340 research outputs found
Statistical Limits of Adaptive Linear Models: Low-Dimensional Estimation and Inference
Estimation and inference in statistics pose significant challenges when data
are collected adaptively. Even in linear models, the Ordinary Least Squares
(OLS) estimator may fail to exhibit asymptotic normality for single coordinate
estimation and have inflated error. This issue is highlighted by a recent
minimax lower bound, which shows that the error of estimating a single
coordinate can be enlarged by a multiple of when data are allowed to
be arbitrarily adaptive, compared with the case when they are i.i.d. Our work
explores this striking difference in estimation performance between utilizing
i.i.d. and adaptive data. We investigate how the degree of adaptivity in data
collection impacts the performance of estimating a low-dimensional parameter
component in high-dimensional linear models. We identify conditions on the data
collection mechanism under which the estimation error for a low-dimensional
parameter component matches its counterpart in the i.i.d. setting, up to a
factor that depends on the degree of adaptivity. We show that OLS or OLS on
centered data can achieve this matching error. In addition, we propose a novel
estimator for single coordinate inference via solving a Two-stage Adaptive
Linear Estimating equation (TALE). Under a weaker form of adaptivity in data
collection, we establish an asymptotic normality property of the proposed
estimator.Comment: This paper is accepted at NeurIPS 202
(1,10-Phenanthroline-κ2 N,N′)(triphenylphosphine-κP)silver(I) trifluoromethanesulfonate
The structure of the title complex, [Ag(C12H8N2)(C18H15P)]CF3SO3, is based on a distorted trigonal–planar N2P coordination of the AgI ion, provided by two N atoms of the bidentate phenanthroline ligand and one P atom of the triphenylphosphine ligand. The phenanthroline ligand and one phenyl ring of the triphenylphosphine ligand almost lie in one plane (maximum deviation = 0.014 Å from the best planes). The crystal structure may be stabilized by an intermolecular C—H⋯O hydrogen bond between the phenanthroline ligand and the O atom of the trifluoromethanesulfonate anion
Tetraaqua(1,10-phenanthroline-κ2 N,N′)cadmium(II) sulfate dihydrate
In the title mononuclear complex, [Cd(C12H8N2)(H2O)4]SO4·2H2O, the coordination geometry around the CdII atom is a distorted octahedron, with two aqua ligands occupying the axial positions. Intermolecular O—H⋯O hydrogen bonds lead to the formation of a two-dimensional layer structure parallel to (001). The layers are connected by π–π interactions between the pyridyl and benzene rings of the phenanthroline ligands [centroid–centroid distances = 3.591 (1) and 3.610 (1) Å]
5,6-Dimethyl-1,2,4-triazin-3-amine
In the crystal structure of the title compound, C5H8N4, adjacent molecules are connected through N—H⋯N hydrogen bonds, resulting in a zigzag chain along [100]. The amino groups and heterocyclic N atoms are involved in further N—H⋯N hydrogen bonds, forming R
2
2(8) motifs
A tetrasilver(I)ditungsten(VI) cluster with sulfide and bis(diphenylphosphino)methane ligands
The asymmetric unit of the title complex, [Ag4W2S8(C25H22P2)3]·2C3H7NO, tris[μ2-bis(diphenylphosphino)methane]-3:6κ2
P:P′;4:5κ2
P:P′;5:6κ2
P:P′-μ5-sulfido-2:3:4:5:6κ5
S-μ3-sulfido-1:3:4κ3
S-tetra-μ2-sulfido-1:3κ2
S;1:4κ2
S;2:5κ2
S;2:6κ2
S-disulfido-1κS,2κS-tetrasilver(I)ditungsten(VI) N,N-dimethylformamide disolvate, contains two [WS4]2− anions, four silver cations, three bidentate–bridging bis(diphenylphosphino)methane (dppm) ligands and two N,N-dimethylformamide (DMF) solvent molecules. The coordination geometry of each Ag atom is distorted tetrahedral. Two Ag ions are coordinated by μ2-S and μ5-S atoms, and by two P atoms from two dppm ligands, while the other two Ag atoms are coordinated by μ2-S, μ3-S and μ5-S atoms, and by one P atom from a dppm ligand
catena-Poly[[(isoquinoline-κN)(triphenylphospane-κP)copper(I)]-μ-thiocyanato-κ2 N:S]
In the title coordination compound, [Cu(NCS)(C9H7N)(C18H15P)]n, the CuI atom is tetrahedrally coordinated by one N atom from an isoquinoline ligand, one P atom from a triphenylphospane ligand, and one N and one S atom from two thiocyanate anions. The thiocyanide anions bridge the CuI atoms into a chain along [100]. π–π interactions between the pyridine and benzene rings of the isoquinoline ligands connect the chains [centroid-to-centroid distance = 3.722 (3) Å]
The environments of Type Ia supernovae with different relative equivalent width of Si II feature in their spectra
Although type Ia supernovae are so important in many astrophysical field,
e.g. in cosmology, their explosion mechanism and progenitor system are still
unclear. In physics, the relative equivalent width (REW) of the Si II 635.5 nm
absorption feature reflects the velocity interval of silicon in the supernova
ejecta and then may provide constraints on the explosion mechanism of SNe Ia.
In this paper, we divide the SNe Ia into broad line (BL) and normal line (NL)
subsamples based on their REW of Si II 635.5 nm absorption lines around maximum
light, and find that the BL SNe Ia have a dimmer mean brightness than NL ones,
which possibly results from their different metallicities. However, based on
the pixel statistics study on the environments of two subsamples, we do not
find any significant potential difference on the environments between BL and NL
SNe Ia, which implies that the explosion mechanism of SNe Ia could be
independent of their progenitor populations.Comment: 17 pages, 13 figures, accepted for publication in Ap
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