References

[AD 1 ADLER R.J. (1990). An introduction to continuity, extrema, and Re­lated topics for general Gaussian processes. Inst . of Math. Statist., Hayward, Californi

[AN-PO 1 AN'NGOZE P. and PORTIER B. (1994). Estimation of the density and of the regression functions of an absolutely regular stationary process. Publ. ISUP 38, 59-87.

[A-O J ANTONIADIS A. and OPPENHEIM G. (1995) editors. Wavelets and statistics. Springer Verlag.

[A-Z J ARAK T. and ZAIZSEV A. (1988). Uniform limit theorems for sums of independent random variables. Publ. Steklov math. institute, 1.

[A-G J ASH R.B. and GARDNER M.F. (1975). Topics in stochastic processes. Academic Press.

[AS J AzMs J.M. (1990). Conditions for convergence of number of crossings to the local time. Probab. and Math. Stat., 11, 1, 19-36.

[A-F J AZAIS J.M. and FLORENS D. (1987). Approximation du temps local des processus Gaussiens stationnaires par regularisation des trajectoires. Probab. theory and reI. fields 76, 121-132.

[BA J BANON G. (1978). Nonparametric identification for diffusion processes. Siam J. Control and Optimisation V16, 380-395.

[BA-NG1 1 BANON G. and NGUYEN H.T. (1978). Sur l'estimation recurrente de la densite et de sa derivee pour un processus de Markov, C.R. Acad. Sci. Paris t. 286, ser. A, 691-694.

[BA-NG2 J BANON G. and NGUYEN H.T. (1981). Recursive estimation in diffu­sion model. Siam J. Control and optimisation VIO, 676-685.

[BA-Y J BARLOW M.T. and YOR M. (1981). (Semi) Martingales inequalities and local times. Z. Fur Wahrscheinlichkeit. und Geb. 55, 237-254.

[BW-PR J BASAWA I.V. and PRAKASA RAO B.1.S. (1980) . Statistical inference for stochastic processes. Academic Press.

[BE 1 BENNETT G. (1962). Probability inequalities for sum of independent random variables. J. Amer. Statis. Assoc. 57, 33-45

198 REFERENCES

[BB 1 BERBEE H.C.P.(1979). Random walks with stationary increments and renewal theory. Math. Centro Tract. Amsterdam.

[BL-DV 1 BERLINET A. and DEVROYE L. (1994). A comparison of kernel density estimates. Publ. ISUP Vol. 38, 3, 3-59.

[BM 1 BERMAN S.M. (1983) . Local nondeterminism and local times of general stochastic processes. Ann. Inst. H. Poincare, 19, 189-207.

[BI-MA 1 BIRGE L. and MASSART P. (1995). From model selection to adaptive estimation. Preprint 95.41 Univ. Paris Sud.

[BII 1 BILLINGSLEY P. (1965). Ergodic theory and information. Wiley.

[BI2 1 BILLINGSLEY P. (1968). Convergence of Probability Measures. Wiley.

[BI3 1 BILLINGSLEY P. (1986) . Probability and Measure. (2nd edition). Wiley.

[BKI 1 BLANKE D. (1997). Estimation non parametrique de la densite pour des processus a temps continu : vitesse minimax. C.R. Acad. Sci. Paris t. 325, I. p. 527-530.

[BK2 1 BLANKE D. (1997). Ph.D thesis - University of Paris 6.

[BK-B01 1 BLANKE D. and BOSQ D. (1997). Accurate rates of density estimators for continuous time processes. Stat. and Proba. letters 33, 2, 185-191.

[BK-B02 1 BLANKE D. and BOSQ D. (1998). A family of minimax rates for density estimators in continuous time. 32 p. to appear.

[BT-F 1 BOENTE G. and FRAIMAN R. (1995). Asymptotic distribution of data driven smoothers in density and regression under dependence. The Canadian Journ. of Statist. 23,4, 383-397.

[BV BOLLERSLEV T . (1986) . Generalized autoregressive conditional het­eroskedaticity. J. of Econometrics 31, 307-327.

