메뉴 건너뛰기




Volumn 58, Issue 2, 1996, Pages 162-181

Bivariate tensor-product B-splines in a partly linear model

Author keywords

B spline functions; M estimator; Mean regression; Median regression; Partly linear model; Rate of convergence; Regression quantile

Indexed keywords


EID: 0030215506     PISSN: 0047259X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jmva.1996.0045     Document Type: Article
Times cited : (139)

References (46)
  • 1
    • 0001066856 scopus 로고
    • Asymptotic integrated mean square error using least squares and bias minimizing splines
    • Agarwal, G. G., and Studden, W. J. (1980). Asymptotic integrated mean square error using least squares and bias minimizing splines. Ann. Statist. 8 1307-1325.
    • (1980) Ann. Statist. , vol.8 , pp. 1307-1325
    • Agarwal, G.G.1    Studden, W.J.2
  • 2
    • 0000501656 scopus 로고
    • Information theory and an extension of the maximum likelihood principle
    • Akaike, H. (1973). Information theory and an extension of the maximum likelihood principle. In 2nd International Symposium on Information Theory, pp. 267-281.
    • (1973) 2nd International Symposium on Information Theory , pp. 267-281
    • Akaike, H.1
  • 4
    • 30244511944 scopus 로고
    • The II method for estimating multivariate functions from noisy data
    • Breiman, L. (1991). The II method for estimating multivariate functions from noisy data (with discussion), Technometrics 33 125-143.
    • (1991) Technometrics , vol.33 , pp. 125-143
    • Breiman, L.1
  • 5
    • 0001742891 scopus 로고
    • Nonparametric estimates of regression quantiles and their local Bahadur representation
    • Chaudhuri, P. (1991). Nonparametric estimates of regression quantiles and their local Bahadur representation, Ann. Statist. 19 760-777.
    • (1991) Ann. Statist. , vol.19 , pp. 760-777
    • Chaudhuri, P.1
  • 6
    • 0000354504 scopus 로고
    • Convergence rates for parametric components in a partly linear model
    • Chen, H. (1988). Convergence rates for parametric components in a partly linear model. Ann. Statist. 16 136-146.
    • (1988) Ann. Statist. , vol.16 , pp. 136-146
    • Chen, H.1
  • 7
    • 0000480367 scopus 로고
    • Polynomial splines and nonparametric regression
    • Chen, H. (1991). Polynomial splines and nonparametric regression. J. Nonparametric Statist. 1 143-156.
    • (1991) J. Nonparametric Statist. , vol.1 , pp. 143-156
    • Chen, H.1
  • 8
    • 0001004569 scopus 로고
    • A two-stage spline smothing method for partially linear models
    • Chen, H., and Shiau, J. G. (1991). A two-stage spline smothing method for partially linear models. J. Statist. Planning & Inference 25 187-201.
    • (1991) J. Statist. Planning & Inference , vol.25 , pp. 187-201
    • Chen, H.1    Shiau, J.G.2
  • 9
    • 21344493554 scopus 로고
    • Data-driven efficient estimators for a partially linear model
    • Chen, H., and Shiau, J. G. (1994). Data-driven efficient estimators for a partially linear model. Ann. Statist. 22 211-237.
    • (1994) Ann. Statist. , vol.22 , pp. 211-237
    • Chen, H.1    Shiau, J.G.2
  • 10
    • 0000317016 scopus 로고
    • Interaction spline models and their convergence rates
    • Chen, Z. (1991). Interaction spline models and their convergence rates, Ann. Statist. 19 1855-1868.
    • (1991) Ann. Statist. , vol.19 , pp. 1855-1868
    • Chen, Z.1
  • 12
    • 0011675806 scopus 로고
    • Computation of box splines and B-splines on triangulations of nonuniform rectangular partitions
    • Chui, C. K., and Lai, M. J. (1987). Computation of box splines and B-splines on triangulations of nonuniform rectangular partitions. Approx. Theory Appl. 3 37-62.
    • (1987) Approx. Theory Appl. , vol.3 , pp. 37-62
    • Chui, C.K.1    Lai, M.J.2
  • 13
    • 0002057896 scopus 로고
    • Regression percentiles using asymmetric squared error loss
    • Efron, B. (1991). Regression percentiles using asymmetric squared error loss. Statistica Sinica 1 93-125.
