Orthogonal Series Estimation of Regression Functions in Nonstationary Conditions

2015 ◽  
pp. 427-435 ◽  
Author(s):  
Tomasz Galkowski ◽  
Miroslaw Pawlak
Keyword(s):  
Orthogonal Series ◽  
Series Estimation ◽  
Regression Functions ◽  
Nonstationary Conditions

scholarly journals On orthogonal series estimation of bounded regression functions

2001 ◽  
Vol 28 (3) ◽  
pp. 257-270
Author(s):  
Waldemar Popiński
Keyword(s):  
Orthogonal Series ◽  
Series Estimation ◽  
Regression Functions

SPECIFICATION TESTING DRIVEN BY ORTHOGONAL SERIES FOR NONLINEAR COINTEGRATION WITH ENDOGENEITY

2017 ◽  
Vol 34 (4) ◽  
pp. 754-789 ◽  
Author(s):  
Chaohua Dong ◽  
Jiti Gao
Keyword(s):  
Null Hypothesis ◽  
Asymptotic Theory ◽  
Orthogonal Series ◽  
Regression Function ◽  
Time Series Models ◽  
Finite Sample ◽  
Specification Testing ◽  
Specification Tests ◽  
Starting Point ◽  
Regression Functions

This paper proposes two simple and new specification tests based on the use of an orthogonal series for a considerable class of bivariate nonlinearly cointegrated time series models with endogeneity and nonstationarity. The first test is proposed for the case where the regression function is integrable, which fills a gap in the literature, and the second test, which nests the first one, deals with regression functions in a quite large function space that is sufficient for both theoretical and practical use. As a starting point of our asymptotic theory, the first test is studied initially and then the theory is extended to the second test. Endogeneity in two general forms is allowed in the models to be tested. The finite sample performance of the tests is examined through several simulated examples. Our experience generally shows that the proposed tests are easily implementable and also have stable sizes and good power properties even when the ‘distance’ between the null hypothesis and a sequence of local alternatives is asymptotically negligible.

Approximation of regression functions

Optimization ◽  
1973 ◽  
Vol 4 (4) ◽  
pp. 315-325
Author(s):  
Helga Bunke
Keyword(s):  
Regression Functions
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