[BOll BOSQ D. (1989). Non parametric estimation of a Non Linear Filter using a Density Estimator with zero-one "explosive" behaviour in ]Rd.

Statistics and Decisions 7, 229 - 241.

[B02 1 BOSQ D. (1991). Modelization, Nonparametric estimation and pre­diction for continuous time processes in "Nonparametric functional es­timation and related topics". Ed. G. ROUSSAS - NATO ASI Series, 509-529.

[B03 1 BOSQ D. (1991). Nonparametric prediction for unbounded almost sta­tionary processes. Nonparametric functional estimation and related top­ics. NATO ASI series Vol. 335 - ed. G. ROUSSAS. 389-404.

REFERENCES 199

[B04 1 BOSQ D. (1993). Vitesses optimales et superoptimales des estimateurs fonctionnels pour un processus it temps continuo C.R. Acad. Sci. Paris 317, ser. I, 1075-1078.

[B05 1 BOSQ D. (1993) . Optimal and superoptimal quadratic error of func­tional estimators for continuous time processes. Preprint, Univ. Paris VI.

[B06 1 BOSQ D. (1993). Bernstein-type large deviation inequalities for partial sums of strong mixing processs. Statistics,24, 59-70.

[B07 1 BOSQ D. (1995). Sur Ie comportement exotique de l'estimateur it noyau de la densite marginale d'un processus a temps continuo C.R. Acad. Sci. Paris t. 320, skI, 369-372.

[B08 1 BOSQ D. (1995). Optimal Asymptotic quadratic Error of Density Esti­mators for strong mixing or chaotic data. Statistics and Probab. Letters 22, 339-347.

[B09 1 BOSQ D. (1997). Parametric rates of nonparametric estimators and predictors for continuous time processes. Annals of Statistics, 25, 3, 982-1000.

[BOlO 1 BOSQ D. (1997). Temps local et estimation sans biais de la densite en temps continuo C.R. Acad. Sci. Paris t. 325, 1, 527-530.

[BO-C 1 BOSQ D. and CHEZE-PAYAUD N. (1995). Optimal asymptotic quadratic error of nonparametric regression function estimates for a continuous-time process from sampled data. To appear.

[BO-D 1 BOSQ D. and DAVYDOV Y. (1998) . Local time and density estimation in continuous time. Publ. IRMA. Univ. Lille 1, Vol. 44, W III.

[BO-L 1 BOSQ D. and LECOUTRE J.P. (1987) . TMorie de l'estimation fonc­tionnelle. Economica.

[BMP 1 BOSQ D., MERLEVEDE F . and PELIGRAD M. (1997). Asymptotic normality for kernels estimators of densities in discrete and continuous time. To appear.

[BO-S 1 BOSQ D. and SHEN J. (1998). Estimation of an autoregressive nonlin­ear model with exogenous variable . Accepted by Journ. of Stat. infer­ence.

[B-J 1 BOX G. and JENKINS G. (1970). Time series analysis : forecasting and control. Holden Day.

[BR1 1 BRADLEY R. (1983). Approximation theorems for strongly mixing random variables. Michigan Maths. J. 30, 69-81.

200 REFERENCES

[BR2 1 BRADLEY R. (1986) . Basic Properties of strong mixing conditions. in E.Eberlein and M.S. Taqqu editors, Dependence in Probability and Statistics, p.165-192. Birkhiiuser.

[B-D 1 BROCKWELL P.J. and DAVIS R.A. (1991). Time series: theory and methods. Springer Verlag.

[BRO 1 BRONIATOWSKI M. (1993) . Cross validation methods in kernel non­parametric density estimation: a survey. Pub!. ISUP, 38, 3-4, 3-28.

[C 1 CARBON M. (1993). Une nouvelle inegalite de grandes deviations. Applications. Pub!. IRMA, Vo!' 32 n° II.

[C-DE 1 CARBON M. and DELECROIX M. (1993). Nonparametric forecasting in time series: a computational point of view. Applied Stoch. Models and data analysis 9, 3, 215-229.

