By Laura Azzimonti, Francesca Ieva (auth.), Matteo Grigoletto, Francesco Lisi, Sonia Petrone (eds.)
The use of computational equipment in facts to stand advanced difficulties and hugely dimensional information, in addition to the common availability of desktop know-how, isn't any information. the variety of purposes, as a substitute, is unheard of.
As usually happens, new and intricate info kinds require new innovations, not easy for the advance of novel statistical equipment and suggesting stimulating mathematical difficulties.
This publication is addressed to researchers operating on the vanguard of the statistical research of advanced platforms and utilizing computationally in depth statistical methods.
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Additional info for Complex Models and Computational Methods in Statistics
On the other hand, increasing the value of m is expected to increase efficiency. For m D n, we recover the maximum likelihood estimator as a special case. 46 L. Bauwens and G. 044 B1 B2 B3 B4 T1 T2 T3 T4 B1 B2 B3 B4 T1 T2 T3 T4 Fig. 1 Simulation results for the estimation of the ˛ parameter by CML with bivariate (B) and trivariate (T ) marginals. Key to graph: 1 D estimator based on contiguous sets; 2 D estimator based on m1 D ŒNm =3 subsystems; 3 D estimator based on m2 D ŒNm =2 subsystems; 4 D estimator based on m3 D Nm subsystems where Nm D min(M,5000) and Œ: indicates rounding to the closest integer 5 Monte Carlo Simulation In this section we present the results of a Monte Carlo simulation study aimed at evaluating and comparing the finite sample efficiencies of the CML estimator derived under different implementation settings.
Grigoletto et al. 1007/978-88-470-2871-5 3, © Springer-Verlag Italia 2013 27 28 F. G. Dias This paper illustrates the enormous potential of this type of longitudinal latent variable modeling that combines discrete and continuous latent variables. The application estimates the evolution of financial product ownership at household level in Italy in the period of 2000–2006. , whether a given household owns a certain type of financial asset) as multiple indicators of a latent process that can differ at segment level.
The results have been summarized in Figs. 1, for ˛, and 2, for ˇ. Both CL2 and 48 L. Bauwens and G. e. (se)/simulated O mean ( O )) of parameter estimates for CML estimators based on bivariate (Bi) and trivariate (Ti) marginals, respectively se. b/ O se. 0033 CL3 result to be approximately unbiased even for the shorter sample size. As far as efficiency of the estimators is concerned, in comparative terms, it is evident that CL3 is remarkably more efficient than CL2 while it appears that, within the range of values considered for the simulation, the number of lower dimensional subsystems used to compute the CL function is not dramatically affecting the efficiency of the CL estimators.