Ktisis Collection: Τεχνικές Αναφορές (Technical Reports)

Causal inference for multiple treatments via sufficiency and ratios of generalized propensity scores

Sat, 29 Oct 2011 22:58:59 GMT

Title: Causal inference for multiple treatments via sufficiency and ratios of generalized propensity scores

Authors: Yatracos, Yannis G.

Abstract: The coarsest balancing score for multiple treatments T is the minimalsufficient statistic s for the covariates' distributions, DT ; ofpopulations {Pt; t ∈ T } receiving each treatment t ∈ T : A unit inPr with covariates x is a good match with respect to T for a unitin Pt with covariates y; when x and y provide similar informationfor DT ; i.e. when s(x) ≈ s(y): For finite, countably finite and oftencontinuous treatments, s(x) is shown to be equivalent to ~e; a vectorof propensities' ratios. The units in {Pt; t ∈ T } can be divided intosubpopulations where causal comparisons are simultaneously valid.Satisfactory s-matchings are obtained for simulated covariates in R3:The use of ~e's estimate rather than s's estimate allows to avoid thex-curse of dimensionality, but the available data's size in each caseis critical for the final choice.

Pitman's closeness criterion and shrinkage estimates of the variance and the S.D.

Fri, 29 Oct 2010 22:58:59 GMT

Title: Pitman's closeness criterion and shrinkage estimates of the variance and the S.D.

Authors: Yatracos, Yannis G.

Abstract: Pitman’s closeness criterion (PCC) became a controversial topic since somestatisticians expressed their wish to exclude it from the evaluation criteria ofestimates. Herein, PCC is studied for an estimate t and its shrinkage ct,when the unknown parameter of interest is positive; 0 < c < 1. PCC istransitive for shrinkage estimates with decreasing shrinkage coefficients andonly t’s distribution is needed to compute its value. When is the variance 2or the standard deviation , exact calculations and simulations confirm thatct, which improves t’s mean square error, may not improve often t’s distancefrom and PCC takes large values. Consequently, some statisticians, theirclients and some statistics’ users will not use shrinkage estimates of 2 andof . For this group, PCC is a useful information tool to be used along withother evaluation criteria, as suggested by Rao (1993).