[C-L 1 CASTELLANA J .V. and LEADBETTER M.R. (1986) On smoothed Probability density estimation for stationary processes. Stoch. Proc. App!., 21, 179-193.

[CP J CHEZE-PAYAUD N. (1994) . Regression, prediction et discretisation des processus a temps continuo Thesis Univ. Paris 6.

[CH-W J CHUNG K.L. and WILLIAMS R.J . (1990) . Introduction to stochastic integration (2nd ed.) 276 p., Birkhiiuser (Boston) .

[CO J COLLOMB G. (1981). Estimation non parametrique de la regression. Revue bibliographique. Ins. Statist. Rev. 49, 75-93.

[DC-OP-TH J DACUNHA-CASTELLE D., THOMASSONE R. and OPPENHEIM G.(1995) . Prevision des pointes d'ozone a Paris (preprint).

[Dl J DAVYDOV YA. (1968). Convergence of distributions generated by stationary stochastic Processes. Theor. Probab. Appl. 13, 691-696.

[D2 1 DAVYDOV Y (1976). Local times of random processes. Th. Probab. and Appl. 21 , 1, p. 172-179.

[D3 J DAVYDOV Y. (1996). Approximation du temps local des processus a trajectoires regulieres. C.R. Acad. Sci. Paris, t . 322, Serie I, p. 471-474.

[D4 J DAVYDOV Y (1998) . The rate of approximation of local time for random processes with smooth sample paths. Preprint Univ. Lille I.

[D-H J DEHEUVELS P. and HOMINAL P. (1980). Estimation automatique de la densite. Rev. Statist. App!. 28, 25-55.

REFERENCES 201

[DEll DELECROIX M. (1980). Sur l'estimation des densites d'un processus stationnaire a temps continuo Pub!. ISUP, XXV, 1-·2, 17-39.

[DE2 1 DELECROIX M. (1987). Sur l'estimation et la prevision non parame­trique des processus ergodiques. These de Doctorat d'Etat, Universite de Lille.

[DE-RO 1 DELECROIX M. and ROSA A.C. (1995). Ergodic processes prediction via estimation of the conditional distribution function. Pub!. ISUP, XXXIX, 2, 35-56.

[DV 1 DEVROYE, L. (1987). A course in density estimation. Birkhiiuser.

[DV-GY 1 DEVROYE L. and GYORFI L. (1985). Nonparametric density estima­tion. The L1 view. Wiley.

[DO 1 DOOB J.L. (1967). Stochastic Processes. (7th printing). Wiley.

[DK1 1 DOUKHAN P. (1991). Consistency of delta-sequence estimates of a den­sity or a regression function for a weakly stationary sequence. Seminaire Univ. Orsay 1989-90, 121-14l.

[DK2 1 DOUKHAN P. (1994). Mixing -Properties and Examples. Lecture Notes in Statistics. Springer Verlag.

[DK-LN 1 DOUKHAN P. and LEON J. (1994). Asymptotics for the local time of a strongly dependent vector-valued Gaussian random field . Universite de Paris-Sud, Mathematiques 94.3l.

[E 1 ENGLE R. (1982) . Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation. Economica 50, 987-1007.

[EP 1 EPANECHNIKOV V.A. (1969) . Nonparametric estimation of a multi­dimensional probability density. Theory Probab. App!. 14, 153-158.

[Fl 1 FAN (1991). On the optimal rates of convergence for nonparametric deconvolution problems. Annals of Statist. , 19, 1257-1272.

[F2 1 FAN (1991). Asymptotic normality for deconvolving kernel density estimators, Sankhya, Ser. A 53, 97-110.

[F3 1 FAN (1992). Deconvolution with supersmooth distributions. Canad J . Statist. 20, 155-169.

[FA 1 FARREL R. (1972). On the best obtainable asymptotic rates of con­vergence in estimation of a density function at a point. Ann. of Math. Stat. 43,1,170-180.