    • (1991) Statistica Sinica , vol.1 , pp. 93-125
    • Efron, B.1
  • 15
    • 0012921755 scopus 로고
    • Semiparametric estimates of the relation between weather and electricity sales
    • Engle, R. F., Granger, C. W. J., Rice, J., and Weiss, A. (1986). Semiparametric estimates of the relation between weather and electricity sales. J. Amer. Statist. Assoc. 81 310-320.
    • (1986) J. Amer. Statist. Assoc. , vol.81 , pp. 310-320
    • Engle, R.F.1    Granger, C.W.J.2    Rice, J.3    Weiss, A.4
  • 16
    • 38249005142 scopus 로고
    • Convergence rates for estimation in certain partially linear models
    • Eubank, R. L., and Whitney, P. (1989). Convergence rates for estimation in certain partially linear models. J. Statistical Planning and Inference 23 33-43.
    • (1989) J. Statistical Planning and Inference , vol.23 , pp. 33-43
    • Eubank, R.L.1    Whitney, P.2
  • 17
    • 0002432565 scopus 로고
    • Multivariate additive regression splines
    • Friedman, J. H. (1991). Multivariate additive regression splines, (with discussion). Ann. Statist. 19 1-67.
    • (1991) Ann. Statist. , vol.19 , pp. 1-67
    • Friedman, J.H.1
  • 18
    • 0024607448 scopus 로고
    • Flexible parsimonious smoothing and additive modeling
    • Friedman, J. H., and Silverman, B. W. (1989). Flexible parsimonious smoothing and additive modeling (with discussion). Technometrics 31 3-21.
    • (1989) Technometrics , vol.31 , pp. 3-21
    • Friedman, J.H.1    Silverman, B.W.2
  • 19
    • 0002515748 scopus 로고
    • The computation of generalized gross-validation functions through householder tridiagonalization with applications to the fitting of interaction spline models
    • Gu, C., Bates, D. M., Chen, Z., and Wahba, G. (1989). The computation of generalized gross-validation functions through Householder tridiagonalization with applications to the fitting of interaction spline models, SIAM J. Matrix Anal. Appl. 10 457-480.
    • (1989) SIAM J. Matrix Anal. Appl. , vol.10 , pp. 457-480
    • Gu, C.1    Bates, D.M.2    Chen, Z.3    Wahba, G.4
  • 22
    • 0001589192 scopus 로고
    • Convergence rate of B-spline estimators of nonparametric conditional quantile functions
    • He, X., and Shi, P. (1994). Convergence rate of B-spline estimators of nonparametric conditional quantile functions, J. Nonparametric Statist. 3 299-308.
    • (1994) J. Nonparametric Statist. , vol.3 , pp. 299-308
    • He, X.1    Shi, P.2
  • 23
    • 0001558410 scopus 로고
    • Spline smoothing in a partly linear model
    • Heckman, N. E. (1986). Spline smoothing in a partly linear model. J. Roy. Statist. Soc. B 48 244-248.
    • (1986) J. Roy. Statist. Soc. B , vol.48 , pp. 244-248
    • Heckman, N.E.1
  • 24
    • 0001834407 scopus 로고
    • Hierarchical spline models for conditional quantiles and the demand for electricity
    • Hendricks, W., and Koenker, R. (1992). Hierarchical spline models for conditional quantiles and the demand for electricity. J. Amer. Statistical Assn. 87 58-68.
    • (1992) J. Amer. Statistical Assn. , vol.87 , pp. 58-68
    • Hendricks, W.1    Koenker, R.2
  • 26
    • 70349119250 scopus 로고
    • Regression and time series model selection in small samples
    • Hurvich, C. M., and Tsai, C. L. (1989). Regression and time series model selection in small samples. Biometrika 76 297-307.
    • (1989) Biometrika , vol.76 , pp. 297-307
    • Hurvich, C.M.1    Tsai, C.L.2
  • 27
    • 0000273843 scopus 로고
    • Regression quantiles
    • Koenker, R., and Bassett, G. (1978). Regression quantiles. Econometrica 46 33-50.
    • (1978) Econometrica , vol.46 , pp. 33-50
    • Koenker, R.1    Bassett, G.2
  • 28
    • 0001652263 scopus 로고
    • Quantile smoothing splines
    • Koenker, R., Ng, P., and Portnoy, S. (1994). Quantile smoothing splines. Biometrika 81 673-680.
    • (1994) Biometrika , vol.81 , pp. 673-680
    • Koenker, R.1    Ng, P.2    Portnoy, S.3
  • 29
    • 0000930441 scopus 로고
