Consider a semiparametric regression modelyi=XTi β+g(ti)+ei,1≤i≤n.Based on nonparameter g(t) dealed with wavelet method,the M-estimators of the model are reseached.The linear strong representative of M-estimators parameter β and nonparameter g(t) are given.As their applications,the rate of convergence,law of iterated logarithm and bound of the Berry-Esseen are investigated.
Useing the wavelet method,consider the semiparametric regression model given by y_i=X_i~Tβ+g(t_i)+e_i(1≤i≤n) whereβis a d×1 unknown parametric vector,g(t) is an unknown Borel function on[0,1],X_i is a d×1 random design vector,random error{e_i} is martingale difference sequences,{t_i} is constant sequence on[0,1].In the paper,the q-order moments consistency of parametric and nonparametric wavelet estimators are studied.
During surveying data processing,systematic error is always eliminated and compensated as harmful component.With the further development of science and technique of surveying and mapping,however,a few researchers extract systematic error or nonparametric signal by penalized least squares method or others when it is not random variable,thus there is more understanding of it so as to satisfy the need of high precise surveying.While systematic error is random variable in the paper,consider the semiparametric regression model by using the penalized least squares method,estimators of parameter and nonparameter are got.Then,some properties of estimators are discussed.And that,using the penalized least squares method,gravity anomaly in gravimetry are studied,estimations of gravity anomaly are achieved,which are the same with the results from least squares collocation,it demonstrates that the method is valid.
This paper is concerned with the testing hypotheses of regression parameters in linear models in which errors are negatively superadditive dependent (NSD). A robust M-test base on M-criterion is proposed. The asymptotic distribution of the test statistic is obtained and the consistent estimates of the redundancy parameters involved in the asymptotic distribution are established. Finally, some Monte Carlo simulations are given to substantiate the stability of the parameter estimates and the power of the test, for various choices of M-methods, explanatory variables and different sample sizes.
In this paper,a Markov risk model with a constant dividend barrier is considered.A system of integro-differential equations satisfied by the expected present value of the total dividends until ruin is derived and solved.Some dividend related problems are also obtained.
In surveying data processing,when the distribution of observational errors is symmetry and has only one peak value,we may assume that it is p _norm distribution.By choosing a specific value of p ,the p _norm distribution can be closer to the real distribution of the errors than a normal one.Equations about parameters of p _norm distribution could not be directly solved using average method,so the estimations of the parameters could not be obtained directly.In this paper,we try to discuss them under the conditions that the values of the parameter μ and p are known.The following results are derived. First,the estimator of parameter σ is given by the method of maximum likelihood.Second,because the expectancy and variance are very important to depict the statistical property of a random variance,we give the calculating formulas of the expectancy and variance of estimator p ,and prove that p is a unbiased estimator.Third,we derive that the estimate of npλ p pσ p is χ p distributed.Lastly,by using the above results,hypothesis testing about p is discussed.The testing method of hypothesis to the variance is concluded when the hypothetical universe is a p _norm distribution.
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