202 REFERENCES

[G-H1 1 GEMAN D. and HOROWITZ J. (1973). Occupation times for smooth stationary processes. Annals of Probab. 1, 1, 131-137.

[G-H2 1 GEMAN D. and HOROWITZ J. (1980). Occupation densities, 8, 1, 1-67.

[G-M 1 GOURIEROUX C. and MONFORT A. (1983). Cours de serie tem­porelle. Economica.

[GR 1 GRENANDER U. (1981). Abstract inference. Wiley.

[GG 1 GUEGAN D. (1994). Series chronologiques non lineaires it temps dis­cret. Economica.

[GU 1 GUERRE E. (1995). The General behavior of Estimators of the Box­Cox model for integrated Time Series. Preprint INSEE.

[GY 1 GYORFI L. (1997). How far one can learn probability law from data? Pub!. ISUP, Vo!' 41, Fasc. 3, p. 3-20.

GL GYORFI L. and LUGOSI G. (1992). Kernel density estimation for er­godic sample is not universally consistent . Comput. Statist. and data Anal. 14,437-442.

[GHSV 1 GYORFI L., HARDLE W., SARDA P., VIEU P. (1989). Nonparametric Curve Estimation from Time Series. Lecture Notes in Statist. Springer Verlag.

[HA-l 1 HARDLE W. (1990). Applied nonparametric regression. Cambridge University Press.

[HA-2 1 HARDLE W. (1991). Smoothing Techniques with implementation in S. Springer Verlag.

[HO 1 HOEFFDING (1963). Probability inequalities for sums of bounded random variables. J. Amer. Statist. Assoc. 58, 13-30.

[IB 1 IBRAGIMOV LA. (1962). Some limits theorems for stationary Pro­cesses. Theor. Prob. Appl. 7, 349-382.

[IB-HA 1 IBRAGIMOV l.A. and HASMINSKII R.Z. (1981). Statistical estima­tion - Asymptotic theory. Springer-Verlag, New York.

[IB-RZ 1 IBRAGIMOV LA. and ROZANOV YA. (1978). Gaussian random pro­cesses. Springer Verlag, New York.

[K-S 1 KENDALL M. and STUART A. (1976). The advanced theory of Statis­tics. Vol. 3 - C. Griffin and Co., third edition.

REFERENCES 203

[KO-TS I KOROSTELEV A.P. and TSYBAKOV A.B. (1993) . Minimax theory of image reconstruction. Springer Verlag.

[K I KUTOYANTS Yu.A. (1997). Some problems of nonparametric esti­mation by observations of ergodic diffusion processes. Stat. and Proba. letters 32, 311-320.

[LM I LASOTA A. and MACKEY M.C. (1985). Probabilistic Properties of deterministic systems. Cambridge Univ. Press.

[LEI I LEBLANC F. (1995). PhD thesis, Univ. Paris VI.

[LE2 I LEBLANC F. (1997) . Density estimation for a class of continuous time process. Maths. Method. of Stat., 6, 2, 171-199.

[M I MAES J. (1994) . Estimation non parametrique de la fonction chaotique et des exposants de Lyapunov d'un systeme dynamique. c.R. Acad., Sci. Paris t. 319 ser. 1 p. 1005-1008.

[MA I MARLE CM. (1974). Mesures et probabilites. Hermann (Paris).

[MR I MARRON J .J. (1991). Root n bandwith selection. Nonparametric functional estimation and related topics. NATO ASI series, Vol 335, ed. G. ROUSSAS, 251-260.

[MSI I MASRY E. (1983) . Probability density estimation from sampled data. IEEE transf. inf. tho 29, 696-709.

[MS2 I MASRY E. (1986). Recursive Probability Density Estimation for weakly Dependent Stationary processes. IEEE Trans. inform. Theory. II, 32, 2, 254-267.

[MS3 I MASRY E. (1988). Continuous-parameter stationary process: Statisti­cal properties of joint density estimators, J. of multo Anal., 26, 133-165.

[MS4 I MASRY E. (1991). Multivariate Probability Density deconvolution for stationary random processes. IEEE Trans. inform. Theory II, 37, 1105-1115.

