Abstract: In this paper, a linear mixed model which has two
random effects is broken up into two models. This thesis gets
the parameter estimation of the original model and an estimation’s
statistical qualities based on these two models. Then many important
properties are given by comparing this estimation with other general
estimations. At the same time, this paper proves the analysis of
variance estimate (ANOVAE) about σ2 of the original model is equal
to the least-squares estimation (LSE) about σ2 of these two models.
Finally, it also proves that this estimation is better than ANOVAE
under Stein function and special condition in some degree.
Abstract: In statistics parameter theory, usually the
parameter estimations have two kinds, one is the least-square
estimation (LSE), and the other is the best linear unbiased
estimation (BLUE). Due to the determining theorem of
minimum variance unbiased estimator (MVUE), the parameter
estimation of BLUE in linear model is most ideal. But since
the calculations are complicated or the covariance is not
given, people are hardly to get the solution. Therefore, people
prefer to use LSE rather than BLUE. And this substitution
will take some losses. To quantize the losses, many scholars
have presented many kinds of different relative efficiencies in
different views. For the linear weighted regression model, this
paper discusses the relative efficiencies of LSE of β to BLUE
of β. It also defines two new relative efficiencies and gives
their lower bounds.
Abstract: Three novel and significant contributions are made in
this paper Firstly, non-recursive formulation of Haar connection
coefficients, pioneered by the present authors is presented, which
can be computed very efficiently and avoid stack and memory
overflows. Secondly, the generalized approach for state analysis of
singular bilinear time-invariant (TI) and time-varying (TV) systems
is presented; vis-˜a-vis diversified and complex works reported by
different authors. Thirdly, a generalized approach for parameter
estimation of bilinear TI and TV systems is also proposed. The unified
framework of the proposed method is very significant in that the
digital hardware once-designed can be used to perform the complex
tasks of state analysis and parameter estimation of different types
of bilinear systems single-handedly. The simplicity, effectiveness and
generalized nature of the proposed method is established by applying
it to different types of bilinear systems for the two tasks.
Abstract: This paper presents the convergence analysis
of a prediction based blind equalizer for IIR channels.
Predictor parameters are estimated by using the recursive
least squares algorithm. It is shown that the prediction
error converges almost surely (a.s.) toward a scalar
multiple of the unknown input symbol sequence. It is
also proved that the convergence rate of the parameter
estimation error is of the same order as that in the iterated
logarithm law.