![]() A sequential sum of squares quantifies how much variability we explain (increase in regression sum of squares) or alternatively how much error we reduce (reduction in the error sum of squares). In essence, when we add a predictor to a model, we hope to explain some of the variability in the response, and thereby reduce some of the error. Or, it is the increase in the regression sum of squares ( SSR) when one or more predictor variables are added to the model.It is the reduction in the error sum of squares ( SSE) when one or more predictor variables are added to the model.Math.The numerator of the general linear F-statistic - that is, \(SSE(R)-SSE(F)\) is what is referred to as a "sequential sum of squares" or "extra sum of squares." Definition What is a " sequential sum of squares?" It can be viewed in either of two ways: Woodroofe, M.: Nonlinear Renewal Theory in Sequential Analysis. Wang, L., Renner, R.: One-shot classical-quantum capacity and hypothesis testing. Wald, A., Wolfowitz, J.: Optimum character of the sequential probability ratio test. Wald, A.: Sequential tests of statistical hypotheses. Tomamichel, M., Hayashi, M.: A hierarchy of information quantities for finite block length analysis of quantum tasks. Slussarenko, S., Weston, M.M., Li, J.G., Campbell, N., Wiseman, H.M., Pryde, G.J.: Quantum state discrimination using the minimum average number of copies. Salek, F., Hayashi, M., Winter, A.: When are Adaptive Strategies in Asymptotic Quantum Channel Discrimination Useful? (2020). Princeton University Press, Princeton (1970) ![]() In: Information Theory and Applications Workshop (ITA) (2011). Polyanskiy, Y., Verdú, S.: Binary hypothesis testing with feedback. Ogawa, T., Nagaoka, H.: Strong converse and Stein’s lemma in quantum hypothesis testing. Ogawa, T., Hayashi, M.: On error exponents in quantum hypothesis testing. Nussbaum, M., Szkoła, A.: The Chernoff lower bound for symmetric quantum hypothesis testing. Naghshvar, M., Javidi, T.: Active sequential hypothesis testing. Nagaoka, H.: The converse part of the theorem for quantum Hoeffding bound. Martínez-Vargas, E., Hirche, C., Sentís, G., Skotiniotis, M., Carrizo, M., Muñoz-Tapia, R., Calsamiglia, J.: Quantum sequential hypothesis testing. Luenberger, D.G.: Optimization by Vector Space Methods. Li, Y., Tan, V.Y.F.: Second-order asymptotics of sequential hypothesis testing. Li, K.: Second-order asymptotics for quantum hypothesis testing. In: IEEE International Symposium on Information Theory (ISIT), pp. Lalitha, A., Javidi, T.: Reliability of sequential hypothesis testing can be achieved by an almost-fixed-length test. Hoeffding, W.: Asymptotically optimal tests for multinomial distributions. Hiai, F., Petz, D.: The proper formula for relative entropy and its asymptotics in quantum probability. Helstrom, C.W.: Detection theory and quantum mechanics. Hayashi, M., Nagaoka, H.: General formulas for capacity of classical-quantum channels. Hayashi, M.: Discrimination of two channels by adaptive methods and its application to quantum system. Hayashi, M.: Error exponent in asymmetric quantum hypothesis testing and its application to classical-quantum channel coding. ![]() ![]() Cambridge University Press, Cambridge (2019) ĭurrett, R.: Probability: Theory and Examples, 5th edn. Ĭhubb, C.T., Tan, V.Y.F., Tomamichel, M.: Moderate deviation analysis for classical communication over quantum channels. Ĭheng, H.C., Hsieh, M.H.: Moderate deviation analysis for classical-quantum channels and quantum hypothesis testing. īlahut, R.: Hypothesis testing and information theory. īerta, M., Fawzi, O., Tomamichel, M.: On variational expressions for quantum relative entropies. Īudenaert, K.M.R., Nussbaum, M., Szkoła, A., Verstraete, F.: Asymptotic error rates in quantum hypothesis testing. Audenaert, K.M.R., Calsamiglia, J., Muñoz Tapia, R., Bagan, E., Masanes, L., Acin, A., Verstraete, F.: Discriminating states: the quantum Chernoff bound. ![]()
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