[MS5 I MASRY E. (1993). Strong consistency and rates for deconvolution of multivariate densities of stationary processes. Stoch. Proc. and Applic. 47, 53- 74.

[MS6 I MASRY E. (1993). Asymptotic Normality for deconvolution estimators of multivariate densities of stationary processes. J. Multivariate Analysis, 44,47- 68.

[MS7 I MASRY E. (1994). Multivariate regression estimation with errors in variables for stationary processes. Nonparametric Statist . 3 in press.

204 REFERENCES

[MIl MILCAMPS B. (1995). Analyse des correlations inter-marcM. Memoire ISUP (Paris).

[NA 1 NADARAJA E.A. (1964). On estimating regression. Theory Probab. An., 141-142.

[NG 1 NGUYEN H.T. (1979). Density estimation in a continuous-time sta­tionary Markov process, Annals of Statist., 7, 2, 341-348.

[NG-PHI 1 NGUYEN H.T. and PHAM D.T. (1980) . Sur l'utilisation du temps local en Statistique des processus, C.R. Acad. Sci. Paris, 290, A, 165-170.

[NG-PH2 1 NGUYEN H.T. and PHAM D.T. (1981). Nonparametric estimation in diffusion model by discrete sampling. Preprint.

[PA 1 PARZEN E . (1962). On the estimation of probability density function and mode. Ann. Math. Statist . 33, 1065-1076.

[P 1 PANKRATZ A. (1983). Forecasting with univariate Box-Jenkins mod­els. Concepts and cases. Wiley.

[PH-TIl PHAM D.T . and TRAN L.T. (1985). Some strong mixing properties of time series models. Stoch. Proc. App!. 19, 207-303.

[PH-T2 1 PHAM T .D. and TRAN L.T. (1991). Kernel Density Estimation under a locally Mixing condition - in Nonparametric Functional Estimation and Related Topics. Ed. G. ROUSSAS NATO ASI SERIES V. 335, 419-430.

[PRI 1 PRASAKA RAO B.L.S. (1979) . Nonparametric estimation for continu­ous time Markov processes via delta-families. Pub!. ISUP, XXIV, 81-97.

[PR2 1 PRASAKA RAO B.L.S. (1983) . Nonparametric functional estimation. Academic Press.

[PR3 1 PRASAKA RAO B.L.S. (1990) . Nonparametric density estimation for stochastic process from sampled data. Pub!. ISUP, XXXV, 51-84.

[PO 1 POGGI J.M. (1994) . Prevision non parametrique de la consommation electrique. Rev. Statist. Appliq. XLII (4), 83-98.

[RA 1 RAO (1992). Probability Theory. Acad. Press.

[RH ] RHOMARI N. (1994) . Filtrage non parametrique pour les processus non Markoviens. Applications. Ph D. Thesis University Pierre et Marie Curie (Paris).

[RB ] ROBINSON P.M. (1983). Nonparametric Estimators for time series. J. Time Series Anal. 4, 185-297.

REFERENCES 205

[RB-ST 1 ROBINSON P.M. and STOYANOV J .M. (1991). Semiparametric and nonparametric inference from irregular observations on continuous time stochastic processes in "Nonparametric functional es1;imation and related topics" . Ed. G. ROUSSAS NATO ASI Series, 553-5.58.

[RIl 1 RIO E. (1993) . Covariance inequalities for strongly mixing processes. Ann. Inst. Henri Poincare, 29, 4, 587-597.

[RI2 1 RIO E. (1995) . The functional law of the iterated logarithm for station­ary strongly mixing sequences. Annals of Probab. 22, 3, 1188-1203.

RA ROSA A.C.M. (1993). Prevision robuste sous une hypothese ergodique. Phd Thesis. Un. of Tououse 1.

[ROIl ROSENBLATT M. (1956). Remarks on some non parametric estimates of a density function . Ann. Math. Statist. 27, 832-837.