    • Logspline density estimation for censored data
    • Koopersberg and Stone (1992). Logspline density estimation for censored data. J. Comput. Graph. Statist. 1 301-328.
    • (1992) J. Comput. Graph. Statist. , vol.1 , pp. 301-328
    • Koopersberg1    Stone2
  • 31
    • 0000981525 scopus 로고
    • 2/n is large. I. Consistency
    • 2/n is large. I. Consistency. Ann. Statist. 12 1298-1309.
    • (1984) Ann. Statist. , vol.12 , pp. 1298-1309
    • Portnoy, S.1
  • 32
    • 0000196746 scopus 로고
    • Convergence rates for partially splines models
    • Rice, J. (1986). Convergence rates for partially splines models, Statist. Probab. Lett. 4 203-208.
    • (1986) Statist. Probab. Lett. , vol.4 , pp. 203-208
    • Rice, J.1
  • 33
    • 0000197891 scopus 로고
    • Achieving information bounds in non-and semiparametric models
    • Ritov, Y., and Bickel, P. J. (1990). Achieving information bounds in non-and semiparametric models, Ann. Statist. 18 925-938.
    • (1990) Ann. Statist. , vol.18 , pp. 925-938
    • Ritov, Y.1    Bickel, P.J.2
  • 36
    • 0000120766 scopus 로고
    • Estiamting the dimension of a model
    • Schwarz, G. (1978). Estiamting the dimension of a model. Ann. Statist. 6 461-464.
    • (1978) Ann. Statist. , vol.6 , pp. 461-464
    • Schwarz, G.1
  • 37
    • 21844489169 scopus 로고
    • Convergence rates for sieve estimators
    • in print
    • Shen and Wang (1994). Convergence rates for Sieve estimators. Ann. Statist. 22, in print.
    • (1994) Ann. Statist. , vol.22
    • Shen1    Wang2
  • 39
    • 0011611735 scopus 로고
    • Smoothness priors and nonlinear regression
    • Shiller, R. J. (1984). Smoothness priors and nonlinear regression. J. Amer. Statist. Assoc. 79 609-615.
    • (1984) J. Amer. Statist. Assoc. , vol.79 , pp. 609-615
    • Shiller, R.J.1
  • 40
    • 0000713437 scopus 로고
    • Kernel smoothing in partial linear models
    • Speckman, P. (1988). Kernel smoothing in partial linear models, J. Roy. Statist. Soc. B 50 413-436.
    • (1988) J. Roy. Statist. Soc. B , vol.50 , pp. 413-436
    • Speckman, P.1
  • 41
    • 0000439527 scopus 로고
    • Optimal global rates of convergence for nonparametric regression
    • Stone, C. (1982). Optimal global rates of convergence for nonparametric regression. Ann. Statist. 10 1040-1053.
    • (1982) Ann. Statist. , vol.10 , pp. 1040-1053
    • Stone, C.1
  • 42
    • 0001227575 scopus 로고
    • Additive regression and other nonparametric models
    • Stone, C. (1985). Additive regression and other nonparametric models. Ann. Statist. 13 689-705.
    • (1985) Ann. Statist. , vol.13 , pp. 689-705
    • Stone, C.1
  • 43
    • 0000287642 scopus 로고
    • Asymptotic for doubly flexible logspline response models
    • Stone, C. (1991). Asymptotic for doubly flexible logspline response models. Ann. Statist. 19 1832-1854.
    • (1991) Ann. Statist. , vol.19 , pp. 1832-1854
    • Stone, C.1
  • 44
    • 0346862811 scopus 로고
    • The use of polynomial splines and their tensor products in multivariate function estimation
    • Stone, C. (1994). The use of polynomial splines and their tensor products in multivariate function estimation. Ann. Statist. 22 118-184.
    • (1994) Ann. Statist. , vol.22 , pp. 118-184
    • Stone, C.1
  • 45
    • 0002989657 scopus 로고
    • Cross validation spline methods for the estimation of multivariate functions from data on functionals
    • (H. A. David and H. T. David, Eds.), Iowa State Univ. Press, Ames, IA
    • Wahba, G. (1984). Cross validation spline methods for the estimation of multivariate functions from data on functionals. In Statistics: An Appraisal, Proceedings 50th Anniversary Conference Iowa State Statistical Laboratory (H. A. David and H. T. David, Eds.), pp. 205-235. Iowa State Univ. Press, Ames, IA.
    • (1984) Statistics: An Appraisal, Proceedings 50th Anniversary Conference Iowa State Statistical Laboratory , pp. 205-235
    • Wahba, G.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.