計.在均方誤差矩陣準則下,分別與加權混合兩參數(shù)估計、加權混合估計、加權混合嶺估計和兩參數(shù)估計進行比較,得到了該估計優(yōu)于這些估計的充要條件,并通過數(shù)值模擬驗證了相關的理論結果.其次,利用了幾乎無偏的思想,在加權混合兩參數(shù)估計的基礎上,將幾乎無偏兩參數(shù)估計與加權混合估計相結合,提出了一種新的加權混合幾乎無偏兩參數(shù)估計.在二次偏差的準則下,比較了加權混合兩參數(shù)估計和加權混合幾乎無偏兩參數(shù)估計的偏差,得到了加權混合幾乎無偏兩參數(shù)估計是對加權混合兩參數(shù)估計的偏差進行矯正的估計.然后在均方誤差矩陣準則下,與加權混合估計、加權混合幾乎無偏嶺估計、幾乎無偏兩參數(shù)估計相比較,得到了加權混合幾乎無偏兩參數(shù)估計優(yōu)于這些估計的充要條件,并通過數(shù)值模擬驗證了相關的理論結果.最后,在廣義隨機約束估計的基礎上,通過尋找最優(yōu)算子,使得其均方誤差達到最小,提出了一種兩步估計——廣義最優(yōu)隨機約束估計,并通過蒙特卡羅模擬驗證了新估計的優(yōu)良性.
[Abstract]:Linear model is an important statistical model, which is widely used in many fields such as medicine, industry, economy, management, biology and so on. In this paper, the problem of parameter estimation for linear models with stochastic constraints is studied. Because constrained least squares estimators are no longer "good" estimators when complex collinearity exists in design matrices, many biased estimators have been proposed to replace constrained least squares estimators. In this paper, three new biased estimators are proposed and their related properties are discussed. Firstly, based on the two-parameter estimation, a new weighted mixed two-parameter estimation is proposed. Under the criterion of mean square error matrix, compared with weighted mixed two-parameter estimation, weighted mixed ridge estimate and two-parameter estimation, the sufficient and necessary conditions for the estimator to be superior to these estimates are obtained. The relevant theoretical results are verified by numerical simulation. Secondly, using the idea of almost unbiased, a new weighted mixed almost unbiased two-parameter estimation is proposed by combining the almost unbiased two-parameter estimation with the weighted mixed two-parameter estimation. Under the criterion of quadratic deviation, the difference between weighted mixed two-parameter estimation and weighted mixed almost unbiased two-parameter estimation is compared. It is obtained that the weighted mixed almost unbiased two-parameter estimation is an estimate that corrects the deviation of the weighted mixed two-parameter estimation. Then under the mean square error matrix criterion, compared with the weighted mixed estimators, the weighted mixed almost unbiased estimators and almost unbiased two-parameter estimators, the sufficient and necessary conditions for the weighted mixed almost unbiased two-parameter estimators to be superior to these estimates are obtained. The relevant theoretical results are verified by numerical simulation. Finally, on the basis of generalized stochastic constraint estimation, the mean square error is minimized by finding the optimal operator, and a two-step estimator-generalized optimal stochastic constraint estimation is proposed. The superiority of the new estimator is verified by Monte Carlo simulation.
【學位授予單位】：華北水利水電大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：O212.1

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