[R02 1 ROSENBLATT M. (1956). A central limit theorem and a strong mixing condition. Proc. Nat. Ac. Sc. USA 42, 43-47.

[R03 1 ROSENBLATT M. (1985) . Stationary Sequences and Random fields. Bir khiiuser .

[RS1 1 ROUSSAS G. (1967). Nonparametric Estimation in Markov Processes. Ann. Inst. Stat. Math. 21, 73-87.

[RS2 1 ROUSSAS G. (1988). Nonparametric Estimation in mixing sequences of random variables. J. Stat. Plan. and Inf. 18, 135-149.

[RS3 1 ROUSSAS G. (1990) . Nonparametric regression estimation under mix­ing conditions. Stoch. Processes Appl. 36, 107-116.

[RS-IO 1 ROUSSAS G. and IOANNIDES D. (1987) . Moment inequalities for mixing sequences of random variables . Stochastic Anal. Appl. 5(1), 61-120.

[RS-TR 1 ROUSSAS G. and TRAN L.T. (1992) . Asymptotic normality of the recursive kernel regression estimate under dependence conditions. Annals of Statist. 20, 1,98-120.

[RU 1 RUELLE D. (1989) . Chaotic Evolution and Strange Attractors. Cam­bridge Univ. Press.

[SA 1 SARDA P. (1993). Smoothing parameter selection for smooth distribu­tion function . J. Statist. Plan. Infer 35, 65-75.

[SC 1 SCHIPPER M. ( 1997). Sharp asymptotics in nonparametric estima­tion. Ph.D. Thesis. Utrecht .

206 REFERENCES

lSI I SILVERMAN B.W. (1986). Density estimation for Statistics and Data Analysis . Chapman and Hall.

[ST-TR I STONE C.J. and TRUONG YK. (1992). Nonparametric function esti­mation involving time series , Annals of Statist., 20, 1, 77-97.

[SU I STOUT W.F . (1974). Almost sure convergence. Academic Press.

[SR I STRASSEN V. (1964) . An invariance principle for the law of the iterated logarithm. Z. fUr Wahrscheinlichkeit. unt Geb. 3, 211-226.

[SE I STUTE W. (1982) . A law of the logarithm for kernel density estimators. Ann. Probab. 10, 414-422.

[TR1 I TRAN L.T. (1989) . The £1 convergence of kernel density estimates under dependence. The Canad. J. of Statist. 17, 2, 197-208.

[TR2 I TRAN L.T. (1990). Kernel density and regression estimation for depen­dent random variables and time series. Techn. report . Univ. Indiana.

[TR3 I TRAN L.T . (1993). Nonparametric function for time series by local average estimators. Ann. Statist . 21(2), 1040-1057.

[T-S I TRUONG YK. and STONE C.J . (1992) . Nonparametric function esti­mation involving time series. Ann. Statist. 20, 77-98.

[V I VERETENNIKOV A. YU. (1996). On a Castellana-Leadbetter's con­dition for a diffusion density estimation. Preprint Univ. du Maine.

[VI I VIEU P. (1994) . Quelques n~sultats en estimation fonctionnelle. Memoire d'Habilitation, Univ. P. Sabatier, Toulouse (France).

[WA I WATSON G.S. (1964). Smooth regression analysis. Sankhya Ser. A, 26, 359-372.

[WE I WENTZEL A.D. (1975) . Stochastic processes. Nauka (in russian). Moscou.

[Y I YAKOWITZ S. (1985) . Markov flow models and the flood warning problem. Water resources research, 21, 81-88.

[YO I YOKOYAMA R. (1980) . Moments bound for stationary mixing se­quences. Z. Wahrsch. Gebiete, 52, 45-57.

[YR I YOR M. (1995). Local times and excursions for Brownian motion. Un. Centro de Venezuela.

