Resolution Of Parameter Estimation For Linear Regression Model

In the field of signal processing,signal division plays an important role in dealing with issues such as audio recognition and spectrum detection.Parameter estimation is one of the key problems in the field of signal partitioning.In order to measure whether similar signals can be separated,this paper introduces the concept of parameter resolution.The introduction of parameter resolution provides a new metric for measuring the algorithm's ability on distinguishing similar signals,and also provides an effective index for evaluating the accuracy of model fitting.The main researches of this paper are as follows.1.Aiming at the problem of whether each cluster needs to be re-divided of linear signal division,this paper combines the clustering algorithm and loss function to give a general definition and calculation of parameter resolution,and uses the parameter estimation results of least square method for unary linear regression model to analyze the parameter resolution.With a fixed signal to noise ratio(SNR),the parameter resolution r of the algorithm on the model can be obtained through experiments.When the relative distance between the slope parameters of two unary linear regression signals is less than r,the two signals need to be treated as the same signal,otherwise,they should be treated as two different signals.The results show that as the SNR increases,the accuracy of the parameter resolution increases.The local parameter resolution is consistent with the global parameter resolution.The standard deviation of the noise and the parameter resolution of the least square method satisfy a linear relationship which is proved by using the interval estimation theory.In addition,the distribution of the theoretical results and experimental results of the parameter resolution of the unary linear regression model under different confidence levels are obtained.These experimental results all show that the parameter resolution is reasonable as an evaluation standard for signal division.2.In order to verify the effectiveness of parameter resolution as a criterion for signal division,the parameter resolutions of different algorithms for the same set of data under the same model is compared.First,the parameter resolution of the least square method and the total least absolute deviation method for the same set of signals with Gaussian noise is calculated.The experimental results are consistent with Gauss-Markov theorem.And then,calculate the parameter resolution of the least square method and the total least absolute deviation method for two similar audio signals.The experimental results both show that different algorithms have different discrimination capabilities for the same set of signals,thus indicating that parameter resolution is effective as an criterion for signal division.3.Aiming at the problem that the indicators used to measure the effect of parameter estimation in the existing literature are insufficient,the parameter resolution is compared with other accuracy indicators.The goodness of fit,the residual standard deviation,and the parameter resolution of different models to the same set of data under the same algorithm are calculated.The results show that the parameter resolution can not only be used to measure the accuracy of model fitting,but also more effective than the goodness of fit and the residual standard deviation in measuring the accuracy of model fitting.