Dissertation > Excellent graduate degree dissertation topics show

The Double-smoothing Local Linear Estimation in Partly Linear Models

Author: ZhangCui
Tutor: ZuoGuoXin
School: Central China Normal University
Course: Probability Theory and Mathematical Statistics
Keywords: partly linear models double-smoothing local linear estimator local linearestimator optimal rate of convergence asymptotic normal distribution
CLC: O212.1
Type: Master's thesis
Year: 2012
Downloads: 18
Quote: 0
Read: Download Dissertation

Abstract


Local linear regression is frequently used in practice because of its excellent numerical and theoretical properties. It involves fitting a straight line segment over a small region, and the local linear estimate at x is the estimated intercept of that straight line segment. Local linear estimation has an asymptotic bias of order h2and variance of order (nh)-1with h the bandwidth. But the double-smoothing local linear estimator is constructed by integrally combining all fitted values at x of local lines in its neighborhood with another round of smoothing. In contrast to using only an intercept in the local linear regression, the new method attempts to make use of all information obtained from fitting local lines.Without changing the order of variance, the new estimator can reduce the bias to an order of h4. Compared to local linear regression, the new estimator has better performance in situations with considerable bias effects.In partly linear models, the estimator a has the order of n-1/2, and the estimator m(x) achieves the best possible rates of convergence in the indicated semi-parametric problems. Under appropriate conditions, asymptotic distributions of estimates of m(-) and a are established. In this paper, the estimators also satisfy these properties by using the double-smoothing local linear regression. It’s proved that the new method can be used in many applications. Let (X, Y, B) denote a random vector such that B and X are real-valued, and B and X are correlated. In partly linear models, the double-smoothing local linear regression method is used to estimate the two regression functions E(B|X)=u(X) and E(Y|X)=v(X). Then a is estimated by the least square method. In the end, m(·) is estimated by the double-smoothing local linear regression method Under appropriate conditions, asymptotic distributions of estimates of a and m(·) are established. Moreover, it is shown that these estimates achieve the best possible rates of convergence in the indicated semi-parametric problems.Before the major theorems are proved, five lemmas are given. Theorem1describes the rate of convergence and the asymptotic distribution. At the same time, it shows that the squared bias of a is asymptotically negligible compared with its variance without requiring m(·) to be under-smoothed. Theorem2describes the asymptotic normal distribution of α. Theorem3deals with the bias and variance of m(·) and shows that the bias is obtained without the differentiability condition of the density function f(·).To achieve such a bound,kernel-based estimates would require the density functionf(·) to be differentiable. Theorem4shows the asymptotic normal distribution of m(·).

Related Dissertations

  1. Approximate Confidence Region of Parameters for Several Distributions Under Type-I Life Test,O212
  2. Estimation on Semi-varying Coefficient Models with Different Degrees of Smoothness,O212
  3. Based on statistics of the lognormal distribution heteroscedasticity model inferred,O212.1
  4. Prediction of the Long-term and Medium-term Development Trends of Shanxi Population,O212.1
  5. The Research about Influencing Factors of Using Estimation Formula to Estimate Variance Compoents under Sparse Data Matrix,O212.1
  6. Bayesian methods under two ordinal value of multi-value data model with simultaneous identification of outliers,O212.1
  7. The Introduction of Combination Forecast Method and Empirical Analysis,O212.1
  8. The Symmetry Identification Simulation and Statistical Analysis,O212.6
  9. Discussion on a New Test of Conventional Asymptotics in GMM,O212.1
  10. Data Analysis of Multiple Repeated Measures of Children’s Behavior,O212.1
  11. The New Conclusion of 100 Run Mixed Orthogonal Arrays,O212.6
  12. Evaluation of the Pairwise Approach for Fitting Joint Linear Mixed Models,O212.1
  13. Model Selection for Longitudinal Data Based on the Quadratic Inference Function under a Simple Order Restriction,O212.1
  14. The B-spline Two-stage Least Square Estimation of Varying-coefficient Model Function Coefficients,O212.1
  15. Using Reversible Jump MCMC to Solve Latent Class Analysis,O212
  16. Sampling Based on Stochastic Optimization,O212.2
  17. Quantitative Study of Credibility on Poverty Students,O212.1
  18. Study on Seneral Issues in Zero-Inflated Model,O212
  19. The Classification and Discrimination Methods among Several Populations Based on Size Series of Cocoon Filament and Their Comparison,O212
  20. Multi-Unidimensional IRT Model and Its Application,O212
  21. The Cumulative logistic Regression Classification of Students’ Poverty Data,O212.1

CLC: > Mathematical sciences and chemical > Mathematics > Probability Theory and Mathematical Statistics > Mathematical Statistics > General mathematical statistics
© 2012 www.DissertationTopic.Net  Mobile