A

Absolute regularity 18 Adaptive methods 14

Index

Admissible sampling 14, 122, 140 a-mixing 7, 18 ARCH 1, 178 ARMA process 1, 177, 179, 180 Asymptotic normality 9, 11, 36, 54, 75, 80, 89, 118, 138, 160-161 Autoregressive processes (infinite dimensional) 14

B

tJ-mixing 18 Berbee's lemma 19 Bernstein's inequality 24 Billingley's inequality 22 Black-Scholes formula 182 Bochner's lemma 44, 100 Borel-Cantelli lemma in continuous time 108 Box-Cox transformation 170 Box-Jenkins (method) 1, 177 Bradley's lemma 20

C

Cadlag 90, 121 Cars registrations 184 Central limit theorem 36 Chaos 86 Chaotic data 57 Conditional mode predictor 180 Consistency of local time density estimator 150 Coupling 19 Covariance inequalities 20, 21, 22 Cramer's conditions 24 Cross validation 175-176 Cynical method 172

208

D

Davydov's inequality 21-22 Density kernel estimator 3, 42, 90 Deseasonalization 14, 170-172 Dichotomy 119, 140 Differencing 13 Differentiable sample paths 104 Diffusion process 101 Double kernel method 176 Dynamical system 86

E

Electricity consumption 184 Elimination of trend and seasonality 171-172 Empirical measure 12, 42, 68 Epanechnikov kernel 42, 176, 182 Ergodic 150, 153 Ergoduc theorem 151, 152, 154 Errors in variables (processes with) 64-65, 86 Exogeneous variables 15, 177 Exponential type inequalities 7, 24-33

F

<p-mixing 18 <prev-mixing 80, 143 Forecasting : see Prediction Full rate 101

G

GARCH 180 Gaussian process 10, 19, 74, 100, 104, 122, 153, 160 General stationary processes (prediction for) 81 Geometrically strongly mixing (GSM) processes 46, 90

H

Histogram 3 Hoeffding's inequality 24

I

Implementation of nonparametric method 169-177 Intermediate rates 102-107, (minimaxity of) 107-108 Interpolator 85 Irregular sampling 121 Iterated logarithm (functional law of) 161

INDEX

INDEX

K

Kernel 39 Kernel of order (k, A) 90 Kolmogorov extension theorem 4 Kutoyants theorem 102 L

Large deviations inequalities 7, 24-33 Law of large numbers 34-35 Linear process 18, 46 Local time 145, 146 Local time estimator 149 Local time for semimartingales (existence) 146 Logistic trend 83-84

M

Markov process 76, 141 Markov process of order k 76 Martingale 82 m-dependent 19 Minimax 9, 46, 97, 101, 102, 107, 108 Minimaxity of intermediate rates 107-108 MISE 91 Mixing 7,17 Mixture 4

N

Naive kernel 3, 40 Nonparametric predictor 1, 6, 76, 82, 141, 172, 177 Nonstationary process (prediction for) 82

o Optimal rate 8, 93 Occupation measure 145 Ornstein-Uhlenbeck process 122 Outliers 84

p

p-adic Process 58 Parametric rate 10 Parametric predictors 177, 180 Periodic 83 Plug-in method 173 Pollution 184

209

210

Pseudo-regression 84

Q

Quadratic error (asymptotic) 43, 69, 91, 125, 155

R

Rate 33 Regression kernel estimator 69, 130 Regression with error 86 Regressogram 5 Rio's inequality 20 Robust 5, 14, 180

s Sampling 14, 15, 118, 140 SARIMA process 1 Seasonality 13, 170 Semi parametric 14 Similarity 13 Singular distribution 61 Stationary process 7 Statistical error of prediction 6 Superoptimal rate 10, 98, 104, 116, 136, 155, 157

T

Trend 170 Two-a-mixing 19

u Unbiased density estimator 3, 12, 150, 156 Uniform convergence 8, 10, 11, 46, 72, 108, 139, 153, 162

v Variance (stabilization of) 169

w Wavelets 15, 127

y

Yields 2, 182.

INDEX

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Vol. 105 : Constantine Gatsonis, James S. Hodges. Robert E. Kass, Nozer D. Singpurwalla(Editors), Case Studies in Bayesian Statistics, Volume II. x, 354 pages, 1995.

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