Morales González, DomingoPardo Llorente, LeandroPardo Llorente, María del CarmenVadja, Igor2023-06-202023-06-202000-12Barndorf-Nielsen OE (1978) Information and Exponential Families. John Wiley, Gluchester Barndorf-Nielsen OE and Sørensen M (1991) Information quantities in non classical setttings. Computational Statistic and Data Analysis 12:143-158 Barndorf-Nielsen OE and Sørensen M (1994) A review of some aspects of asymptotic likelihood theory for stochastic processes. International StatiStical Review 62:133-165 Brown LD (1986) Fundamentals of Statistical Exponential Families. Lecture Notes vol. 9. Inst. of Mathematical Statistics, Hayward, California Casalis M and Letac G (1994) Characterization of the Jorgensen set in generalized linear models. Test 3:145-162 Gihman II and Skorokhod AV (1975) The Theory o! StochaStic ProceSSeS, vol. 1. Springer-Verlag, Berlin Ikada N and Watanabe S (1981) Stochastic Differential Equations and Diffussion Processes. North-Holland, Amsterdam Küchler U and Sørensen M (1994) Exponential families of stochastic processes and Levy processes. Journal of Statistical Planning and Inference 39:211-237 Küchler U and Sørensen M (1997) Exponential Families of Stochastic Processes. Springer-Verlag, Berlin Morales D, Pardo L and Vajda I (1999) Renyi statistics in directed families of exponential experiments. Statistics 34:151-174 Rockafellar RT (1970) Convex Analysis. Princeton University Press, Princeton, New Jersey Serfing RJ (1976) Approximation Theorems of Mathematical Statistics. Wiley, New York0026-133510.1007/s001840000060https://hdl.handle.net/20.500.14352/57869A generalization of the Wald statistic for testing composite hypotheses is suggested for dependent data from exponential models which include Levy processes and diffusion fields. The generalized statistic is proved to be asymptotically chi-squared distributed under regular composite hypotheses. It is simpler and more easily available than the generalized likelihood ratio statistic. Simulations in an example where the latter statistic is available show that the generalized Wald test achieves higher average power than the generalized likelihood ratio test.engjournal articlehttp://link.springer.com/article/10.1007%2Fs001840000060http://link.springer.com/restricted access519.2composite parametric hypothesesgeneralized likelihood ratio statisticgeneralized Wald statisticconvergent exponential modelsLevy processesdiffusion fieldsstochastic-processesProcesos estocásticos1208.08 Procesos Estocásticos