Abstract
經由研究隨機參數之訊息不等式，一個條件偏差測度準則在本論文中被提出。偏差測度來自於估測器之誤差互變異量與對應之訊息下界的差值。進一步而言，這準則能視為一個由參數估測器在統計實驗中所攜帶訊息損失之測度。藉由使用這準則，我們推演得到倆個估測器。其中一個被限制在線性模式的條件下，另外一個則不需要如此之假設。前者被證明在某種條件下等效於最小變異估測器和線性最小偏差估測器。同樣地，後者也被證明在類似的條件下等效於最小均方估測器和一般化的最小偏差估測器。此外，在輕度的正則條件下，我們證明最小條件偏差估測器存在且唯一。同時，最小條件偏差估測器也被證明是一致且漸近有效的，也就是說，它是最佳漸近常態分佈的估測器。結果，最小條件偏差估測器被確信在有限的取樣下具有最小的訊息損失而且當取樣數量趨近無窮大時沒有訊息損失。最後，模擬結果顯示最小條件偏差估測器優於最小偏差估測器和最小均方估測器。另一方面，在事先預知參數空間範圍時，發現此項優點可以被併入估測器中。同時，模擬結果也證實最小條件偏差估測器在沒有先驗的密度分佈情況下優於最大相似估測器。因此，當系統之參數藉由經驗得知範圍時，可以將此有利條件考慮進最小條件偏差估測器中以便改善性能。By way of studying the information inequality forrandomparameters, a conditional discrepancy meas-ure (CDM) criterionis proposed in this thesis. T-he discrepancy measure comesfrom the differencebetween the error covariance of estimatorand itscorresponding information lower bound. Furthermore,this criterion can be regarded as a measure ofinformationloss carried by a parameter estimationin statisticalexperiment. By using this criterion, we derive two estimators.One is constrained in the linear model case, the other ismore general without such an assumption. In the former case,it is shown that it is equivalent to the minimum var- ianceestimator(MVE) and linear minimum discrepan- cy estimator(MDE)under certain conditions. Simil- arly, in latter case, it canalso be shown that it is equivalent to the minimum mean-squaredestimat- or(MSE) and general MDE under similar conditions. Inaddition, under mild regularity conditions, we prove that theminimum conditional discrepancy es- timator(MCDE) exists and isunique. The MCDE is a- lso shown to be consistent andasymptotically ef- ficient,i.e., it is a best asymptoticallynormal (BAN) estimator. As a result, the MCDE is ensured tohave the minimum loss of information in finite samples and noloss of information when the sample size tends to infinity.Finally,simulation results also indicate that the MCDE issuperior to the MDE and MSE.